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arXiv:1707.02852 · Physical Review A

Hybrid quantum key distribution using coherent states and photon-number-resolving detectors

Marco Cattaneo, Matteo G. A. Paris, Stefano Olivares

Published Jul 30, 2018• 36 citations
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Abstract

We put forward a hybrid quantum key distribution protocol based on coherent states, Gaussian modulation, and photon-number-resolving (PNR) detectors, and show that it may enhance the secret key generation rate (KGR) compared to homodyne-based schemes. Improvement in the KGR may be traced back to the dependence of the two-dimensional discrete output variable on both the input quadratures, thus overcoming the limitations of the original protocol. When reverse reconciliation is considered, the scheme based on PNR detectors outperforms the homodyne one both for individual and collective attacks. In the presence of direct reconciliation, the PNR strategy is still the best one against individual attacks, but for the collective ones the homodyne-based scheme is still to be preferred as the channel transmissivity decreases.

DOI
10.1103/physreva.98.012333

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We put forward a hybrid quantum key distribution protocol based on coherent states, Gaussian modulation, and photon-number-resolving (PNR) detectors, and show that it may enhance the secret key generation rate (KGR) compared to homodyne-based schemes. Improvement in the KGR may be traced back to the dependence of the two-dimensional discrete output variable on both the input quadratures, thus overcoming the limitations of the original protocol. When reverse reconciliation is considered, the scheme based on PNR detectors outperforms the homodyne one both for individual and collective attacks. In the presence of direct reconciliation, the PNR strategy is still the best one against individual attacks, but for the collective ones the homodyne-based scheme is still to be preferred as the channel transmissivity decreases.
What we believe to be a new architecture based on dual-branch photon-number-resolving (DB-PNR) detectors for the receiver in the hybrid quantum key distribution (QKD) is introduced. DB-PNR scheme empowers the receiver to detect both quadratures of the coherent state simultaneously. Our results show that using DB-PNR detectors, the key generation rate (KGR) is almost doubled as compared to homodyne detection which detects only one quadrature at a time. The mutual information is enhanced by around 0.85 bits/symbol using DB-PNR as compared to heterodyne detection. DB-PNR is also found to outperform the heterodyne detection against Eve's individual and collective attacks. PNR-based detection schemes require less local oscillator (LO) power compared to homodyne/heterodyne detection schemes and thereby, the power efficiency of the receiver is enhanced.
Quantum key distribution (QKD) enables secret-key establishment through measurements of quantum states, but practical performance depends strongly on the optical receiver, modulation format, decision process, and reconciliation strategy. This thesis develops three receiver-oriented approaches for improving the information advantage of legitimate users under explicitly stated security models. First, a dual-branch photon-number-resolving (DB-PNR) receiver is developed for coherent-state hybrid QKD. Complementary displacement branches and four photon-count outputs reduce the sign ambiguity of single-branch reception and recover information associated with both optical quadratures. Under the adopted pure-loss models, DB-PNR reception improves mutual information and secret-key-generation rate relative to homodyne, heterodyne, and single-branch PNR references. Second, a four-level multi-threshold intensity-modulation and direct-detection (MT-IM–DD) protocol is formulated. Optical intensity levels, five decision thresholds, and two erasure regions are jointly optimized under Gaussian classical, quantum, and thermal receiver-noise terms. The analysis separates conditional key rate from acceptance-weighted secret throughput and evaluates forward and reverse reconciliation under beam-splitting and intercept–resend attacks. Third, binary IM–DD is operated directly in the low-photon-number quantum regime using photon-number-resolving direct detection. Integer Poisson observations are processed with a likelihood-symmetric dual-threshold rule. The closed-form coupling between the two boundaries reduces the threshold optimization from two independent variables to one while preserving most of the benefit of free two-threshold optimization. Across all three studies, improved receiver measurements and deliberate post-selection increase performance under the stated assumptions. The results are comparative asymptotic bounds, not universal composable-security proofs. Finite-key effects, detector nonidealities, soft-information eavesdropping, general quantum attacks, and experimental validation remain necessary extensions.
We designed high-efficiency error correcting codes allowing us to extract an errorless secret key in a continuous-variable quantum key distribution (CVQKD) protocol using a Gaussian modulation of coherent states and a homodyne detection. These codes are available for a wide range of signal-to-noise ratios on an additive white Gaussian noise channel with a binary modulation and can be combined with a multidimensional reconciliation method proven secure against arbitrary collective attacks. This improved reconciliation procedure considerably extends the secure range of a CVQKD with a Gaussian modulation, giving a secret key rate of about ${10}^{\ensuremath{-}3}$ bit per pulse at a distance of 120 km for reasonable physical parameters.
We introduce a ternary quantum key distribution (QKD) protocol and asymptotic security proof based on three coherent states and homodyne detection. Previous work had considered the binary case of two coherent states and here we nontrivially extend this to three. Our motivation is to leverage the practical benefits of both discrete and continuous (Gaussian) encoding schemes creating a best-of-both-worlds approach; namely, the postprocessing of discrete encodings and the hardware benefits of continuous ones. We present a thorough and detailed security proof in the limit of infinite signal states which allows us to lower bound the secret key rate. We calculate this is in the context of collective eavesdropping attacks and reverse reconciliation postprocessing. Finally, we compare the ternary coherent state protocol to other well-known QKD schemes (and fundamental repeaterless limits) in terms of secret key rates and loss.
We present a protocol for quantum key distribution using discrete modulation of coherent states of light. Information is encoded in the variable phase of coherent states which can be chosen from a regular discrete set ranging from binary to continuous modulation, similar to phase-shift-keying in classical communication. Information is decoded by simultaneous homodyne measurement of both quadratures and requires no active choice of basis. The protocol utilizes either direct or reverse reconciliation, both with and without postselection. We analyze the security of the protocol and show how to enhance it by the optimal choice of all variable parameters of the quantum signal.
We present a protocol for quantum key distribution using discrete modulation of coherent states of light. Information is encoded in the variable phase of coherent states which can be chosen from a regular discrete set ranging from binary to continuous modulation similar to phase-shift keying in classical communication. Information is decoded by simultaneous homodyne measurement of both quadratures and requires no active choice of basis. The protocol utilizes either direct or reverse reconciliation both with and without postselection. We analyze the security of the protocol and show how to enhance it by the optimal choice of all variable parameters of the quantum signal.