Extends Fano bounds to sufficiency of low conditional entropy and defines a quantum entanglement task for infinite-dimensional systems with bounds via maximal singlet fraction of finite-dimensional approximations.
Separability and Entanglement-Breaking in Infinite Dimensions
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abstract
In this paper we give a general integral representation for separable states in the tensor product of infinite dimensional Hilbert spaces and provide the first example of separable states that are not countably decomposable. We also prove the structure theorem for the quantum communication channels that are entanglement-breaking, generalizing the finite-dimensional result of M. Horodecki, Ruskai and Shor. In the finite dimensional case such channels can be characterized as having the Kraus representation with operators of rank 1. The above example implies existence of infinite-dimensional entanglement-breaking channels having no such representation.
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quant-ph 1years
2024 1verdicts
UNVERDICTED 1representative citing papers
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On the coherent extension of some Fano-type learning bounds
Extends Fano bounds to sufficiency of low conditional entropy and defines a quantum entanglement task for infinite-dimensional systems with bounds via maximal singlet fraction of finite-dimensional approximations.