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Communications in Theoretical Physics

Realization of Bipartite Positive-Operator-Value Measurements of Two-Photon Polarization States

Lin Qing

Published Feb 1, 2009• 2 citations
Publisher

Abstract

In this letter, we propose a scheme of a special quantum optical Fredkin gate assisted by optical manipulations and postselection from the coincidence measurements, and then modify it with cross-Kerr nonlinearities to be suitable for the realization of all possible positive operator-valued measurements of bipartite polarization states. This scheme is feasible in the lab with the current experimental technology.

DOI
10.1088/0253-6102/51/2/11

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In this letter, we propose a scheme of a special quantum optical Fredkin gate assisted by optical manipulations and postselection from the coincidence measurements, and then modify it with cross-Kerr nonlinearities to be suitable for the realization of all possible positive operator-valued measurements of bipartite polarization states. This scheme is feasible in the lab with the current experimental technology.
In this paper, with the weak cross-Kerr nonlinearity, we first present a special experimental scheme called controlled-path gate with which the realization of all possible bipartite positive-operator-value measurements of two-photon polarization states may be nearly deterministic. Following the same technique, the realization of quantum control gates, including the controlled-NOT gate, Fredkin gate, Toffoli gate, arbitrary controlled-U gate, and even arbitrary multicontrolled-U gate, are proposed. The corresponding probabilities are 1∕21∕21∕2, 1∕81∕81∕8, 2∕232∕232∕23, etc., respectively. Only the coherent states are required but not any ancilla photons, and no coincidence measurement are required, which results in these gates being scalable. The structures of these gates are very simple, therefore we think they are feasible with the current experimental technology in optics.
How to manipulate (operate or measure) single photons efficiently and simply is the basic problem in optical quantum information processing. We first present an efficient scheme to transform a biphoton polarization state to a corresponding single-photon state encoded by its polarization and spatial modes. This single-photon state carries both the information of the controlled and target photons. It will make the realization of bipartite positive-operator-valued measurements efficiently and simply. Moreover, the inverse transformation from the single-photon state back to the corresponding biphoton polarization state is also proposed. Using both the transformations, the realization of the arbitrary two-qubit unitary operation is simple with an M-Z interferometer. All the schemes are feasible with the current experimental technology.
A Fredkin gate is an indispensable logic gate for the applications of the scalable quantum network. Weak cross-Kerr nonlinearities serve as the intermediary between photons and coherent states and thus provide the indirect interaction between photons. By means of weak cross-Kerr nonlinearities, we propose a construction scheme of a nearly deterministic Fredkin gate, where polarization modes of photons carry quantum bits. By virtue of an X homodyne measurement on the coherent state, the appropriate classical feed-forward operations are executed according to the different measurement outcomes. Applying one swap gate and two combination gates and other assistant simple optical elements, the nearly deterministic Fredkin gate is successfully constructed. The unique features of photons as quantum information carriers with high velocity and low decoherence, combined with simple elements and mature operation techniques, afford the possibility to the scheme proposed here which takes aim at feasible quantum logic circuits for practical and scalable quantum computation and quantum communication.
In this paper, we propose an experimental scheme for unambiguous quantum state comparison assisted by linear optical manipulations, twin-photons produced from parametric down-conversion, and postselection from the coincidence measurement. In this scheme the preparation of the general two mixed qubit states with arbitrary prior probabilities and the realization of the optimal POVMs for unambiguous quantum state comparison are presented. This proposal is feasible by current experimental technology, and may be used in single-qubit quantum flngerprinting.
Abstract We propose a theoretical protocol for preparing four-photon polarization entangled decoherence-free states, which are immune to the collective noise. With the assistance of the cross-Kerr nonlinearities, a two-photon spatial entanglement gate, two controlled-NOT gates, a four-photon polarization entanglement gate are inserted into the circuit, where X homodyne measurements are aptly applied. Combined with some swap gates and simple linear optical elements, four-photon polarization entangled decoherence-free states which can be utilized to represent two logical qubits, |0〉L and |1〉L are achieved at the output ports of the circuit. This generation scheme may be implemented with current experimental techniques.