Relation between physical time-energy cost of a quantum process and its information fidelity

Chi-Hang Fred Fung and H. F. Chau
Phys. Rev. A 90, 022333 – Published 27 August 2014

Abstract

A quantum system can be described and characterized by at least two different concepts, namely, its physical and informational properties. Here, we explicitly connect these two concepts, by equating the time-energy cost which is the product of the largest energy of a Hamiltonian of quantum dynamics and the evolution time, and the entanglement fidelity which is the informational difference between an input state and the corresponding output state produced by a quantum channel characterized by the Hamiltonian. Specifically, the worst-case entanglement fidelity between the input and output states is exactly the cosine of the channel's time-energy cost (except when the fidelity is zero). The exactness of our relation makes a strong statement about the intimate connection between information and physics. Our exact result may also be regarded as a time-energy uncertainty relation for the fastest state that achieves a certain fidelity.

  • Received 18 April 2014
  • Revised 14 August 2014

DOI:https://doi.org/10.1103/PhysRevA.90.022333

©2014 American Physical Society

Authors & Affiliations

Chi-Hang Fred Fung* and H. F. Chau

  • Department of Physics and Center of Theoretical and Computational Physics, University of Hong Kong, Pokfulam Road, Hong Kong

  • *chffung@hku.hk

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Issue

Vol. 90, Iss. 2 — August 2014

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