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Quantum monotone metrics induced from trace non-increasing maps and additive noise
- Publication Year :
- 2020
- Publisher :
- arXiv, 2020.
-
Abstract
- Quantum monotone metric was introduced by Petz [Linear Algebra Appl. 244, 81–96 (1996)], and it was proved that quantum monotone metrics on the set of quantum states with trace one were characterized by operator monotone functions. Later, these were extended to monotone metrics on the set of positive operators whose traces are not always the one based on completely positive, trace preserving maps. It was shown that these extended monotone metrics were characterized by operator monotone functions continuously parameterized by traces of positive operators and did not have some ideal properties such as monotonicity and convexity with respect to the positive operators. In this paper, we introduce another extension of quantum monotone metrics that have monotonicity under completely positive, trace non-increasing maps and additive noise. We prove that our extended monotone metrics can be characterized only by static operator monotone functions from few assumptions without assuming continuities of metrics. We show that our monotone metrics have some natural properties such as additivity of direct sum, convexity, and monotonicity with respect to positive operators.
- Subjects :
- TheoryofComputation_MISCELLANEOUS
Quantum Physics
Pure mathematics
Trace (linear algebra)
Direct sum
010102 general mathematics
TheoryofComputation_GENERAL
FOS: Physical sciences
Statistical and Nonlinear Physics
Monotonic function
Mathematical Physics (math-ph)
01 natural sciences
Convexity
Operator (computer programming)
Monotone polygon
Quantum state
0103 physical sciences
Linear algebra
010307 mathematical physics
0101 mathematics
Quantum Physics (quant-ph)
Mathematical Physics
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....46ee655a590ff8d66c89aa2f0ab61c8f
- Full Text :
- https://doi.org/10.48550/arxiv.2006.05739