Post-selection technique for quantum channels with applications to quantum cryptography

Abstract

We propose a general method for studying properties of quantum channels acting on an n-partite system, whose action is invariant under permutations of the subsystems. Our main result is that, in order to prove that a certain property holds for any arbitrary input, it is sufficient to consider the special case where the input is a particular de Finetti-type state, i.e., a state which consists of n identical and independent copies of an (unknown) state on a single subsystem. A similar statement holds for more general channels which are covariant with respect to the action of an arbitrary finite or locally compact group. Our technique can be applied to the analysis of information-theoretic problems. For example, in quantum cryptography, we get a simple proof for the fact that security of a discrete-variable quantum key distribution protocol against collective attacks implies security of the protocol against the most general attacks. The resulting security bounds are tighter than previously known bounds obtained by proofs relying on the exponential de Finetti theorem [Renner, Nature Physics 3,645(2007)].

3.5 pages

References in corpus (1)

• One-and-a-half quantum de Finetti theorems

Cited by in corpus (6)

• Device-independent quantum key distribution secure against collective attacks
• Finite-size analysis of continuous-variable quantum key distribution
• Finite-key security against coherent attacks in quantum key distribution
• Device-Independent Quantum Key Distribution with Commuting Measurements
• Fundamental Quantitative Security In Quantum Key Distribution
• A Study of Channel Estimation and Postprocessing in Quantum Key Distribution Protocols