Brian Kirby, Ph.D.
brian.t.kirby4.civ@army.mil
bkirby1@tulane.edu
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2024
Entanglement distillation has many applications in quantum information processing and is an important tool for improving the quality and efficiency of quantum communication, cryptography, computing, and simulation. We propose an entanglement distillation scheme using only one pair of polarization-frequency hyperentangled photons, which can be equivalently viewed as containing two pairs of entangled logical qubits: a pair of polarization-entangled qubits and a pair of frequency-entangled qubits. To perform the required controlled NOT (CNOT) operation between the two qubits we consider the use of a polarization-dependent frequency converter. Compared to past methods of entanglement distillation that relied on polarization and spatial-mode/energy-time degree of freedom, the utilization of frequency-encoded qubits offers an advantage in that it is immune to bit-flip errors when the channel is linear. After distillation, the fidelity of polarization entanglement can be significantly improved by sacrificing the frequency degree of freedom. Through simulation, we show that high fidelity gains, large yield, and high distillation rate can be achieved. Our distillation scheme is simple to implement with current technologies, compatible with existing telecommunication fiber networks, and is a promising approach for achieving efficient quantum communication.
- SMC Is All You Need: Parallel Strong Scaling
X. Liang, S. Lohani, J. M. Lukens, B. T. Kirby, T. A. Searles, K. J.H. Law
arXiv:2402.06173
In the general framework of Bayesian inference, the target distribution can only be evaluated up-to a constant of proportionality. Classical consistent Bayesian methods such as sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC) have unbounded time complexity requirements. We develop a fully parallel sequential Monte Carlo (pSMC) method which provably delivers parallel strong scaling, i.e. the time complexity (and per-node memory) remains bounded if the number of asynchronous processes is allowed to grow. More precisely, the pSMC has a theoretical convergence rate of MSE=O(1/NR), where N denotes the number of communicating samples in each processor and R denotes the number of processors. In particular, for suitably-large problem-dependent N, as R→∞ the method converges to infinitesimal accuracy MSE=O(ε2) with a fixed finite time-complexity Cost=O(1) and with no efficiency leakage, i.e. computational complexity Cost=O(ε−2). A number of Bayesian inference problems are taken into consideration to compare the pSMC and MCMC methods.
- Policies for multiplexed quantum repeaters: theory and practical performance analysis
S. Haldar, P. J. Barge, X. Cheng, K.-C. Chang, B. T. Kirby, S. Khatri, C. W. Wong, H. Lee
arXiv:2401.13168
Future quantum networks will have nodes equipped with multiple quantum memories, providing the possibility to perform multiplexing and distillation strategies in order to increase fidelities and reduce waiting times for end-to-end entanglement distribution. In this paper, we introduce two policies that adapt the well-known swap-as-soon-as-possible (swap-asap) policy to multiplexed quantum repeater chains. Unlike the usual, fully local swap-asap policy, these policies are ``quasi-local", making effective use of knowledge of the states of the repeaters along the chain to optimize waiting times and end-to-end fidelities. Our policies also make use of entanglement distillation. We demonstrate via simulations one of our key findings, which is that these policies can outperform the well-known and widely studied nested purification and doubling swapping policy in practically relevant parameter regimes. Our work also provides the tools to carefully examine the role of entanglement distillation. We identify the parameter regimes in which performing distillation makes sense and is useful. In these regimes, we also address the question: ``Should we distill before swapping, or vice versa?" We thus formalize the trade-off between the advantages of adding distillation capabilities to quantum networks against their technological and practical challenges. Finally, to provide further practical guidance, we propose an experimental implementation of a multiplexing-based linear network, and experimentally demonstrate the key element, a high-dimensional biphoton frequency comb (BFC). We then evaluate the anticipated performance of our multiplexing-based policies in such a real-world network through simulation results for two concrete memory platforms, namely rare-earth ions and diamond vacancies.
