Quantum Cryptography with Imperfect Apparatus

TL;DR

This paper introduces a self-checking photon source for quantum key distribution that ensures security despite source imperfections, supported by a mathematical theorem about quantum states and EPR pairs.

Contribution

It proposes a practical self-checking source design and proves a structural theorem linking EPR-type equations to quantum state composition.

Findings

The self-checking source guarantees security with certain tests.

The structural theorem characterizes quantum states satisfying EPR equations.

The approach enhances the robustness of quantum cryptography protocols.

Abstract

Quantum key distribution, first proposed by Bennett and Brassard, provides a possible key distribution scheme whose security depends only on the quantum laws of physics. So far the protocol has been proved secure even under channel noise and detector faults of the receiver, but is vulnerable if the photon source used is imperfect. In this paper we propose and give a concrete design for a new concept, {\it self-checking source}, which requires the manufacturer of the photon source to provide certain tests; these tests are designed such that, if passed, the source is guaranteed to be adequate for the security of the quantum key distribution protocol, even though the testing devices may not be built to the original specification. The main mathematical result is a structural theorem which states that, for any state in a Hilbert space, if certain EPR-type equations are satisfied, the state must be essentially the orthogonal sum of EPR pairs.