Tuesday, July 23, 2013

1307.5368 (Saikat Guha et al.)

Quantum enigma machines and the locking capacity of a quantum channel    [PDF]

Saikat Guha, Patrick Hayden, Hari Krovi, Seth Lloyd, Cosmo Lupo, Jeffrey H. Shapiro, Masahiro Takeoka, Mark M. Wilde
The locking effect is a phenomenon which is unique to quantum information theory and represents one of the strongest separations between the classical and quantum theories of information. The Fawzi-Hayden-Sen (FHS) locking protocol harnesses this effect in a cryptographic context, whereby one party can encode n bits into n qubits while using a log(n)-bit secret key, with the guarantee that an eavesdropper who performs a measurement on the encoded qubits can recover only an arbitrarily small number of the encoded bits. This is an extreme violation of Shannon's classical theorem, which states that information-theoretic security holds in the classical case if and only if the secret key is the same size as the message. Given this intriguing phenomenon, it is of practical interest to study this effect in the presence of noise, which can occur on both the system of the legitimate receiver and the eavesdropper. This paper formally defines the locking capacity of a quantum channel as the maximum amount of locked information that can be reliably transmitted to a legitimate receiver by exploiting many independent uses of a quantum channel and an amount of secret key sublinear in the number of channel uses. We provide general operational bounds on the locking capacity in terms of other well-known capacities from quantum Shannon theory. We also study the important case of bosonic channels, finding limitations on these channels' locking capacity when coherent-state encodings are employed and particular locking protocols for these channels that might be physically implementable.
View original: http://arxiv.org/abs/1307.5368

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