2023
- Photonic crystal cavity IQ modulators in thin-film lithium niobate for coherent communications
H. Larocque, D. L. P. Vitullo, A. Sludds, H. Sattari, I. Christen, G. Choong, I. Prieto, J. Leo, H. Zarebidaki, S. Lohani, B. T. Kirby, O. O. Soykal, M. Soltani, A. H. Ghadimi, D. Englund, and M. Heuck
arXiv:2312.16746
Thin-Film Lithium Niobate (TFLN) is an emerging integrated photonic platform showing great promise due to its large second-order nonlinearity at microwave and optical frequencies, cryogenic compatibility, large piezoelectric response, and low optical loss at visible and near-infrared wavelengths. These properties enabled Mach-Zehnder interferometer-based devices to demonstrate amplitude- and in-phase/quadrature (IQ) modulation at voltage levels compatible with complementary metal-oxide-semiconductor (CMOS) electronics. Maintaining low-voltage operation requires centimeter-scale device lengths, making it challenging to realize the large-scale circuits required by ever-increasing bandwidth demands in data communications. Reduced device sizes reaching the 10 um scale are possible with photonic crystal (PhC) cavities. So far, their operation has been limited to modulation of amplitudes and required circulators or lacked cascadability. Here, we demonstrate a compact IQ modulator using two PhC cavities operating as phase shifters in a Fabry-Perot-enhanced Michelson interferometer configuration. It supports cascadable amplitude and phase modulation at GHz bandwidths with CMOS-compatible voltages. While the bandwidth limitation of resonant devices is often considered detrimental, their compactness enables dense co-integration with CMOS electronics where clock-rate-level operation (few GHz) removes power-hungry electrical time-multiplexing. Recent demonstrations of chip-scale transceivers with dense-wavelength division multiplied transceivers could be monolithically implemented and driven toward ultimate information densities using TFLN electro-optic frequency combs and our PhC IQ modulators.
- Deep learning for enhanced free-space optical communications
M. P. Bart, N. J. Savino, P. Regmi, L. Cohen, H. Safavi, H. C. Shaw, S. Lohani, T. A. Searles, B. T. Kirby, H. Lee, and R. T. Glasser
Mach. Learn. Sci. Technol. 4 045046 (2023)
arXiv:2208.07712
Atmospheric effects, such as turbulence and background thermal noise, inhibit the propagation of light used in ON–OFF keying (OOK) free-space optical (FSO) communication. Here we present and experimentally validate a convolutional neural network (CNN) to reduce the bit error rate of FSO communication in post-processing that is significantly simpler and cheaper than existing solutions based on advanced optics. Our approach consists of two neural networks, the first determining the presence of bit sequences in thermal noise and turbulence and the second demodulating the bit sequences. All data used for training and testing our network is obtained experimentally by generating OOK bit streams, combining these with thermal light, and passing the resultant light through a turbulent water tank which we have verified mimics turbulence in the air to a high degree of accuracy. Our CNN improves detection accuracy over threshold classification schemes and has the capability to be integrated with current demodulation and error correction schemes.
- An Exponential Reduction in Training Data Sizes for Machine Learning Derived Entanglement Witnesses
A. R. Rosebush, A. C. B. Greenwood, B. T. Kirby, and L. Qian
arXiv:2311.18162
In this work, we propose an improved method of training linear support vector machines (SVMs) to generate entanglement witnesses for systems of 3, 4, and 5 qubits. SVMs generate hyperplanes represented by a weighted sum of expectation values of local observables, whose coefficients are optimized to provide a positive sum for all separable states and a negative sum for as many entangled states as possible near a specific target state. We use the eigenstates of generalized Pauli matrices as training data, and correct the witnesses with a differential program. This method requires only O (6n) training states, whereas an existing method needs O (24n). We use this method to construct witnesses of 4 and 5 qubit GHZ states with coefficients agreeing with stabilizer formalism witnesses to within 6.5 percent and 1 percent, respectively. We also use the same training states to generate 4 and 5 qubit W state witnesses. Finally, we propose methods for physical and computational verification of these witnesses.
