2018/01/31 by Yuan Su, John Watrous
Computer Science · Physics and Astronomy · #Class (philosophy) #Function (biology) #Property (philosophy) #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum capacity #Quantum information #Quantum operation #Quantum process #Set (abstract data type) #quant-ph
paper · pdf · doi:10.22331/q-2018-10-04-98
published as Quantum 2, 98 (2018) · 17 pages
openalex created_date 2018/02/02 · arxiv created 2018/10/01 · openalex publication_date 2018/10/04 · arxiv updated 2018/10/22 · openalex updated_date 2026/08/06
The <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mtext class="MJX-tex-mathit" mathvariant="italic">quantum strategy</mml:mtext></mml:mrow></mml:math> (or <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mtext class="MJX-tex-mathit" mathvariant="italic">quantum combs</mml:mtext></mml:mrow></mml:math>) framework is a useful tool for reasoning about interactions among entities that process and exchange quantum information over the course of multiple turns. We prove a time-reversal property for a class of linear functions, defined on quantum strategy representations within this framework, that corresponds to the set of rank-one positive semidefinite operators on a certain space. This time-reversal property states that the maximum value obtained by such a function over all valid quantum strategies is also obtained when the direction of time for the function is reversed, despite the fact that the strategies themselves are generally not time reversible. An application of this fact is an alternative proof of a known relationship between the conditional min- and max-entropy of bipartite quantum states, along with generalizations of this relationship.