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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Entangling probes of QKD

Howard E. Brandt

Published May 5, 2006• 1 citation
Publisher

Abstract

Following a review of the measure of Renyi information gain and its optimization, the quantum circuits and designs are reviewed of optimized entangling probes for attacking the BB84 protocol of quantum key distribution (QKD), extracting maximum Renyi information on the pre-privacy amplified key. Probe photon polarization states become optimally entangled with the signal states on their way between the legitimate transmitter and receiver. Standard symmetric von Neumann projective measurements of the probe yield maximum information on the pre-privacy amplified key.

DOI
10.1117/12.661536

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Following a review of the measure of Renyi information gain and its optimization, the quantum circuits and designs are reviewed of optimized entangling probes for attacking the BB84 protocol of quantum key distribution (QKD), extracting maximum Renyi information on the pre-privacy amplified key. Probe photon polarization states become optimally entangled with the signal states on their way between the legitimate transmitter and receiver. Standard symmetric von Neumann projective measurements of the probe yield maximum information on the pre-privacy amplified key.
Abstract The mathematical physical bases are given for quantum cryptographic probes which exploit entanglement to eavesdrop on quantum key distribution. The quantum circuits and designs are presented for two different optimized entangling probes for attacking the BB84 Protocol of quantum key distribution (QKD) and yielding maximum information to the probes. Probe photon polarization states become optimally entangled with the signal states on their way between the legitimate transmitter and receiver. The designs are based on different optimum unitary transformations, each yielding the same maximum information on the pre-privacy amplified key. In each of the designs, the main quantum circuit consists of a single CNOT gate which produces the optimum entanglement between the BB84 signal states and the correlated states of the probe. For each design a different well-defined single-photon polarization state serves as the initial state of the probe, and in each case the probe is projectively measured. Symmetric projective measurements of the probe yield maximum information on the pre-privacy amplified key once basis information becomes available during basis reconciliation.
A design is given for an optimized entangling probe attacking the BB84 (Bennett-Brassard 1984) protocol of quantum key distribution and yielding maximum information to the probe for a full range of induced error rates. Probe photon polarization states become optimally entangled with the signal states on their way between the legitimate transmitter and receiver. Although standard von-Neumann projective measurements of the probe yield maximum information on the pre-privacy amplified key, if instead the probe measurements are performed with a certain positive operator valued measure, then the measurement results are conclusive, at least some of the time, for a full range of inconclusive rates.
A generalized quantum circuit and design are given for an optimal entangling probe to be used in attacking the BB84 protocol of quantum key distribution and yielding maximum information to the probe. Probe photon polarization states become optimally entangled with the BB84 signal states on their way between the legitimate transmitter and receiver. The present design generalizes an earlier one by Brandt [J. Mod. Optics 52 2177 (2005)] to include a complete range of error rates that can be induced by the probe.
It is argued that the BB84 (Bennett–Brassard 1984) protocol of quantum key distribution has a vulnerability similar to the well-known vulnerability of the B92 (Bennett 1992) protocol in the presence of losses. The quantum circuit and design are first reviewed for an optimized entangling probe attacking the BB84 protocol of quantum key distribution and yielding maximum information to the probe. Probe photon polarization states become optimally entangled with the signal states on their way between the legitimate transmitter and receiver. Although standard von Neumann projective measurements of the probe yield maximum information on the pre-privacy amplified key, if instead the probe measurements are performed with a certain positive operator valued measure, then the measurement results are unambiguous, at least some of the time, resulting in complete information gain by the probe for sufficient loss in the key distribution channel.
For the four-state protocol of quantum key distribution, optimum sets of probe parameters are calculated for the most general unitary probe in which each individual transmitted photon is made to interact with the probe so that the signal and the probe are left in an entangled state, and projective measurement by the probe, made subsequent to projective measurement by the legitimate receiver, yields information about the signal state. The probe optimization is based on maximizing the Renyi information gain by the probe on corrected data for a given error rate induced by the probe in the legitimate receiver. An arbitrary angle is included between the nonorthogonal linear polarization states of the signal photons. Two sets of optimum probe parameters are determined which both correspond to the same optimization. Also, a larger set of optimum probe parameters is found than was known previously for the standard BB84 protocol. A detailed comparison is made between the complete and incomplete optimizations, and the latter simpler optimization is also made complete. Also, the process of key distillation from the quantum transmission in quantum key distribution is reviewed, with the objective of calculating the secrecy capacity of the four-state protocol in the presence of the eavesdropping probe. Emphasis is placed on information leakage to the probe.