- On the connection between least squares, regularization, and classical shadows
Z. Zhu, J. M. Lukens, and B. T. Kirby
arXiv:2310.16921
Classical shadows (CS) offer a resource-efficient means to estimate quantum observables, circumventing the need for exhaustive state tomography. Here, we clarify and explore the connection between CS techniques and least squares (LS) and regularized least squares (RLS) methods commonly used in machine learning and data analysis. By formal identification of LS and RLS "shadows" completely analogous to those in CS -- namely, point estimators calculated from the empirical frequencies of single measurements -- we show that both RLS and CS can be viewed as regularizers for the underdetermined regime, replacing the pseudoinverse with invertible alternatives. Through numerical simulations, we evaluate RLS and CS from three distinct angles: the tradeoff in bias and variance, mismatch between the expected and actual measurement distributions, and the interplay between the number of measurements and number of shots per measurement. Compared to CS, RLS attains lower variance at the expense of bias, is robust to distribution mismatch, and is more sensitive to the number of shots for a fixed number of state copies -- differences that can be understood from the distinct approaches taken to regularization. Conceptually, our integration of LS, RLS, and CS under a unifying "shadow" umbrella aids in advancing the overall picture of CS techniques, while practically our results highlight the tradeoffs intrinsic to these measurement approaches, illuminating the circumstances under which either RLS or CS would be preferred, such as unverified randomness for the former or unbiased estimation for the latter.
The fact that quantum mechanics predicts stronger correlations than classical physics is an essential cornerstone of quantum information processing. Indeed, these quantum correlations are a valuable resource for various tasks, such as quantum key distribution or quantum teleportation, but characterizing these correlations in an experimental setting is a formidable task, especially in scenarios where no shared reference frames are available. By definition, quantum correlations are reference-frame independent, i.e., invariant under local transformations; this physically motivated invariance implies, however, a dedicated mathematical structure and, therefore, constitutes a roadblock for an efficient analysis of these correlations in experiments. Here we provide a method to directly measure any locally invariant property of quantum states using locally randomized measurements, and we present a detailed toolbox to analyze these correlations for two quantum bits. We implement these methods experimentally using pairs of entangled photons, characterizing their usefulness for quantum teleportation and their potential to display quantum nonlocality in its simplest form. Our results can be applied to various quantum computing platforms, allowing simple analysis of correlations between arbitrary distant qubits in the architecture.
The ability to prepare systems in specific target states through quantum engineering is essential for realizing the new technologies promised by a second quantum revolution. Here, we recast the fundamental problem of state preparation in high-dimensional Hilbert spaces as ManQala, a quantum game inspired by the West African sowing game mancala. Motivated by optimal gameplay in solitaire mancala, where nested nearest-neighbor permutations and actions evolve the state of the game board to its target configuration, ManQala acts as a pre-processing approach for deterministically arranging particles in a quantum control problem. Once pre-processing with ManQala is complete, existing quantum control methods are applied, but now with a reduced search space. We find that ManQala-type strategies match, or outperform, competing approaches in terms of final state variance even in small-scale quantum state engineering problems where we expect the slightest advantage since the relative reduction in search space is the least. These results suggest that ManQala provides a rich platform for designing control protocols relevant to near-term intermediate-scale quantum technologies.
- Demonstration of machine-learning-enhanced Bayesian quantum state estimation
S. Lohani, J. M. Lukens, A. A. Davis, A. Khannejad, S. Regmi, D. E. Jones, R. T. Glasser, T. A. Searles, B. T. Kirby
New J. Phys. 25, 083009 (2023)
arXiv:2212.08032
Machine learning (ML) has found broad applicability in quantum information science in topics as diverse as experimental design, state classification, and even studies on quantum foundations. Here, we experimentally realize an approach for defining custom prior distributions that are automatically tuned using ML for use with Bayesian quantum state estimation methods. Previously, researchers have looked to Bayesian quantum state tomography due to its unique advantages like natural uncertainty quantification, the return of reliable estimates under any measurement condition, and minimal mean-squared error. However, practical challenges related to long computation times and conceptual issues concerning how to incorporate prior knowledge most suitably can overshadow these benefits. Using both simulated and experimental measurement results, we demonstrate that ML-defined prior distributions reduce net convergence times and provide a natural way to incorporate both implicit and explicit information directly into the prior distribution. These results constitute a promising path toward practical implementations of Bayesian quantum state tomography.
