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arXiv:1105.2811 · Physical Review A

Efficient heralding of photonic qubits with applications to device-independent quantum key distribution

David Pitkanen, Xiongfeng Ma, Ricardo Wickert, Peter van Loock, Norbert Lütkenhaus

Published Aug 19, 2011• 63 citations
arXivHTMLPDF

Abstract

We present an efficient way of heralding photonic qubit signals using linear optics devices. First, we show that one can obtain asymptotically perfect heralding and unit success probability with growing resources. Second, we show that even using finite resources, we can improve qualitatively and quantitatively over earlier heralding results. In the latter scenario, we can obtain perfect heralded photonic qubits while maintaining a finite success probability. We demonstrate the advantage of our heralding scheme by predicting key rates for device-independent quantum key distribution, taking imperfections of sources and detectors into account.

DOI
10.1103/physreva.84.022325

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We present an efficient way of heralding photonic qubit signals using linear optics devices. First, we show that one can obtain asymptotically perfect heralding and unit success probability with growing resources. Second, we show that even using finite resources, we can improve qualitatively and quantitatively over earlier heralding results. In the latter scenario, we can obtain perfect heralded photonic qubits while maintaining a finite success probability. We demonstrate the advantage of our heralding scheme by predicting key rates for device-independent quantum key distribution, taking imperfections of sources and detectors into account.
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We study decoy-state measurement-device-independent quantum key distribution using heralded single-photon sources. This has the advantage that the observed error rate in the XXX basis is at higher order and not so large. We calculate the key rate and transmission distance for two cases: one using only triggered events, and the other using both triggered and nontriggered events. We compare the key rates of various protocols and find that our scheme using triggered and nontriggered events can give a higher key rate and a longer secure distance. Moreover, we also show the different behavior of our scheme when using different heralded single-photon sources, i.e., in Poisson or thermal distributions. We demonstrate that the former can generate a higher secure key rate than the latter and can thus work more efficiently in practical quantum key distributions.
Linear optical quantum Fredkin gate can be applied to quantum computing and quantum multi-user communication networks. In the existing linear optical scheme, two single photon detectors (SPDs) are used to herald the success of the quantum Fredkin gate while they have no photon count. But analysis results show that for non-perfect SPD, the lower the detector efficiency, the higher the heralded success rate by this scheme is. We propose an improved linear optical quantum Fredkin gate by designing a new heralding scheme with an auxiliary qubit and only one SPD, in which the higher the detection efficiency of the heralding detector, the higher the success rate of the gate is. The new heralding scheme can also work efficiently under a non-ideal single photon source. Based on this quantum Fredkin gate, large-scale quantum switching networks can be built. As an example, a quantum Beneš network is shown in which only one SPD is used.
Quantum communication attempts to harness the unique rules of quantum mechanics to perform communication tasks that are difficult or impossible using classical rules. To realize these benefits, information must be carried on quantum systems. Photons make excellent carriers because they interact very little with the environment, move quickly, and can naturally store quantum information in their polarization. However, it is notoriously difficult to detect a single photon without destroying it. Standard detectors simply absorb the photon, losing the quantum information. This is a critical outstanding problem in quantum communication, as advanced protocols need to know exactly when a photon has arrived at a receiver after transmission through the atmosphere or an optical fibre before performing further quantum-information-processing tasks. Certifying a photon’s presence is of particular interest in tests of Bell’s inequalities, which have only recently been performed without loopholes arising from photon loss, and in device-independent quantum cryptography, which relies on such Bell tests for security. \n \nIn this thesis, I first present work on directly reducing losses in a successful loophole-free Bell test. This is an extremely difficult task that cannot be extended for long-distance communication. Therefore I then focus on ways to circumvent loss by detecting photons without destroying them while preserving their quantum information. First I analyze theoretically a way to herald photons using only linear-optical elements (beam splitters and phase shifters) and extra ancilla photons. Similar but older methods have been demonstrated experimentally by other groups, and my improvements will help future advanced quantum communication protocols. \n \nThe main experiment in this thesis certifies the presence of a photon in a rather simple way: split the photon into two using a nonlinear optical crystal, then detect one of the pair to herald the other. I show in this first proof-of-principle experiment that photonic qubit precertification indeed preserves qubit states, with up to (92.3 ± 0.6)% fidelity and rates of 1100 events per hour. With reductions in detector dark counts, precertification could outperform direct transmission, even with extremely lossy fibre links. \n \nFinally, I present two sources of photons based on nonlinearities in optical fibres. One of the limitations of the photon splitting scheme for heralding is the low success probability due to the very low likelihood of splitting a photon in two. In these fibre photon sources I investigate increasing the splitting likelihood in four-wave mixing through advanced materials and fibre designs. I use polarization-maintaining fibres to generate entangled photon pairs as a prerequisite to precertification, with (92.2 ± 0.2)% fidelity to a maximally-entangled state. Then I show that one type of highly nonlinear chalcogenide glass, never before used for photon pair generation, could outperform standard nonlinear crystals by two orders of magnitude, with calculated conversion efficiency up to 10^-3. To approach the single photon regime, I generate photon pairs in chalcogenide microwires with pump powers as low as 480 nW and verify their timing correlations. \n \nThese advances demonstrate the capability of nondestructive precertification of photons to allow advanced quantum communications protocols even over long distance, and could lead to the first implementations of fully device-independent quantum cryptography.
In device-independent quantum key distribution (DIQKD), the violation of a Bell inequality is exploited to establish a shared key that is secure independently of the internal workings of the QKD devices. An experimental implementation of DIQKD, however, is still awaited, since hitherto all optical Bell tests are subject to the detection loophole, making the protocol unsecured. In particular, photon losses in the quantum channel represent a fundamental limitation for DIQKD. Here we introduce a heralded qubit amplifier based on single-photon sources and linear optics that provides a realistic solution to overcome the problem of channel losses in Bell tests.
Linear optical quantum Fredkin gate can be applied to quantum computing and quantum multi-user communication network. In the existing linear optical scheme, two single photon detectors (SPDs) are used to heralding the success of the quantum Fredkin gate while they have no photon count. But analysis results show that for non-perfect SPD the lower the detector efficiency, the higher the heralded success rate by this scheme. We propose an improved linear optical quantum Fredkin gate by designing a new heralding scheme with an auxiliary qubit and only one SPD, in which the higher the detection efficiency of the heralding detector, the higher the success rate of the gate. The new heralding scheme can also work efficiently under non-ideal single photon source. Based on this quantum Fredkin gate, large-scale quantum switching networks can be built. As an example, a quantum Benes network in which only one SPD is used is shown.