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Physical Review A

Preparation and entanglement purification through two-step measurements

Nan Qiu, Shu‐chao Wang, L. C. Kwek, Xiang‐Bin Wang

Published Jul 13, 2012• 5 citations
Publisher

Abstract

A method of purification through Zeno-like measurements has been proposed by Nakazato and co-workers [H. Nakazato, T. Takazawa, and K. Yuasa, Phys. Rev. Lett. 90, 060401 (2003); H. Nakazato, M. Unoki, and K. Yuasa, Phys. Rev. A 70, 012303 (2004)]. A series of frequent measurements on a quantum system is demonstrated to result in the purification of another quantum system in interaction with the former. Inspired by this idea, we have designed a strategy to obtain entangled states through only two measurements. A deterministic purification method is also provided in this article.

DOI
10.1103/physreva.86.012313

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A method of purification through Zeno-like measurements has been proposed by Nakazato and co-workers [H. Nakazato, T. Takazawa, and K. Yuasa, Phys. Rev. Lett. 90, 060401 (2003); H. Nakazato, M. Unoki, and K. Yuasa, Phys. Rev. A 70, 012303 (2004)]. A series of frequent measurements on a quantum system is demonstrated to result in the purification of another quantum system in interaction with the former. Inspired by this idea, we have designed a strategy to obtain entangled states through only two measurements. A deterministic purification method is also provided in this article.
A method of purification, purification through Zeno-like measurements [H. Nakazato, T. Takazawa, and K. Yuasa, Phys. Rev. Lett. 90, 060401 (2003)], is discussed extensively and applied to a few simple qubit systems. It is explicitly demonstrated how it works and how it is optimized. As possible applications, schemes for initialization of multiple qubits and entanglement purification are presented, and their efficiency is investigated in detail. Simplicity and flexibility of the idea allow us to apply it to various kinds of settings in quantum information and computation, and would provide us with useful and practical methods of state preparation.
We present a novel procedure to purify quantum states, i.e., purification through Zeno-like measurements. By simply repeating one and the same measurement on a quantum system, one can purify another system in interaction with the former. The conditions for the (efficient) purification are specified on a rather general setting, and the framework of the method possesses wide applicability. It is explicitly demonstrated on a specific setup that the purification becomes very efficient by tuning relevant parameters.
In work by Howell and Yeazell [Phys. Rev. A 62, 012102 (2000)], a proposal is made to generate entangled macroscopically distinguishable states of two spatially separated traveling optical modes. After considering a preparation with nonperfect photodetection, we discuss a random mode of entanglement purification without manual intervention using a number of preparations transmitted over a lossy optical transmission line. An efficiency greater than 1/2 of the purification scheme is required to increase entanglement at all. Furthermore, we study a nondemolition configuration to measure the purity of the state as contrast of interference fringes in a double-slit setup. As a consequence of the relationship between purity and entanglement of formation resulting from treating the entangled coherent states as a state of a bipartite quantum system, the contrast of interference fringes provides a direct means to measure entanglement.
Enlightened by the idea of purification through Zeno-like measurements (Nakazato et al 2003 Phys. Rev. Lett. 90 060401), we propose a scheme for generating three- and four-qubit decoherence-free states with respect to collective amplitude damping. The whole system is in a star configuration of a spin network and the outer spin qubits construct the decoherence-free state via measuring the state of central spin qubit at intervals of τ repeatedly. An interesting feature is found: namely, that in order to prepare the three-qubit decoherence-free state successfully, the value of τ for the projected time-evolution operator must be set definitely, while this restrictive condition is relaxed for achieving the four-qubit decoherence-free state. The simulation results reveal that the fidelity approaches one asymptotically, and the corresponding success probability reaches a stable value by increasing the number of measurements N.