The coexistence of quantum and classical signals over the same optical fiber with minimal degradation of the transmitted quantum information is critical for operating large-scale quantum networks within the existing communications infrastructure. Here, we systematically characterize the quantum channel that results from simultaneously distributing approximate single-photon polarization-encoded qubits and classical light of varying intensities through fiber-optic channels of up to 15~km. Using spectrally resolved quantum process tomography with a newly developed Bayesian reconstruction method, we estimate the full quantum channel from experimental photon counting data, both with and without classical background. Furthermore, although we find the exact channel description to be a weak function of the pump polarization, we nevertheless show that the coexistent fiber-based quantum channel has high process fidelity with an ideal depolarizing channel when the noise is dominated by Raman scattering. These results provide a basis for the future development of quantum repeater designs and quantum error correcting codes for real-world channels and inform models used in the analysis and simulation of quantum networks.
Quantum networks exploit the unique properties of quantum mechanics to enable communication and networking tasks unavailable to existing distributed classical systems. Recently, the research community has focused considerable effort on the simulation of large-scale quantum networks with the ultimate goal of understanding their general properties, developing technical standards, and estimating their expected performance. However, comparatively little effort has been spent considering how quantum networks may impact tactical scenarios of military relevance where both quantum and classical resources may be severely constrained. Here, we develop a custom framework, called QuanTACT, for quantum network simulation explicitly designed for future integration into existing tactical simulation tools. In particular, our framework extends the existing quantum networking tool, SQUANCH, to include channel models required to simulate deployed fiber environments. Furthermore, we implement the additional subroutines needed to simulate entanglement-based quantum key distribution (QKD) and use published results from various field-deployed QKD experiments to benchmark the performance of our framework.
In this work, we show a correspondence between linear support vector machines (SVMs) and entanglement witnesses, and use this correspondence to generate entanglement witnesses for bipartite and tripartite qubit (and qudit) target entangled states. An SVM allows for the construction of a hyperplane that clearly delineates between separable states and the target entangled state; this hyperplane is a weighted sum of observables ('features') whose coefficients are optimized during the training of the SVM. Our SVM-derived entanglement witness consists of a weighted sum of observables ("features") with coefficients defined by the training of our SVM to maximize the separation in feature space between our entangled target state and the set of all separable states. We demonstrate with this method the ability to obtain witnesses that require only local measurements even when the target state is a non-stabilizer state. Furthermore, we show that SVMs are flexible enough to allow us to rank features, and to reduce the number of features systematically while bounding the inference error. This allows us to derive W state witnesses capable of detecting entanglement with fewer measurement terms than the fidelity method dominant in today's literature. The utility of this novel approach is demonstrated on quantum hardware furnished through the IBM Quantum Experience.
We introduce an approach for performing quantum state reconstruction on systems of n qubits using a machine-learning-based reconstruction system trained exclusively on m qubits, where m≥n. This approach removes the necessity of exactly matching the dimensionality of a system under consideration with the dimension of a model used for training. We demonstrate our technique by performing quantum state reconstruction on randomly sampled systems of one, two, and three qubits using machine-learning-based methods trained exclusively on systems containing at least one additional qubit. The reconstruction time required for machine-learning-based methods scales significantly more favorably than the training time; hence this technique can offer an overall savings of resources by leveraging a single neural network for dimension-variable state reconstruction, obviating the need to train dedicated machine-learning systems for each Hilbert space.
