Quantum discord in quantum computation

Quantum discord is a measure of the quantumness of correlations. After reviewing its different versions and properties, we apply it to the questions of quantum information processing. First we show that changes in discord in the processed unentangled states indicate the need for entanglement in the distributed implementation of quantum gates. On the other hand, it was shown that zero system-environment discord is a necessary and sufficient condition for applicability of the standard completely positive description of the system's evolution. We demonstrate that this result does not translate into useful quantum process tomography. Depending on the details of the preparation procedure only absence of any initial correlations may guarantees consistency of the process tomography.

[1]  Wojciech Hubert Zurek.  Quantum discord and Maxwell's demons , 2003 .

[2]  Raoul Dillenschneider,et al.  Quantum discord and quantum phase transition in spin chains , 2008, 0809.1723.

[3]  R. Jozsa,et al.  On the role of entanglement in quantum-computational speed-up , 2002, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[4]  V. Vedral,et al.  Classical, quantum and total correlations , 2001, quant-ph/0105028.

[5]  Daniel R. Terno,et al.  Vectorization of quantum operations and its use , 2009, 0911.2539.

[6]  Daniel A. Lidar,et al.  Vanishing quantum discord is necessary and sufficient for completely positive maps. , 2008, Physical review letters.

[7]  E. Sudarshan,et al.  Completely positive maps and classical correlations , 2007, quant-ph/0703022.

[8]  Aharon Brodutch,et al.  Quantum discord, local operations, and Maxwell's demons , 2010 .

[9]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[10]  E. Sudarshan,et al.  How state preparation can affect a quantum experiment: Quantum process tomography for open systems , 2007, 0706.0394.

[11]  C. J. Wood.  Non-completely positive maps: properties and applications , 2009, 0911.3199.

[12]  M. Horodecki,et al.  Irreversibility for all bound entangled states. , 2005, Physical Review Letters.

[13]  D. Bruß,et al.  Lectures on Quantum Information , 2007 .

[14]  E. Sudarshan,et al.  Non-Markovian Open Quantum Systems , 2008, 0803.1183.

[15]  Animesh Datta,et al.  Quantum discord and the power of one qubit. , 2007, Physical review letters.

[16]  M. Horodecki,et al.  Local versus nonlocal information in quantum-information theory: Formalism and phenomena , 2004, quant-ph/0410090.

[17]  H. Imai,et al.  Sufficient and necessary condition for zero quantum entropy rates under any coupling to the environment. , 2010, Physical review letters.

[18]  R. M. Serra,et al.  Quantum and classical thermal correlations in the XY spin-(1/2) chain , 2010, 1002.3906.

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

[20]  J. Eisert,et al.  Optimal local implementation of nonlocal quantum gates , 2000 .

[21]  L. Ballentine,et al.  Quantum Theory: Concepts and Methods , 1994 .

[22]  A. Wehrl.  General properties of entropy , 1978 .

[23]  A. Acín,et al.  Almost all quantum states have nonclassical correlations , 2009, 0908.3157.

[24]  Aharon Brodutch,et al.  Entanglement, discord, and the power of quantum computation , 2010, 1009.2571.

[25]  Karol Życzkowski,et al.  Dynamics beyond completely positive maps : some properties and applications , 2008 .

[26]  Vedral,et al.  Local distinguishability of multipartite orthogonal quantum states , 2000, Physical review letters.

[27]  C. H. Bennett,et al.  Quantum nonlocality without entanglement , 1998, quant-ph/9804053.

[28]  W. Zurek,et al.  Quantum discord: a measure of the quantumness of correlations. , 2001, Physical review letters.