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A Sharp Fannes-type Inequality for the von Neumann Entropy

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arxiv quant-ph/0610146 v1 pith:FA2ONE2Q submitted 2006-10-18 quant-ph

classification quant-ph
keywords inequalitydistanceentropynormtraceattainedderivedifference
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We derive an inequality relating the entropy difference between two quantum states to their trace norm distance, sharpening a well-known inequality due to M. Fannes. In our inequality, equality can be attained for every prescribed value of the trace norm distance.

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Cited by 4 Pith papers

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    quant-ph 2025-10 conditional novelty 7.0 of 10

    Under random brickwork circuits, regions larger than half the system have complexity growing linearly in time, while a smaller region thermalizes to essentially zero complexity by T=ℓ/2 — with holographic and replica ...

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    quant-ph 2025-10 unverdicted novelty 6.0 of 10

    In random unitary circuits, small-subsystem complexity grows linearly up to time ℓ/2 then collapses to zero while complementary large subsystems grow for exponentially long times.

  4. SharedRep-RLHF: A Shared Representation Approach to RLHF with Diverse Preferences

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    SharedRep-RLHF learns a shared preference representation across groups to improve worst-case reward estimates for minority annotators, but the theoretical guarantees are undermined by proof errors.

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