Journal
PHYSICAL REVIEW A
Volume 87, Issue 3, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevA.87.032308
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Funding
- EU STREP Project HIP [221889]
- MNiSW [IP2011 044271, IP2011 046871]
- Polish NCN research grant [DEC-2011/02/A/ST2/00305]
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Spectral properties of an arbitrary matrix can be characterized by the entropy of its rescaled singular values. Any quantum operation can be described by the associated dynamical matrix or by the corresponding superoperator. The entropy of the dynamical matrix describes the degree of decoherence introduced by the map, while the entropy of the superoperator characterizes the a priori knowledge of the receiver of the outcome of a quantum channel Phi. We prove that for any map acting on an N-dimensional quantum system the sum of both entropies is not smaller than lnN. For any bistochastic map this lower bound reads 2 ln N. We investigate also the corresponding Renyi entropies, providing an upper bound for their sum, and analyze the entanglement of the bi-partite quantum state associated with the channel. DOI: 10.1103/PhysRevA.87.032308
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