[QIP-Sem] QIP seminar, Mon 12/3, 4pm, 36-428, Saikat Guha

[Peter Shor]

MIT Quantum Information Processing seminar
Monday 12/3 at 4pm in 36-428
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Saikat Guha (MIT RLE)

The entropy photon-number inequality and capacity of bosonic channels

Abstract:

Determining the ultimate classical information carrying capacity of electromagnetic waves requires quantum-mechanical analysis to properly account for the bosonic nature of these waves. Our previous work has established capacity theorems for the bosonic single-user channel with additive thermal noise, under the presumption of a minimum output entropy conjecture. More recent work has established capacity theorems for the bosonic broadcast, and wiretap channels under the presumption of a second minimum output entropy conjecture, which is in some sense the dual of the first conjecture. Now, with Graeme Smith's recent results on the equivalence of privacy capacity and the quantum capacity of degradable quantum channels, proving the second minimum output entropy conjecture would also establish the quantum capacity of the single-user lossy bosonic channel. Despite considerable accumulated evidence that supports the validity of these conjectures, they have yet to be proven. Both con
 jectures have been proven if the input states are restricted to be Gaussian, and we have shown that they are equivalent under this input-state restriction. The Entropy Power Inequality (EPI) from classical information theory is widely used in coding theorem converse proofs for Gaussian channels.  By analogy with the EPI, we conjecture its quantum version, viz., the Entropy Photon-number Inequality (EPnI).  In this talk we show that the preceding two minimum output entropy conjectures are simple corollaries of the EPnI.  Hence, proving the EPnI would immediately establish key results for the capacities of bosonic communication channels.

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