Recovering full coherence in a qubit by measuring half of its environment

Miatto, F. M., Piche, K., Brougham, T. and Boyd, R. W. (2015) Recovering full coherence in a qubit by measuring half of its environment. Physical Review A: Atomic, Molecular and Optical Physics, 92(6), 062331. (doi: 10.1103/PhysRevA.92.062331)

Abstract

When a quantum system interacts with its environment it may incur in decoherence. Quantum erasure makes it possible to restore coherence in a system by gaining information about its environment, but measuring the whole of it may be prohibitive: Realistically, one might be forced to address only an accessible subspace and neglect the rest. In such a case, under what conditions will quantum erasure still be effective? In this work we compute analytically the largest recoverable coherence of a random qubit plus environment state and we show that it approaches 100% with overwhelmingly high probability as long as the dimension of the accessible subspace of the environment is larger than D−−√, where D is the dimension of the whole environment. Additionally, we find a sharp transition between a linear behavior and a power-law behavior as soon as the dimension of the inaccessible environment exceeds the dimension of the accessible one. Our results imply that the typical states of a qubit plus environment system admit a measurement spanning only about D−−√ degrees of freedom, any outcome of which projects the qubit on a maximally coherent state. This suggests, for instance, that in the dynamics of open quantum systems, if the interactions are known, it would in principle be possible to gain sufficient information and restore coherence in a qubit by dealing with a fraction of the physical resources.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Boyd, Professor Robert and Piche, Mr Kevin and Brougham, Dr Thomas
• Authors: Miatto, F. M., Piche, K., Brougham, T., and Boyd, R. W.
• College/School: College of Science and Engineering > School of Physics and Astronomy
• Journal Name: Physical Review A: Atomic, Molecular and Optical Physics
• Publisher: American Physical Society
• ISSN: 1050-2947
• ISSN (Online): 2469-9934
• Published Online: 18 December 2015
• Copyright Holders: Copyright © 2015 American Physical Society
• First Published: First published in Physical Review A: Atomic, Molecular and Optical Physics 92(6):062331
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher