期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 60, 期 3, 页码 1536-1548出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2014.2298436
关键词
Quantum information; entropy-power inequality; differential entropy; Gaussian channels
资金
- NSERC
- IBM Watson Research
- DARPA QUEST Program [HR0011-09-C-0047]
When two independent analog signals, X and Y are added together giving Z = X + Y, the entropy of Z, H(Z), is not a simple function of the entropies H(X) and H(Y), but rather depends on the details of X and Y's distributions. Nevertheless, the entropy power inequality (EPI), which states that e(2H(Z)) >= e(2H(X)) + e(2H(Y)), gives a very tight restriction on the entropy of Z. This inequality has found many applications in information theory and statistics. The quantum analogue of adding two random variables is the combination of two independent bosonic modes at a beam splitter. The purpose of this paper is to give a detailed outline of the proof of two separate generalizations of the EPI to the quantum regime. Our proofs are similar in spirit to the standard classical proofs of the EPI, but some new quantities and ideas are needed in the quantum setting. In particular, we find a new quantum de Bruijin identity relating entropy production under diffusion to a divergence-based quantum Fisher information. Furthermore, this Fisher information exhibits certain convexity properties in the context of beam splitters.
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