2022
The rising demand for transmission capacity in optical networks has motivated steady interest in expansion beyond the standard C-band (1530-1565 nm) into the adjacent L-band (1565-1625 nm), for an approximate doubling of capacity in a single stroke. However, in the context of quantum networking, the ability to leverage the L-band will require advanced tools for characterization and management of entanglement resources which have so far been lagging. In this work, we demonstrate an ultrabroadband two-photon source integrating both C- and L-band wavelength-selective switches for complete control of spectral routing and allocation across 7.5 THz in a single setup. Polarization state tomography of all 150 pairs of 25 GHz-wide channels reveals an average fidelity of 0.98 and total distillable entanglement greater than 181 kebits/s. This source is explicitly designed for flex-grid optical networks and can facilitate optimal utilization of entanglement resources across the full C+L-band.
We propose a series of data-centric heuristics for improving the performance of machine learning systems when applied to problems in quantum information science. In particular, we consider how systematic engineering of training sets can significantly enhance the accuracy of pre-trained neural networks used for quantum state reconstruction without altering the underlying architecture. We find that it is not always optimal to engineer training sets to exactly match the expected distribution of a target scenario, and instead, performance can be further improved by biasing the training set to be slightly more mixed than the target. This is due to the heterogeneity in the number of free variables required to describe states of different purity, and as a result, overall accuracy of the network improves when training sets of a fixed size focus on states with the least constrained free variables. For further clarity, we also include a "toy model" demonstration of how spurious correlations can inadvertently enter synthetic data sets used for training, how the performance of systems trained with these correlations can degrade dramatically, and how the inclusion of even relatively few counterexamples can effectively remedy such problems.
The quantum Zeno effect reveals that the continuous observation of a quantum system can result in significant alterations to its evolution. Here, we present a method for establishing polarization entanglement between two initially unentangled photons in coupled waveguides via the quantum Zeno effect. We support our analytical investigation with numerical simulations of the underlying Schrodinger equation describing the system. Further, we extend our technique to three coupled waveguides in a planar configuration and determine the parameter regime required to generate three-qubit W-states. Our findings offer a powerful quantum state engineering approach for photonic quantum information technologies.
Hyperentanglement, the simultaneous and independent entanglement of quantum particles in multiple degrees of freedom, is a powerful resource that can be harnessed for efficient quantum information processing. In photonic systems, the two degrees of freedom (DoF) often used to carry quantum and classical information are polarization and frequency, thanks to their robustness in transmission, both in free space and in optical fibers. Telecom-band hyperentangled photons generated in optical fibers are of particular interest because they are compatible with existing fiber-optic infrastructure, and can be distributed over fiber networks with minimal loss. Here, we experimentally demonstrate the generation of telecom-band biphotons hyperentangled in both the polarization and frequency DoFs using a periodically-poled silica fiber and observe entanglement concurrences above 0.95 for both polarization and frequency DOFs. Furthermore, by concatenating a Hong-Ou-Mandel interference test for frequency entanglement and full state tomography for polarization entanglement in a single experiment, we can demonstrate simultaneous entanglement in both the polarization and frequency DOFs. The states produced by our hyperentanglement source can enable protocols such as dense coding and high-dimensional quantum key distribution.
2021
We consider the properties of a specific distribution of mixed quantum states of arbitrary dimension that can be biased towards a specific mean purity. In particular, we analyze mixtures of Haar-random pure states with Dirichlet-distributed coefficients. We analytically derive the concentration parameters required to match the mean purity of the Bures and Hilbert--Schmidt distributions in any dimension.
Numerical simulations suggest that this value recovers the Hilbert--Schmidt distribution exactly, offering an alternative and intuitive physical interpretation for ensembles of Hilbert--Schmidt-distributed random quantum states. We then demonstrate how substituting these Dirichlet-weighted Haar mixtures in place of the Bures and Hilbert--Schmidt distributions results in measurable performance advantages in machine-learning-based quantum state tomography systems and Bayesian quantum state reconstruction. Finally, we experimentally characterize the distribution of quantum states generated by both a cloud-accessed IBM quantum computer and an in-house source of polarization-entangled photons. In each case, our method can more closely match the underlying distribution than either Bures or Hilbert--Schmidt distributed states for various experimental conditions.
