Preparation and entanglement purification of qubits through Zeno-like measurements

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.

[1]  J. Cirac,et al.  Creation of entangled states of distant atoms by interference , 1998, quant-ph/9810013.

[2]  Knight,et al.  Generation and detection of nonclassical field states by conditional measurements following two-photon resonant interactions. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[3]  Zhi-Ming Zhang,et al.  Entangling distant atoms by interference of polarized photons. , 2003, Physical review letters.

[4]  Charles H. Bennett,et al.  Purification of noisy entanglement and faithful teleportation via noisy channels. , 1995, Physical review letters.

[5]  H. Kimble,et al.  Efficient engineering of multiatom entanglement through single-photon detections. , 2003, Physical review letters.

[6]  H. Häffner,et al.  How to realize a universal quantum gate with trapped ions , 2003, quant-ph/0312162.

[7]  Purification of quantum state through Zeno-like measurements , 2004, quant-ph/0402183.

[8]  J. Cirac,et al.  Long-distance quantum communication with atomic ensembles and linear optics , 2001, Nature.

[9]  Jian-Wei Pan,et al.  Experimental realization of entanglement concentration and a quantum repeater. , 2003, Physical review letters.

[10]  F. Schmidt-Kaler,et al.  Realization of the Cirac–Zoller controlled-NOT quantum gate , 2003, Nature.

[11]  M. B. Plenio,et al.  Cavity-loss-induced generation of entangled atoms , 1999 .

[12]  C. K. Law,et al.  PREPARATION OF ARBITRARY ENTANGLED QUANTUM STATES OF A TRAPPED ION , 1998 .

[13]  P. Facchi,et al.  Zeno dynamics yields ordinary constraints , 2001 .

[14]  M. Koashi,et al.  Experimental extraction of an entangled photon pair from two identically decohered pairs , 2003, Nature.

[15]  David P. DiVincenzo,et al.  Quantum information and computation , 2000, Nature.

[16]  Hiromichi Nakazato,et al.  Purification through Zeno-like measurements. , 2003, Physical review letters.

[17]  A. Messina.  A single atom-based generation of Bell states of two cavities , 2002, quant-ph/0203140.

[18]  A. Vaziri,et al.  Concentration of higher dimensional entanglement: qutrits of photon orbital angular momentum. , 2003, Physical review letters.

[19]  I. Chuang,et al.  Quantum Computation and Quantum Information: Introduction to the Tenth Anniversary Edition , 2010 .

[20]  V. Subrahmanyam.  Entanglement dynamics and quantum-state transport in spin chains (4 pages) , 2003, quant-ph/0307135.

[21]  Matthias Christandl,et al.  Perfect state transfer in quantum spin networks. , 2004, Physical review letters.

[22]  Dipankar Home,et al.  A Conceptual Analysis of Quantum Zeno; Paradox, Measurement, and Experiment , 1997 .

[23]  Hai-Woong Lee,et al.  Quasideterministic generation of entangled atoms in a cavity. , 2002, Physical review letters.

[24]  Tosio Kato.  Perturbation theory for linear operators , 1966 .

[25]  J. Raimond,et al.  Generation of Einstein-Podolsky-Rosen Pairs of Atoms , 1997 .

[26]  Y. Pashkin,et al.  Coherent control of macroscopic quantum states in a single-Cooper-pair box , 1999, Nature.

[27]  Cirac,et al.  Preparation of macroscopic superpositions in many-atom systems. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[28]  A. Osterloh,et al.  Dynamics of entanglement in one-dimensional spin systems (24 pages) , 2003, quant-ph/0307048.

[29]  P. Facchi,et al.  Quantum Zeno subspaces. , 2002, Physical review letters.

[30]  Horne,et al.  Proposed test of Bell's inequality without a detection loophole by using entangled Rydberg atoms. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[31]  Law,et al.  Arbitrary control of a quantum electromagnetic field. , 1996, Physical review letters.

[32]  O. Astafiev,et al.  Demonstration of conditional gate operation using superconducting charge qubits , 2003, Nature.

[33]  Schumacher,et al.  Purification of noisy entanglement and faithful teleportation via noisy channels. , 1995, Physical review letters.

[34]  Vogel,et al.  Quantum state engineering of the radiation field. , 1993, Physical review letters.

[35]  M. B. Plenio,et al.  Robust creation of entanglement between ions in spatially separate cavities. , 2003 .

[36]  Charles H. Bennett,et al.  Mixed-state entanglement and quantum error correction. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[37]  E.C.G. Sudarshan,et al.  Quantum Zeno dynamics , 2000 .

[38]  Kimble,et al.  Synthesis of arbitrary quantum states via adiabatic transfer of Zeeman coherence. , 1993, Physical review letters.

[39]  D. Leibfried,et al.  Experimental demonstration of a controlled-NOT wave-packet gate. , 2002, Physical Review Letters.

[40]  Entangled-state preparation via dissipation-assisted adiabatic passages , 2003, quant-ph/0305116.

[41]  S. Bose.  Quantum communication through an unmodulated spin chain. , 2002, Physical review letters.