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Journal of Modern Optics

Expanded quantum cryptographic entangling probe

Howard E. Brandt, John M. Myers

Published Jun 30, 2006• 3 citations
Publisher

Abstract

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.

DOI
10.1080/09500340600680041

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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.
I present the design 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 entangled with the signal states on their way between the legitimate transmitter and receiver. Based on an earlier optimization of the unitary transformation representing the probe for a set error rate induced by the probe, I derive the simplest quantum circuit which faithfully yields the correct entangled state produced by the probe. The quantum circuit consists of a single CNOT gate in which the control qubit is a photon polarization-basis state of the signal, the target is a probe photon polarization basis state, and the initial state of the probe is set by the error rate. A method is determined for measuring the appropriate correlated state of the probe, yielding maximum information to the probe. Finally, a possible implementation of the entangling probe is given.
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.
An alternative design is given for an optimized quantum cryptographic entangling probe for attacking the BB84 protocol of quantum key distribution. The initial state of the probe has a simpler analytical dependence on the set error rate to be induced by the probe than in the earlier design. The new device yields the same maximum information to the probe for a full range of induced error rates. As in the earlier design, the probe contains a single CNOT gate which produces the optimum entanglement between the BB84 signal states and the correlated probe states.
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.
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.