We determine the resource scaling of machine learning-based quantum state reconstruction methods, in terms of inference and training, for systems of up to four qubits when constrained to pure states. Further, we examine system performance in the low-count regime, likely to be encountered in the tomography of high-dimensional systems. Finally, we implement our quantum state reconstruction method on an IBM Q quantum computer, and compare against both unconstrained and constrained MLE state reconstruction.
A conceptually simple and experimentally prevalent class of entanglement witnesses, known as fidelity witnesses, detect entanglement via a state's fidelity with a pure reference state. While existence proofs guarantee that a suitable witness can be constructed for every entangled state, such assurances do not apply to fidelity witnesses. Recent results have found that entangled states that cannot be detected by a fidelity witness, known as unfaithful states, are exceedingly common among bipartite states. In this paper, we show that even among two-qubit states, the simplest of all entangled states, unfaithful states can be created through a suitable application of decoherence and filtering to a Bell state. We also show that the faithfulness is not monotonic to entanglement, as measured by the concurrence. Finally, we experimentally verify our predictions using polarization-entangled photons and specifically demonstrate a situation where an unfaithful state is brought to faithfulness at the expense of further reducing the entanglement of the state.
Quantum entanglement shared by remote agents serves as a valuable resource for promising applications in distributed computing, cryptography, and sensing. However, distributing entangled states with high fidelity via fiber optic routes is challenging due to the various decoherence mechanisms in fibers. In particular, one of the primary polarization decoherence mechanism in optical fibers is polarization mode dispersion (PMD), which is the distortion of optical pulses by random birefringences in the system. Among quantum entanglement distillation (QED) algorithms proposed to mitigate decoherence, the recurrence QED algorithms require the smallest size of quantum circuits, and are most robust against severe decoherence. On the other hand, the yield of recurrence QED algorithms drops exponentially with respect to the rounds of distillation, and hence it is critical to minimize the required rounds of distillation. We present a recurrence QED algorithm, which is capable of achieving maximum fidelity in every round of distillation when each photonic qubit individually traverses a PMD-degraded channel. The attainment of optimal fidelity in every round of distillation implies that our algorithm reaches the fastest possible convergence speed and hence requires the minimum rounds of distillation. Therefore, the proposed algorithm provides an efficient method to distribute entangled states with high fidelity via optic fibers.
Two-qubit systems typically employ 36 projective measurements for high-fidelity tomographic estimation. The overcomplete nature of the 36 measurements suggests possible robustness of the estimation procedure to missing measurements. In this paper, we explore the resilience of machine-learning-based quantum state estimation techniques to missing measurements by creating a pipeline of stacked machine learning models for imputation, denoising, and state estimation. When applied to simulated noiseless and noisy projective measurement data for both pure and mixed states, we demonstrate quantum state estimation from partial measurement results that outperforms previously developed machine-learning-based methods in reconstruction fidelity and several conventional methods in terms of resource scaling. Notably, our developed model does not require training a separate model for each missing measurement, making it potentially applicable to quantum state estimation of large quantum systems where preprocessing is computationally infeasible due to the exponential scaling of quantum system dimension.
2020
We build a general quantum state tomography framework that makes use of machine learning techniques to reconstruct quantum states from a given set of coincidence measurements. For a wide range of pure and mixed input states we demonstrate via simulations that our method produces functionally equivalent reconstructed states to that of traditional methods with the added benefit that expensive computations are front-loaded with our system. Further, by training our system with measurement results that include simulated noise sources we are able to demonstrate a significantly enhanced average fidelity when compared to typical reconstruction methods. These enhancements in average fidelity are also shown to persist when we consider state reconstruction from partial tomography data where several measurements are missing. We anticipate that the present results combining the fields of machine intelligence and quantum state estimation will greatly improve and speed up tomography-based quantum experiments.
