The Parity Bit in Quantum Cryptography

Details The Parity Bit in Quantum Cryptography The Parity Bit in Quantum Cryptography

1996-04-30

arxiv.org/abs/quant-ph/9604040v1

Physics

Quantum Physics

19 pages, RevTeX

Scientific paper

10.1103/PhysRevA.54.2675

An $n$-bit string is encoded as a sequence of non-orthogonal quantum states. The parity bit of that $n$-bit string is described by one of two density matrices, $\rho_0^{(n)}$ and $\rho_1^{(n)}$, both in a Hilbert space of dimension $2^n$. In order to derive the parity bit the receiver must distinguish between the two density matrices, e.g., in terms of optimal mutual information. In this paper we find the measurement which provides the optimal mutual information about the parity bit and calculate that information. We prove that this information decreases exponentially with the length of the string in the case where the single bit states are almost fully overlapping. We believe this result will be useful in proving the ultimate security of quantum crytography in the presence of noise.

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