Key-Rate Bound of a Semi-Quantum Protocol Using an Entropic Uncertainty Relation

Abstract

In this paper we present a new proof technique for semi-quantum key distribution protocols which makes use of a quantum entropic uncertainty relation to bound an adversary's information. Our new technique provides a more optimistic keyrate bound than previous work relying only on noise statistics (as opposed to using additional mismatched measurements which increase the noise tolerance of this protocol, but at the cost of requiring four times the amount of measurement data). Our new technique may hold application in the proof of security of other semi-quantum protocols or protocols relying on two-way quantum communication.

High-Dimensional Semiquantum Cryptography

“…One of the main contributions of our security proof method is to show how a large class of two-way high-dimensional SQKD protocol may be reduced to an equivalent one-way fully quantum protocol, making it easier to analyze. This extends an earlier result of ours in a conference paper [52] to higher dimensions and a larger class of SQKD protocol. The techniques here may be applicable to other two-way protocols.…”

“…We will comment on general attacks later. Our security analysis extends ideas introduced in our conference paper [52] but to the higher dimensional case and consists of two main parts: First, we will prove that it is sufficient to analyze a particular one-way fully quantum protocol and, once security is proven there assuming the same channel observations are made, security of our SQKD protocol follows immediately. This reduction is very general and can apply to other SQKD protocols.…”

From Classical to Semi-Quantum Secure Communication

“…There are some additional restrictions that may be made on this attack (in particular |e and |f may exist with a two-dimensional subspace of H E spanned by |0 E and a second basis vector); however, this notation is sufficient for the discussion at hand. For further information on the restricted attack, and the proof that security against such attacks implies security against arbitrary collective attacks, the reader is referred to [22]. Note that, by linearity of F, we also have the following:…”

“…This is one of the few statistics A and B actually can estimate and is, in fact, the only observable noise statistic in the forward channel (they cannot measure, for example, p A→B . Note that, by definition of the restricted attack, it is sufficient to consider non-negative q i [22].…”

“…Of course, | 0|e | ≤ 1. We are constrained by the fact that q 3 ≥ 0 (since, for the restricted attack, each q i are non-negative real numbers [22]). We therefore have the following solution for q 3 , looking for the smallest positive root of the above quadratic equation, assuming p A→B a,1 ≥ α 2 p A→B 0,1…”