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arXiv:quant-ph/0112088 · Physical Review A

Linear optical controlled-NOT gate in the coincidence basis

Timothy C. Ralph, Nathan K. Langford, T. B. Bell, Andrew G. White

Published Jun 20, 2002• 345 citations
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Abstract

We describe the operation and tolerances of a nondeterministic, coincidence basis, quantum controlled-NOT gate for photonic qubits. It is constructed solely from linear optical elements and requires only a two-photon source for its demonstration. Its success probability is $1/9.$

DOI
10.1103/physreva.65.062324

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We describe the operation and tolerances of a nondeterministic, coincidence basis, quantum controlled-NOT gate for photonic qubits. It is constructed solely from linear optical elements and requires only a two-photon source for its demonstration. Its success probability is 1/9.1/9.1/9.
We examine three possible implementations of nondeterministic linear optical controlled NOT gates with a view to an in-principle demonstration in the near future. To this end we consider demonstrating the gates using currently available sources, such as spontaneous parametric down conversion and coherent states, and current detectors only able to distinguish between zero and many photons. The demonstration is possible in the coincidence basis and the errors introduced by the nonoptimal input states and detectors are analyzed.
We propose a linear optical scheme to implement the nondeterministic two-qubit controlled phase gate with the certain success probability. The proposed setup involves simple linear optical elements, a pair of the two-photon polarization entangled states, and the conventional photon detectors that only distinguish the vacuum and nonvacuum Fock number states. A sophisticated single-photon detector distinguishing one or two photon states is unnecessary. This can greatly simplify the experimental realization of a linear optical quantum computer.
Knill, Laflamme, and Milburn [Nature (London) 409, 46 (2001)] recently showed that nondeterministic quantum logic operations could be performed using linear optical elements, additional photons (ancilla), and postselection based on the output of single-photon detectors. Here we report the experimental demonstration of two logic devices of this kind, a destructive controlled-NOT (CNOT) gate and a quantum parity check. These two devices can be combined with a pair of entangled photons to implement a conventional (nondestructive) CNOT that succeeds with a probability of 1/4.