Quantumness in a decoherent quantum walk using measurement-induced disturbance

R. Srikanth, Subhashish Banerjee, and C. M. Chandrashekar
Phys. Rev. A 81, 062123 – Published 23 June 2010

Abstract

The classicalization of a decoherent discrete-time quantum walk on a line or an n-cycle can be demonstrated in various ways that do not necessarily provide a geometry-independent description. For example, the position probability distribution becomes increasingly Gaussian, with a concomitant fall in the standard deviation, in the former case, but not in the latter. As another example, each step of the quantum walk on a line may be subjected to an arbitrary phase gate, without affecting the position probability distribution, no matter whether the walk is noiseless or noisy. This symmetry, which is absent in the case of noiseless cyclic walk, but is restored in the presence of sufficient noise, serves as an indicator of classicalization, but only in the cyclic case. Here we show that the degree of quantum correlations between the coin and position degrees of freedom, quantified by a measure based on the disturbance induced by local measurements [Luo, Phys. Rev. A 77, 022301 (2008)], provides a suitable measure of classicalization across both type of walks. Applying this measure to compare the two walks, we find that cyclic quantum walks tend to classicalize faster than quantum walks on a line because of more efficient phase randomization due to the self-interference of the two counter-rotating waves. We model noise as acting on the coin, and given by the squeezed generalized amplitude damping (SGAD) channel, which generalizes the generalized amplitude damping channel.

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  • Received 11 May 2010

DOI:https://doi.org/10.1103/PhysRevA.81.062123

©2010 American Physical Society

Authors & Affiliations

R. Srikanth1,2,*, Subhashish Banerjee3,†, and C. M. Chandrashekar4,5,‡

  • 1Poornaprajna Institute of Scientific Research, Devanahalli, Bangalore 562 110, India
  • 2Raman Research Institute, Sadashiva Nagar, Bangalore, India
  • 3Chennai Mathematical Institute, Siruseri, Chennai, India
  • 4Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
  • 5Center for Quantum Sciences, The Institute of Mathematical Sciences, Chennai 600113, India

  • *srik@poornaprajna.org
  • subhashish@cmi.ac.in
  • cmadaiah@iqc.ca; chandru@imsc.res.in

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Vol. 81, Iss. 6 — June 2010

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