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arXiv:quant-ph/0610254

Simple setups for quantum games in optical networks

Rubens Viana Ramos, Paulo Benicio Melo de Sousa

Published Oct 30, 2006• 0 citations
arXivHTMLPDF

Abstract

In this work, we propose two optical setups for two-players, non-zero and zero sum, quantum games in optical networks using light polarization of single-photon pulses, single-photon detectors and linear optical devices. The optical setups proposed can be easily implemented permitting a fast experimental realization of quantum games with present technology.

DOI
10.48550/arxiv.quant-ph/0610254

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In this work, we propose two optical setups for two-players, non-zero and zero sum, quantum games in optical networks using light polarization of single-photon pulses, single-photon detectors and linear optical devices. The optical setups proposed can be easily implemented permitting a fast experimental realization of quantum games with present technology.
The natural choice of physical qubit for quantum communication is the photon: a photon can be transmitted quickly from the sender to a distant receiver and the technology for creating, manipulating, distributing, and measuring light pulses is well established. Many of these classical techniques can also be employed for quantum communication protocols. We will therefore focus our attention on optical setups for quantum communication. We will study a number of optical setups in the next few sections and use the conventions introduced in Chapter 4 to analyze them. In particular, we will assume that the qubits are encoded in the degrees of freedom of a single photon. Some of the main technical challenges in quantum communication arise from this need to work with single photon pulses. For instance, photons do not interact with each other in vacuum or linear media, and interactions between two photons in non-linear optical media are relatively small, so that realizing entangling two photon gates via coherent interactions is a challenging task. The quantum communication schemes discussed here circumvent this technical problem to a large extent. They only use non-linear optical materials for parametric down-conversion to create Bell-pairs of photons and then exploit standard linear optical devices and photo-detectors to manipulate them. No further non-linear entangling gates are required. Parametric down-conversion In non-linear optical media a single photon can be down-converted into a pair of photons. In this coherent process the incoming photon is destroyed and two photons of lower energy are created.
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.
We propose a protocol to controlled implement the two-photon controlled phase gate within a network by using interference of polarized photons. The realization of this protocol is appealing due to the fact that the quantum state of light is robust against the decoherence, and photons are ideal carriers for transmitting quantum information over long distances. The proposed setup involves simple linear optical elements and the conventional photon detectors that only distinguish the vacuum and nonvacuum Fock number states. This can greatly simplify the experimental realization of a linear optical quantum computer.
Experimental realization of the game is presented using polarization-time-entangled photon pairs on which arbitrary (quantum-) strategies can be performed with adjustable birefringent elements. For the demonstration of the efficiency of quantum strategies, the strategy of each of the two players can be realized as a unitary transformation performed on one spin-1/2 particle. The polarization-entangled photon pairs are generated with high temporal definition in a parametric down-conversion process. Initially they are prepared in a Kraus state on which the two players perform their single-particle operations using the corresponding angular settings of a combination of /spl lambda//2- and /spl lambda//4-waveplates.