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

Multipair signal states in entanglement-based quantum cryptography

Miloslav Dušek, Kamil Brádler

Published Nov 21, 2003• 0 citations
Publisher

Abstract

Pairs of entangled photons can be employed for quantum key distribution. For each bit exactly one pair of photons is needed. Unfortunately, the quantum states produced by real sources, like a parametric down conversion, contain also terms with more than only one photon pair. We discuss several aspects of the use of such states for quantum key distribution. It is shown that the presence of multi-pair signals (together with low detection efficiencies) causes errors in transmission even in the absence of al1 eavesdropper. However, the most important result is that an individual eavesdropping on multi-pair signals increases the error rate. This fact represents the important advantage of the entanglement-based quantum key distribution.

DOI
10.1117/12.545078

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Pairs of entangled photons can be employed for quantum key distribution. For each bit exactly one pair of photons is needed. Unfortunately, the quantum states produced by real sources, like a parametric down conversion, contain also terms with more than only one photon pair. We discuss several aspects of the use of such states for quantum key distribution. It is shown that the presence of multi-pair signals (together with low detection efficiencies) causes errors in transmission even in the absence of al1 eavesdropper. However, the most important result is that an individual eavesdropping on multi-pair signals increases the error rate. This fact represents the important advantage of the entanglement-based quantum key distribution.
Real sources of entangled photon pairs (like parametric down conversion) are not perfect. They produce quantum states that contain more than only one photon pair with some probability. In this paper it is discussed what happens if such states are used for the purpose of quantum key distribution. It is shown that the presence of "multi-pair" signals (together with low detection efficiencies) causes errors in transmission even if there is no eavesdropper. Moreover, it is shown that even the eavesdropping, that draws information only from these "multi-pair" signals, increases the error rate. Information, that can be obtained by an eavesdropper from these signals, is calculated.
Every security analysis of quantum-key distribution (QKD) relies on a faithful modeling of the employed quantum states. Many photon sources, such as for instance a parametric down-conversion (PDC) source, require a multimode description but are usually only considered in a single-mode representation. In general, the important claim in decoy-based QKD protocols for indistinguishability between signal and decoy states does not hold for all sources. We derive bounds on the single-photon transmission probability and error rate for multimode states and apply these bounds to the output state of a PDC source. We observe two opposing effects on the secure key rate. First, the multimode structure of the state gives rise to a new attack that decreases the key rate. Second, more contributing modes change the photon number distribution from a thermal toward a Poissonian distribution, which increases the key rate.
We have implemented the 'six-state' quantum cryptography protocol using polarization-entangled photon pairs, in which the polarization of each photon of a pair is measured in one of three randomly chosen bases. For a given amount of eavesdropping, this protocol results in a larger error rate than in four- or two-state protocols, but reduces the number of key-producing events. We have experimentally investigated several incoherent eavesdropping strategies, and verified the predicted enhancement in error rate. However, we demonstrate that for low error rates, the efficiency for secret key generation is higher when using the four-state protocol.
It is well-known that multi-photon signals in quantum key distribution (QKD) with weak laser pulses represent a security threat resulting in a reduced rate for secret-key production. Similarly, multi-pair contributions from spontaneous-parametric-down-conversion (SPDC) sources may cause information leak. In particular, in the case of polarization coding (i.e., when the polarization of photons is used to encode the logical qubits) a security risk occurs when the polarizations show some degree of correlation. In such a case an eavesdropper can perform a photon number splitting (PNS) attack by getting hold of, and analyzing, one photon out of the multi-photon state without causing any disturbance to the polarization of the other ones. It is therefore important to estimate the relative amount of polarization- correlated multi-pairs in SPDC signals. We present and discuss the results of a recent investigation on this subject. In our study, we consider a CW-SPDC-source scheme of Kwiat type, fully based on polarization-entanglement. The down-converted field is produced continuously, and a suitably chosen coincidence window replaces the concept of pulses.