6533b7d4fe1ef96bd126208d
RESEARCH PRODUCT
Entropic trade-off relations for quantum operations
Wojciech RogaWojciech RogaŁUkasz RudnickiZbigniew PuchałaKarol ŻYczkowskiKarol ŻYczkowskisubject
PhysicsQuantum discordQuantum PhysicsSuperoperatorFOS: Physical sciencesQuantum capacityMathematical Physics (math-ph)Strong Subadditivity of Quantum Entropy01 natural sciencesAtomic and Molecular Physics and OpticsQuantum relative entropy010305 fluids & plasmasQuantum mechanicsConditional quantum entropy0103 physical sciences010306 general physicsAmplitude damping channelQuantum Physics (quant-ph)Joint quantum entropyMathematical Physicsdescription
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 a N--dimensional quantum system the sum of both entropies is not smaller than ln N. For any bistochastic map this lower bound reads 2 ln N. We investigate also the corresponding R\'enyi entropies, providing an upper bound for their sum and analyze entanglement of the bi-partite quantum state associated with the channel.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-03-07 |