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Journal of Modern Optics

Design for a quantum cryptographic entangling probe

Howard E. Brandt

Published Nov 10, 2005• 7 citations
Publisher

Abstract

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.

DOI
10.1080/09500340500275298

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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.
For a general entangling probe attacking the BB84 protocol in quantum key distrobution, I show that the simplest quantum circuit representing the optimal entangling probe, and yielding the maximum information gain on the pre-privacy-amplified key, consisting of a single CNOT gate in which the control qubit consists of two polarization-basis states of the signal, the target qubit consists of two probe-photon polarization basis states, and the initial state of the probe is set by the error rate induced by the probe. A method is determined for measuring the appropriate correlated state of the probe. Finally, a possible implementation of the entangling probe is described. the device is a simple special-purpose quantum cryptography.
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 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.
For a general entangling probe attacking the Bennett-Brassard 1984 protocol in quantum key distribution, I calculate three classes of optimized unitary transformations, all yielding the same maximum information to the probe. The simplest one corresponds to a probe having a two-dimensional Hilbert space of states, and is uniquely determined by the error rate induced by the probe in the legitimate receiver. The second class corresponds to a probe having a four-dimensional Hilbert space of states, and is determined by the error rate and two continuous angle parameters which are mutually constrained by the error rate. The third class corresponds to a probe having a four-dimensional Hilbert space, and is determined by the error rate and two continuous angle parameters, one of which is constrained by the error rate. Furthermore, I show that the simplest quantum circuit representing the optimal entangling probe consists of a single controlled-NOT gate in which the control qubit consists of two polarization-basis states of the signal, the target qubit consists of two probe-basis states, 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. Finally, a possible implementation of the entangling probe is described.
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.