TY - JOUR
T1 - Entropy bounds for quantum processes with initial correlations
AU - Vinjanampathy, Sai
AU - Modi, Kavan
PY - 2015
Y1 - 2015
N2 - Quantum technology is progressing towards fast quantum control over systems interacting with small environments. Hence such technologies are operating in a regime where the environment remembers the system's past, and the applicability of complete-positive trace-preserving maps is no longer valid. The departure from complete positivity means many useful bounds, such as entropy production, Holevo, and data processing inequality are no longer applicable to such systems. We address these issues by deriving a generalized bound for entropy valid for quantum dynamics with arbitrary system-environment correlations. We employ superchannels, which map quantum operations performed by the experimenter, represented in terms of completely positive maps, to states. Our bound has information-theoretic applications, as it generalizes the data processing inequality and the Holevo bound. We prove that both data processing inequality and the Holevo are valid even when a system is correlated with the environment.
AB - Quantum technology is progressing towards fast quantum control over systems interacting with small environments. Hence such technologies are operating in a regime where the environment remembers the system's past, and the applicability of complete-positive trace-preserving maps is no longer valid. The departure from complete positivity means many useful bounds, such as entropy production, Holevo, and data processing inequality are no longer applicable to such systems. We address these issues by deriving a generalized bound for entropy valid for quantum dynamics with arbitrary system-environment correlations. We employ superchannels, which map quantum operations performed by the experimenter, represented in terms of completely positive maps, to states. Our bound has information-theoretic applications, as it generalizes the data processing inequality and the Holevo bound. We prove that both data processing inequality and the Holevo are valid even when a system is correlated with the environment.
UR - http://journals.aps.org.ezproxy.lib.monash.edu.au/pra/pdf/10.1103/PhysRevA.92.052310
U2 - 10.1103/PhysRevA.92.052310
DO - 10.1103/PhysRevA.92.052310
M3 - Article
SN - 1050-2947
VL - 92
SP - 1
EP - 5
JO - Physical Review A
JF - Physical Review A
IS - 5
M1 - 052310
ER -