Characterising the correlations of prepare-and-measure quantum networks

Wang, Yukun; Primaatmaja, Ignatius William; Lavie, Emilien; Varvitsiotis, Antonios; Lim, Charles

doi:10.1038/s41534-019-0133-3

Cited by 63 publications

(98 citation statements)

References 61 publications

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“…By finding such a characterisation and by understanding the trade-off between the two QRACs, we enable self-tests of Bob's instrument, along with self-tests of Alice's preparations and Charlie's measurements. Note that one may also consider alternative generalisations of QRACs to sequential scenarios [17].…”

Section: Sequential Racsmentioning

confidence: 99%

Sequential random access codes and self-testing of quantum measurement instruments

2019

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Quantum random access codes (QRACs) are key tools for a variety of protocols in quantum information theory. These are commonly studied in prepare-and-measure scenarios in which a sender prepares states and a receiver measures them. Here, we consider a three-party prepare-transformmeasure scenario in which the simplest QRAC is implemented twice in sequence based on the same physical system. We derive optimal trade-off relations between the two QRACs. We apply our results to construct semi-device independent self-tests of quantum instruments, i.e. measurement channels with both a classical and quantum output. Finally, we show how sequential QRACs enable inference of upper and lower bounds on the sharpness parameter of a quantum instrument.Subsequently, we apply our results to self-test a quantum instrument. is the task of inferring physical entities (states, channels, measurements) solely from correlations produced in experiments i.e. identifying the unique physical entities that are compatible with observed data. Self-testing is typically studied in Bell experiments where notably methods for self-testing quantum instruments have been developed [15,16]. Recently however, self-testing was introduced in the broad scope of prepare-and-measure scenarios [10], and was further developed using QRACs to robustly self-test both preparations and measurements [10][11][12]. Notably however, prepare-and-measure scenarios do not enable self-tests of general quantum operations. In particular, it does not enable self-tests of quantum instruments since the quantum system after the measurement is irrelevant to the outcome statistics produced in the experiment. We show that our prepare-transform-measure scenario overcomes this conceptual limitation. We find that optimal pairs of sequential QRACs self-test quantum instruments. However, such optimal correlations require idealised (noiseless) scenarios which are never the case in a practical implementation. Therefore, we also show how sequential QRACs allow for inference of noise-robust bounds on the sharpness parameter in a quantum instrument. This is makes our results applicable to experimental demonstrations. Finally, we discuss relevant generalisations of our results. New J. Phys. 21 (2019) 083034 K Mohan et al

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Section: Sequential Racsmentioning

confidence: 99%

Sequential random access codes and self-testing of quantum measurement instruments

2019

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“…By doing so, we have shown that, as long as the magnitude of the correlations is small, a secret key can still be obtained even when there are correlations over a long range of pulses. Moreover, our framework can be directly applied in combination with existing security proofs such as the GLT protocol (18), the GLLP type security proofs involving the quantum coin idea (19)(20)(21), and the numerical techniques recently introduced in (22)(23)(24). Furthermore, we have proposed a new framework for security proofs, which we call the RT.…”

Section: Discussionmentioning

confidence: 99%

“…x > y 2 (22) No measurement, including any measurement performed by Eve, can induce a larger deviation between the probabilities because Eq. 20 holds for any ˆ M .…”

Section: Rt Based On the Original Lt Protocolmentioning

confidence: 99%

Quantum key distribution with correlated sources

Pereira

Kato²,

Mizutani

et al. 2020

Sci. Adv.

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In theory, quantum key distribution (QKD) offers information-theoretic security. In practice, however, it does not due to the discrepancies between the assumptions used in the security proofs and the behavior of the real apparatuses. Recent years have witnessed a tremendous effort to fill the gap, but the treatment of correlations among pulses has remained a major elusive problem. Here, we close this gap by introducing a simple yet general method to prove the security of QKD with arbitrarily long-range pulse correlations. Our method is compatible with those security proofs that accommodate all the other typical device imperfections, thus paving the way toward achieving implementation security in QKD with arbitrary flawed devices. Moreover, we introduce a new framework for security proofs, which we call the reference technique. This framework includes existing security proofs as special cases, and it can be widely applied to a number of QKD protocols.

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“…Commercially available convex optimization tools, such as Mosek 7 , SeDuMi 8 , or SDPT3 9 , can therefore be used to reliably solve the problem. A more recent technique opted to compute the secret key rate by directly bounding the quantum error rate of a protocol using the Gram matrix of the eavesdropper's information 10,11 . Nevertheless, the problems formulated so far still assumed that Alice and Bob have exchanged an infinite number of signals (and an infinite-key length), which is practically impossible.…”

Section: Introductionmentioning

confidence: 99%

Numerical finite-key analysis of quantum key distribution

et al. 2020

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Quantum key distribution (QKD) allows for secure communications safe against attacks by quantum computers. QKD protocols are performed by sending a sizeable, but finite, number of quantum signals between the distant parties involved. Many QKD experiments, however, predict their achievable key rates using asymptotic formulas, which assume the transmission of an infinite number of signals, partly because QKD proofs with finite transmissions (and finite-key lengths) can be difficult. Here we develop a robust numerical approach for calculating the key rates for QKD protocols in the finite-key regime in terms of two semi-definite programs (SDPs). The first uses the relation between conditional smooth min-entropy and quantum relative entropy through the quantum asymptotic equipartition property, and the second uses the relation between the smooth min-entropy and quantum fidelity. The numerical programs are formulated under the assumption of collective attacks from the eavesdropper and can be promoted to withstand coherent attacks using the postselection technique. We then solve these SDPs using convex optimization solvers and obtain numerical calculations of finite-key rates for several protocols difficult to analyze analytically, such as BB84 with unequal detector efficiencies, B92, and twin-field QKD. Our numerical approach democratizes the composable security proofs for QKD protocols where the derived keys can be used as an input to another cryptosystem.

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Characterising the correlations of prepare-and-measure quantum networks

Cited by 63 publications

References 61 publications

Sequential random access codes and self-testing of quantum measurement instruments

Sequential random access codes and self-testing of quantum measurement instruments

Quantum key distribution with correlated sources

Numerical finite-key analysis of quantum key distribution

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