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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Detecting quantum correlations for quantum key distribution

Marcos Curty, Otfried Gühne, Maciej Lewenstein, Norbert Lütkenhaus

Published Jan 11, 2005• 1 citation
Publisher

Abstract

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.

DOI
10.1117/12.575411

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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.
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.
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.
In contrast to classical public-key cryptosystems, where the security of encoded messages relies on on computational assumptions, Quantum Key Distribution (QKD) enables two distant parties to establish a shared secret key that, when combined with a one-time pad, provides information-theoretically secure encryption, provided that the QKD protocol is supported by a rigorous security proof. In the last decades, security proofs robust against a wide range of eavesdropping strategies have established the theoretical soundness of several QKD protocols. However, most proofs are based on idealized models of the physical systems involved in such protocols and often include assumptions that are not satisfied in practical implementations. This mismatch creates a gap between theoretical security guarantees and actual experimental realizations, making QKD protocols vulnerable to attacks. To ensure the security of real-world QKD systems, it is therefore essential to account for imperfections in security analyses. In this article, we present an overview of recent analytical and numerical developments in QKD security proofs, which provide a versatile approach for incorporating imperfections and re-establishing the security of quantum communication protocols under realistic conditions.
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).
Quantum key distribution (QKD) is a secure key generation method between two distant parties by wisely exploiting properties of quantum mechanics. In QKD, experimental measurement outcomes on quantum states are transformed by the two parties to a secret key. This transformation is composed of many logical steps (as guided by security proofs), which together will ultimately determine the length of the final secret key and its security. We detail the procedure for performing such classical postprocessing taking into account practical concerns (including the finite-size effect and authentication and encryption for classical communications). This procedure is directly applicable to realistic QKD experiments and thus serves as a recipe that specifies what postprocessing operations are needed and what the security level is for certain lengths of the keys. Our result is applicable to the BB84 protocol with a single or entangled photon source.
Quantum Key Distribution (QKD) protocols rely on authenticated classical communication. Typical QKD security proofs are carried out in an idealized setting where authentication is assumed to behave honestly: it never aborts, and all classical messages are delivered faithfully with their original timing preserved. Authenticated channels that can be constructed in practice have different properties. Most critically, such channels may abort asymmetrically, such that only the receiving party may detect an authentication failure while the sending party remains unaware. Furthermore, an adversary may delay, reorder, or block classical messages. This discrepancy means that existing security proofs under honest authentication do not directly establish security in the practical authentication setting. We address this gap using an existing security definition from the literature that permits asymmetric aborts while retaining secrecy of any key produced and agreement of the keys whenever both parties accept. Our main result is a reduction theorem showing that, under mild and easily satisfied protocol conditions, any QKD protocol proven secure under the honest authentication setting, for the standard security definition with symmetric aborts, remains secure under a practical authentication setting, for the weaker security definition that allows for asymmetric aborts. This result allows all existing QKD proofs to be retroactively lifted to the practical authentication setting (with asymmetric aborts) with a minor protocol tweak.