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arXiv:0705.3479 · Anais de XXXV Simpósio Brasileiro de Telecomunicações e Processamento de Sinais

Implementation of non-local xor function with coherent-state qubit

João Batista Rosa Silva, Rubens Viana

Published Jan 1, 2007• 0 citations
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Abstract

This work describes how to implement a non-local xor function with coherent-state qubit using only linear optics devices and having efficiency equal to 1/2.The key element that makes possible the realization of the non-local xor function is a tripartite GHZ-type entangled coherent state.Its generation is proposed using an ideal lossless setup.

DOI
10.14209/sbrt.2007.31206

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This work describes how to implement a non-local xor function with coherent-state qubit using only linear optics devices and having efficiency equal to 1/2.The key element that makes possible the realization of the non-local xor function is a tripartite GHZ-type entangled coherent state.Its generation is proposed using an ideal lossless setup.
The or-exclusive function (xor) is one of the most important logical functions, and can be used in several protocols and algorithms, as encryption and error correction. This paper discusses several ways to implement the xor function, in a secure way using quantum communication, between users of a network. It is shown how to implement it using bipartite, tripartite and four-partite maximally entangled states, as well using an optical interferometer and strongly attenuated coherent states. Some protocols for secure communication using the xor, as quantum key distribution, are also proposed.
Optical quantum computation was limited to a few photon applications such as quantum cryptography and partial teleportation until 2001. Then the possibility of performing arbitrary logic conditional on certain detection outcomes was introduced by Knill, Laflamme and Milburn ( Nature 2001 409 46). Simple circuits consisting of single photon sources, entangled pair sources, linear optical elements and high efficiency photon counting detectors can be used to develop probabilistic two-photon logic gates. Initially such gates show a low probability of success but can approach the success rate of deterministic (non-linear) logic at the cost of added complexity. These developments have led to the emergence of a novel field of research aimed at improving the efficiency of linear logic and developing the efficient sources and detectors for its implementation. This topical issue of Journal of Optics B: Quantum and Semiclassical Optics is devoted to recent advances in this field. Key to all linear optics gates is the interference effect between separate photons that have no previous history. In this issue we include the first experiment to show such an effect (Rarity et al ), on which many later experiments are based. These interference effects can then be used to entangle separate pairs of particles into higher order entangled states (Zou et al 2005 J. Opt. B: Quantum Semiclass. Opt. 7 119–121) and also to establish entanglement between matter qubits (Kok et al ). Quantum dot single photon sources suitable for linear optics quantum logic are discussed in the paper by Unitt et al while a waveguide source of pair photons is presented by Ducci et al . The difficulties in scaling linear optics quantum computing arise from the low success probabilities of the gates. Introducing a small amount of non-linearity could allow unit efficiency gates to be designed (Munro et al ) while large non-linearities generated by the collective effects in EIT could be used to implement a wide variety of quantum logic functions (Petrosyan). The development of algorithms suitable for optical implementation is addressed by Ellinas et al . Key contributors to this issue are collaborating in the project IST:38864 RAMBOQ which has a primary goal of developing linear optics computation tools and techniques.
A scheme for the entanglement swapping of entangled states with continuous variable is presented, in which the bipartite maximally entangled coherent state serves as the quantum channel.With the help of the idea of teleportation,using beam splitter and phase-shifter,entanglement swapping of tripartite entangled coherent state can be realized.In this scheme,the entanglement swapping is failure only for one measurement process.The failure probability is very small.The detail results show that the probability and the minimum of total average fidelity for successful swapping an arbitrary tripartite entangled coherent state is nearly 1 when the mean number of photons is larger than 2.
This paper proposes a feasible scheme for the quantum teleportation of tripartite entangled coherent states by using linear optical devices such as beam splitters, phase shifters and photo detectors. The scheme is based on the bipartite maximally entangled coherent state and the tripartite entangled coherent state with bipartite maximal entanglement as quantum channels. It shows that when the mean number of photons is equal to 2, the total minimum of the average fidelity for an arbitrary tripartite entangled state is 1 – 0.67 × 10 −3 .
Abstract Non-locality is a feature of quantum mechanics that cannot be explained by local realistic theory. It can be detected by the violation of Bell’s inequality. In this work, we have considered the evaluation of Bell’s inequality with the help of the XOR game. In the XOR game, a two-qubit entangled state is shared between the two distant players. It may generate a non-local correlation between the players which contributes to the maximum probability of winning of the game. We have aimed to determine the strength of the non-locality through XOR game. Thus, we have defined a quantity S NL called the strength of non-locality, purely on the basis of the maximum probability of winning of the XOR game. We have also derived the relation between the introduced quantity S NL and the quantity M introduced in [R Horodecki, P Horodecki, and M Horodecki, (1995) Phys. Lett. A 200, 340.], to study the non-locality of a two-qubit entangled state problem in depth. The quantity M may be defined as the sum of the two largest eigenvalues of the correlation matrix of the given entangled state and it determines whether the given entangled state under probe is non-local. Further, we have explored the non-locality of any two-qubit entangled state, whose non-locality cannot be detected by the CHSH inequality. Interestingly, we have found that the newly defined quantity S NL fails to detect non-locality for the entangled state, when the witness operator corresponding to CHSH operator cannot detect the entangled state. To overcome this problem, we have modified the definition of the strength of non-locality and have shown that the modified definition may detect the non-locality of such entangled states, which were earlier undetected by S NL . Furthermore, we have provided two applications of the strength S NL of the non-locality such as (i) establishment of a link between the two-qubit non-locality determined by S NL and the three-qubit non-locality determined by the Svetlichny operator and (ii) determination of the upper bound of the power of the controller in terms of S NL in controlled quantum teleportation.