- Exploring classical correlations in noise to recover quantum information using local filtering
D. E Jones, B. T. Kirby, G. Riccardi, C. Antonelli, and M. Brodsky
New J. Phys. 22 073037 (2020)
A general quantum channel consisting of a decohering and a filtering element carries one qubit of an entangled photon pair. As we apply a local filter to the other qubit, some mutual quantum information between the two qubits is restored depending on the properties of the noise mixed into the signal. We demonstrate a drastic difference between channels with bit-flip and phase-flip noise and further suggest a scheme for maximal recovery of the quantum information.
The entanglement of quantum systems can produce a variety of nonclassical effects that have practical applications in quantum information science. One example of this is nonlocal dispersion cancellation, in which the effects of dispersion on one photon can be cancelled out by the dispersion experienced by a second photon at a distant location. In this paper, we extend the analysis of nonlocal dispersion cancellation to three or more photons. We find that energy-time entanglement of three or more photons can lead to a complete or partial cancellation of dispersion depending on the experimental conditions. These results may be useful in implementing quantum key distribution in networks with three or more nodes.
2019
Polarization dependent loss (PDL) is a serious problem that hinders the transfer of polarization qubits through quantum networks. Recently it has been shown that the detrimental effects of PDL on qubit fidelity can be compensated for with the introduction of an additional passive PDL element that rebalances the polarization modes of the transmitted qubit. This procedure works extremely well when the output of the system is postselected on photon detection. However, in cases where the qubit might be needed for further analysis this procedure introduces unwanted vacuum terms into the state. Here we present procedures for the compensation of the effects of PDL using noiseless amplification and attenuation. Each of these techniques introduces a heralding signal into the correction procedure that significantly reduces the vacuum terms in the final state. When detector inefficiency and dark counts are included in the analysis noiseless amplification remains superior, in terms of the fidelity of the final state, to both noiseless attenuation and passive PDL compensation for detector efficiencies greater than 40%.
- Effect of Polarization Dependent Loss on the Quality of Transmitted Polarization Entanglement
B. T. Kirby, D. E. Jones, and M. Brodsky
J. Lightw. Technol. 37, 95 (2019)
Quantum networking brings together several diverse research areas, such as fiber-optic communication, quantum optics, and quantum information, to achieve capabilities in security, secret sharing, and authentication which are unavailable classically. The development of practical fiber-based quantum networks requires an understanding of the reach, rates, and quality of the entanglement of distributed quantum states. Here, we present a theoretical model describing how the magnitude and orientation of polarization dependent loss (PDL), a common impairment in fiber-optic networks, affects the entanglement quality of distributed quantum states. Furthermore, we theoretically characterize how PDL in one fiber channel can be optimally applied in order to nonlocally compensate for the PDL present in another channel. We present experimental results that verify our theoretical model.
2018
Quantum networks entangle remote nodes by distributing quantum states, which inevitably suffer from decoherence while traversing quantum channels. Pertinent decoherence mechanisms govern the channel capacity, its reach, and the quality and rate of distributed entanglement. Hence recognizing, understanding, and modeling those mechanisms is a crucial step in building quantum networks. Here, we study practical fiber-optic quantum channels that partially filter individual modes of transmitted polarization entangled states and are capable of introducing dephasing. First, we theoretically model and experimentally demonstrate the combined effect of two independent and arbitrarily oriented polarization dependent loss elements experienced by each photon of an entangled photon pair. Then, we showcase the compensation of lost entanglement by properly adjusting the channels' properties and discuss the resulting tradeoff between the entanglement quality and rate. Our results provide insights into the capacity of practical fiber-optics channels, thus taking an important step towards the realization of quantum networks.
