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AIP conference proceedings

Quantum Correlations for Quantum Key Distribution Protocols

Marcos Curty

Published Jan 1, 2004• 1 citation
Publisher

Abstract

A necessary precondition for secure quantum key distribution (QKD) is that sender and receiver can prove the presence of entanglement in a quantum state that is effectively distributed between them. In order to deliver this entanglement proof one can use the class of entanglement witness operators that can be constructed from the available measurements results. This criterion provides a necessary and sufficient condition for the existence of quantum correlations even when a quantum state cannot be completely reconstructed. We apply such analysis to three well‐known qubit‐based QKD protocols, namely the 6‐state, the 4‐state and the 2‐state protocols.

DOI
10.1063/1.1834441

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A necessary precondition for secure quantum key distribution (QKD) is that sender and receiver can prove the presence of entanglement in a quantum state that is effectively distributed between them. In order to deliver this entanglement proof one can use the class of entanglement witness operators that can be constructed from the available measurements results. This criterion provides a necessary and sufficient condition for the existence of quantum correlations even when a quantum state cannot be completely reconstructed. We apply such analysis to three well‐known qubit‐based QKD protocols, namely the 6‐state, the 4‐state and the 2‐state protocols.
We demonstrate that a necessary precondition for an unconditionally secure quantum key distribution is that both sender and receiver can use the available measurement results to prove the presence of entanglement in a quantum state that is effectively distributed between them. One can thus systematically search for entanglement using the class of entanglement witness operators that can be constructed from the observed data. We apply such analysis to two well-known quantum key distribution protocols, namely, the 4-state protocol and the 6-state protocol. As a special case, we show that, for some asymmetric error patterns, the presence of entanglement can be proven even for error rates above 25% (4-state protocol) and 33% (6-state protocol).
A necessary precondition for secure quantum key distribution is that sender and receiver can prove the presence of entanglement in a quantum state that is effectively distributed between them. In order to deliver this entanglement proof one can use the class of entanglement witness (EW) operators that can be constructed from the available measurements results. This class of EWs can be used to provide a necessary and sufficient condition for the existence of quantum correlations even when a quantum state cannot be completely reconstructed. The set of optimal EWs for two well-known entanglement-based (EB) schemes, the six-state and the four-state EB protocols, has been obtained recently [M. Curty et al., Phys. Rev. Lett. 92, 217903 (2004).] Here we complete these results, now showing specifically the analysis for the case of prepare and measure (PM) schemes. For this, we investigate the signal states and detection methods of the four-state and the two-state PM schemes. For each of these protocols we obtain a reduced set of EWs. More importantly, each set of EWs can be used to derive a necessary and sufficient condition to prove that quantum correlations are present in these protocols.
Practical quantum key distribution can be understood as a two-step procedure: in a first step two parties exchange quantum mechanical signals and perform measurements on them, in a second step auxiliary classical communication protocols are performed over an authenticated public channel to transform the data of the first step into an information-theoretic secure key. In this article we address the question of necessary conditions on the correlated (classical) data of the first step such that there can be a successful second step at all. As it turns out, a necessary condition is that these data, together with the knowledge about the physical set-up of sender and receiver, allow to establish a proof of effective entanglement between the two parties. We then demonstrate methods to systematically search for such a proof in basic settings, involving the 2-, 4-, and 6-state protocols.
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.
Abstract A novel quantum key distribution (QKD) protocol is proposed, which uses six states of three states in two bases. The protocol provides a greater range of key distribution compared to known QKD protocols. The protocol has an accurate proof of secrecy based on fundamental entropy uncertainty relations, the use of which is possible with the entanglement version of the protocol. The implementation of the protocol does not require adjustment of the polarization state at the output of the communication line, since the receiving side does not use active polarization-sensitive elements—phase modulators, which virtually excludes active probing of the active elements of the system.
We present a technique for proving the security of quantum-key-distribution (QKD) protocols. It is based on direct information-theoretic arguments and thus also applies if no equivalent entanglement purification scheme can be found. Using this technique, we investigate a general class of QKD protocols with one-way classical post-processing. We show that, in order to analyze the full security of these protocols, it suffices to consider collective attacks. Indeed, we give new lower and upper bounds on the secret-key rate which only involve entropies of two-qubit density operators and which are thus easy to compute. As an illustration of our results, we analyze the Bennett-Brassard 1984, the six-state, and the Bennett 1992 protocols with one-way error correction and privacy amplification. Surprisingly, the performance of these protocols is increased if one of the parties adds noise to the measurement data before the error correction. In particular, this additional noise makes the protocols more robust against noise in the quantum channel.