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arXiv:quant-ph/0209127 · Physical Review Letters

Ascertaining the Values of σx , σy , and σz of a Polarization Qubit

O. Schulz, Ruprecht Steinhübl, Markus Weber, Berthold‐Georg Englert, Christian Kurtsiefer, Harald Weinfurter

Published Apr 28, 2003• 21 citations
arXivHTMLPDF

Abstract

In the 1987 spin-retrodiction puzzle of Vaidman, Aharonov, and Albert one is challenged to ascertain the values of sigma(x), sigma(y), and sigma(z) of a spin-1/2 particle by utilizing entanglement. We report the experimental realization of a quantum-optical version in which the outcome of an intermediate polarization projection is inferred by exploiting single-photon two-qubit quantum gates. The experimental success probability is consistently above the 90.2% threshold of the optimal one-qubit strategy, with an average success probability of 95.6%.

DOI
10.1103/physrevlett.90.177901

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In the 1987 spin-retrodiction puzzle of Vaidman, Aharonov, and Albert one is challenged to ascertain the values of sigma(x), sigma(y), and sigma(z) of a spin-1/2 particle by utilizing entanglement. We report the experimental realization of a quantum-optical version in which the outcome of an intermediate polarization projection is inferred by exploiting single-photon two-qubit quantum gates. The experimental success probability is consistently above the 90.2% threshold of the optimal one-qubit strategy, with an average success probability of 95.6%.
In the Mean King's Problem a ship-wrecked physicist is challenged to infer the outcome of an intermediate spin measurement by a suitable preparation in conjunction with an appropriate control measurement -- the 1987 spin retrodiction puzzle of Vaidman, Aharonov, and Albert. We report the experimental realization of a quantum-optical version in which the outcome of an intermediate polarization projection is inferred by exploiting single-photon two-qubit states. The experimental success probability is consistently above the 90.2% threshold of the optimal one-qubit strategy, with an average success probability of 95.6%.
Upon entangling a spatial binary alternative of a photon with its polarization, one can use single photons to study arbitrary 2-qubit states. Sending the photon through a Mach-Zehnder interferometer, equipped with sets of wave plates that change the polarization, amounts to performing a unitary transformation on the 2-qubit state. We show that any desired unitary gate can be realized by a judicious choice of the parameters of the setup and discuss a number of applications. They include the diagnosis of an unknown 2-qubit state, an optical Grover search, and the realization of a thought experiment invented by Vaidman, Aharonov, and Albert.
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.
The information-carrying capacity of a single photon can be vastly expanded by exploiting its multiple degrees of freedom: spatial, temporal, and polarization. Although multiple qubits can be encoded per photon, to date only two-qubit single-photon quantum operations have been realized. Here, we report an experimental demonstration of three-qubit single-photon, linear, deterministic quantum gates that exploit photon polarization and the two-dimensional spatial-parity-symmetry of the transverse single-photon field. These gates are implemented using a polarization-sensitive spatial light modulator that provides a robust, non-interferometric, versatile platform for implementing controlled unitary gates. Polarization here represents the control qubit for either separable or entangling unitary operations on the two spatial-parity target qubits. Such gates help generate maximally entangled three-qubit Greenberger-Horne-Zeilinger and W states, which is confirmed by tomographical reconstruction of single-photon density matrices. This strategy provides access to a wide range of three-qubit states and operations for use in few-qubit quantum information processing protocols.Photons are essential for quantum information processing, but to date only two-qubit single-photon operations have been realized. Here the authors demonstrate experimentally a three-qubit single-photon linear deterministic quantum gate by exploiting polarization along with spatial-parity symmetry.