A protocol of measuring interferometric visibility function using imperfectly entangled states shared between remote telescopes is proposed. We demonstrate how quantum entanglement can be utilized to increase the baseline size of telescopic arrays thereby providing substantial enhancement to the resolution of direct-detection interferometric measurements. We demonstrate, through a comprehensive analysis, how errors in visibility measurements and in the intensity distribution of a distant object show dependence on the entanglement degree of the shared quantum resource. We analyse the feasibility of the protocol using currently available technology and identify the nature of sources that can benefit most from it.
2017
Suppose Alice and Bob share a secret key, of which Eve is initially oblivious. Clearly, Alice and Bob can use this key to ensure that any particular plain-message sent is both authentic and secure. This paper investigates how many plain-messages can be sent per bit of secret key, while still ensuring both secrecy and authentication. In particular the secrecy tolerance relates to the min-entropy of any individual plain message, given all observed cipher-messages, while the authentication tolerance directly relates to the maximum allowable probability of Bob erroneously accepting a cipher-message from Eve. In this paper we characterize the set of all messages to secret bit ratios. We do this by providing a direct and converse, showing that the maximum ratio is directly determined by the tolerance parameters for authentication and secrecy, and is independent of the ratio of the length of the plain-message to the length of the secret key.
2016
We consider entanglement swapping, a key component of quantum network operations and entanglement distribution. Pure entangled states, which are the desired input to the swapping protocol, are typically mixed by environmental interactions, causing a reduction in their degree of entanglement. Thus an understanding of entanglement swapping with partially mixed states is of importance. Here we present a general analytical solution for entanglement swapping of arbitrary two-qubit states. Our result provides a comprehensive method for analyzing entanglement swapping in quantum networks. First, we show that the concurrence of a partially mixed state is conserved when this state is swapped with a Bell state. Then, we find upper and lower bounds on the concurrence of the state resulting from entanglement swapping for various classes of input states. Finally, we determine a general relationship between the ranks of the initial states and the rank of the final state after swapping.
2015
The use of distributed amplifiers may have some potential advantages for the transmission of quantum information through optical fibers. In addition to the quantum noise introduced by the amplifiers, entanglement between atoms in the amplifying media and the optical field corresponds to which-path information that can further reduce the coherence. Here we analyze the effects of decoherence in a phase-insensitive distributed amplifier by using perturbation theory to calculate the state of the entire system including the atomic media. For an initial coherent state, tracing over the atomic states allows the reduced density matrix of the field to be expressed as a mixture of squeezed states with a reduced spread in photon number and an increased phase uncertainty. The amplifier noise and decoherence can be interpreted as being due to entanglement with the environment rather than the amplification of vacuum fluctuation noise. In addition to providing increased insight into the effects of decoherence, these results can be applied to nonclassical superposition states such as Schrodinger cats.
Cross-phase modulation at the single-photon level has a wide variety of fundamental applications in quantum optics including the generation of macroscopic entangled states. Here we describe a practical method for producing a weak cross-phase modulation at the single-photon level using metastable xenon in a high finesse cavity. We estimate the achievable phase shift and give a brief update on the experimental progress towards its realization. A single-photon cross-phase modulation of approximately 20 milliradians is predicted by both a straightforward perturbation theory calculation and a numerical matrix diagonalization method.
2014
The propagation of macroscopic entangled states over large distances in the presence of loss is of fundamental interest and may have practical applications as well. Here we describe two different techniques in which state discrimination can be used to violate Bell's inequality with macroscopic phase-entangled coherent states. We find that Bell's inequality can be violated by these macroscopic states over a distance of approximately 400 km in commercially-available optical fibers.
2013
A method for performing nonlocal interferometry using phase-entangled macroscopic coherent states is described. The required entanglement can be generated using weak nonlinearities while Bell's inequality can be violated using single photons as a probe. The entanglement is relatively robust against photon loss and Bell's inequality can be violated over a relatively large distance in optical fibers despite the fact that a large number of photons are absorbed in the process.