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arXiv · 1404.3309

Physical time-energy cost of a quantum process determines its information fidelity

Chi-Hang Fred Fung·H. F. Chau
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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.

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Chi-Hang Fred Fung, H. F. Chau. 2014-08-25. Physical time-energy cost of a quantum process determines its information fidelity. https://doi.org/10.1103/physreva.90.022333

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