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Fortschritte der Physik

Experimental demonstration of quantum logic operations using linear optical elements

J. D. Franson, B. C. Jacobs, T. B. Pittman

Published Apr 24, 2003• 3 citations
Publisher

Abstract

Abstract Probabilistic quantum logic operations can be implemented using linear optical elements, additional photons (ancilla), and post‐selection based on the results of measurements made on the ancilla photons. Here we describe the experimental demonstration of several quantum logic devices of that kind, including a quantum parity check and a destructive controlled‐NOT (CNOT) gate. An experimental demonstration of feed‐forward control for use in quantum logic operations is also reported. The implementation of a conventional CNOT gate using polarizing beam splitters is described, along with a new “high‐fidelity” approach in which the logic gates always produce an output.

DOI
10.1002/prop.200310050

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Abstract Probabilistic quantum logic operations can be implemented using linear optical elements, additional photons (ancilla), and post‐selection based on the results of measurements made on the ancilla photons. Here we describe the experimental demonstration of several quantum logic devices of that kind, including a quantum parity check and a destructive controlled‐NOT (CNOT) gate. An experimental demonstration of feed‐forward control for use in quantum logic operations is also reported. The implementation of a conventional CNOT gate using polarizing beam splitters is described, along with a new “high‐fidelity” approach in which the logic gates always produce an output.
Summary form only given. Knill, Laflamme, and Milburn (2001) showed that probabilistic quantum logic devices could be implemented using only linear optical elements, additional ancilla photons, and post-selection based on the output of single-photon detectors. These devices produce the desired result with certainty when a specific output from the detectors is obtained, but that will only occur for some fraction of the events. Here we report the experimental demonstration of two logic devices of this kind, a destructive controlled-NOT gate and a quantum parity check. In each of these devices, two polarization-encoded qubits in the form of two single photons from a parametric down-conversion source are incident on a polarizing beam splitter.
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.
It has previously been shown that probabilistic quantum logic operations may be performed using linear optical elements, additional photons (ancilla), and post-selection based on the output of single-photon detectors. Here we describe the operation of several quantum logic operations of an elementary nature, including a quantum parity check and a quantum encoder, and we show how they may be combined to implement a controlled-NOT (CNOT) gate. All of these gates may be constructed using polarizing beam splitters that completely transmit one state of polarization and totally reflect the orthogonal state of polarization, which allows a simple explanation of each operation. We also describe a polarizing beam splitter implementation of a CNOT gate that is closely analogous to the quantum teleportation technique previously suggested by Gottesman and Chuang [Nature 402, 390 (1999)]. Finally, our approach has the interesting feature that it makes practical use of a quantum-eraser technique.
Probabilistic quantum logic operations can be performed using linear optical elements and post-selection based on the results of measurements on ancilla photons. We review the results of a number of recent experiments in this area, including the demonstration of several quantum logic gates, the use of feed-forward control, a new source of single photons, and a quantum memory device for single photons. A high-fidelity approach in which the logic gates always produce an output will also be discussed.
Knill, Laflamme, and Milburn [1] have shown that probabilistic quantum logic operations can be implemented using linear optical elements, such as beam splitters and phase shifters, additional photons (ancilla) and post-selection based on the results of measurements on the ancilla. This may seem somewhat surprising, since logic operations are inherently nonlinear. Here the nonlinearity is produced by the quantum measurement process used in the post-selection. Nonlinearities of this kind are inherently quantum-mechanical and have no classical analogy.