Detecting Bias in Randomness by PT-Symmetric Quantum State Discrimination

2021 ◽  
Author(s):  
Yaroslav Balytskyi ◽  
Manohar Raavi ◽  
Anatoliy Pinchuk ◽  
Sang-Yoon Chang
Keyword(s):  
Quantum State ◽  
Quantum State Discrimination ◽  
State Discrimination ◽  
Symmetric Quantum

scholarly journals PT -symmetric quantum state discrimination

2013 ◽  
Vol 371 (1989) ◽  
pp. 20120160 ◽  
Author(s):  
Carl M. Bender ◽  
Dorje C. Brody ◽  
João Caldeira ◽  
Uwe Günther ◽  
Bernhard K. Meister ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Quantum State ◽  
Success Probability ◽  
Inner Product ◽  
Perfect State ◽  
Quantum State Discrimination ◽  
Single Measurement ◽  
State Discrimination ◽  
Symmetric Quantum ◽  
Ordinary Quantum

The objective of this paper is to explain and elucidate the formalism of quantum mechanics by applying it to a well-known problem in conventional Hermitian quantum mechanics, namely the problem of state discrimination. Suppose that a system is known to be in one of two quantum states, | ψ 1 〉 or | ψ 2 〉. If these states are not orthogonal, then the requirement of unitarity forbids the possibility of discriminating between these two states with one measurement; that is, determining with one measurement what state the system is in. In conventional quantum mechanics, there is a strategy in which successful state discrimination can be achieved with a single measurement but only with a success probability p that is less than unity. In this paper, the state-discrimination problem is examined in the context of quantum mechanics and the approach is based on the fact that a non-Hermitian -symmetric Hamiltonian determines the inner product that is appropriate for the Hilbert space of physical states. It is shown that it is always possible to choose this inner product so that the two states | ψ 1 〉 and | ψ 2 〉 are orthogonal. Using quantum mechanics, one cannot achieve a better state discrimination than in ordinary quantum mechanics, but one can instead perform a simulated quantum state discrimination, in which with a single measurement a perfect state discrimination is realized with probability  p .

scholarly journals Finding optimal strategies for minimum-error quantum-state discrimination

2002 ◽  
Vol 65 (6) ◽  
Author(s):  
M. Ježek ◽  
J. Řeháček ◽  
J. Fiurášek
Keyword(s):  
Quantum State ◽  
Optimal Strategies ◽  
Quantum State Discrimination ◽  
Minimum Error ◽  
State Discrimination

scholarly journals Geometric coherence and quantum state discrimination

2018 ◽  
Vol 51 (41) ◽  
pp. 414005 ◽  
Author(s):  
Chunhe Xiong ◽  
Junde Wu
Keyword(s):  
Quantum State ◽  
Quantum State Discrimination ◽  
State Discrimination

Experimental Quantum State Discrimination

2006 ◽  
pp. 59-67
Author(s):  
Stephen M. Barnett ◽  
Roger B. M. Clarke ◽  
Vivien M. Kendon ◽  
Erling Riis ◽  
Anthony Chefles ◽  
...  
Keyword(s):  
Quantum State ◽  
Quantum State Discrimination ◽  
State Discrimination

scholarly journals Measurement-induced chaos and quantum state discrimination in an iterated Tavis-Cummings scheme

2017 ◽  
Vol 95 (2) ◽  
Author(s):  
Juan Mauricio Torres ◽  
József Zsolt Bernád ◽  
Gernot Alber ◽  
Orsolya Kálmán ◽  
Tamás Kiss
Keyword(s):  
Quantum State ◽  
Quantum State Discrimination ◽  
State Discrimination

scholarly journals Optimal Universal Learning Machines for Quantum State Discrimination

2019 ◽  
Vol 65 (9) ◽  
pp. 5931-5944 ◽  
Author(s):  
Marco Fanizza ◽  
Andrea Mari ◽  
Vittorio Giovannetti
Keyword(s):  
Quantum State ◽  
Quantum State Discrimination ◽  
Learning Machines ◽  
State Discrimination

scholarly journals Solutions to the mean king’s problem: Higher-dimensional quantum error-correcting codes

2016 ◽  
Vol 14 (08) ◽  
pp. 1650048
Author(s):  
Masakazu Yoshida ◽  
Toru Kuriyama ◽  
Jun Cheng
Keyword(s):  
Quantum State ◽  
Error Detection ◽  
Error Correcting Codes ◽  
Quantum State Discrimination ◽  
Delayed Information ◽  
State Discrimination ◽  
Higher Dimensional ◽  
Error Detection And Correction ◽  
The Mean ◽  
Quantum Error

Mean king’s problem is a kind of quantum state discrimination problems. In the problem, we try to discriminate eigenstates of noncommutative observables with the help of classical delayed information. The problem has been investigated from the viewpoint of error detection and correction. We construct higher-dimensional quantum error-correcting codes against error corresponding to the noncommutative observables. Any code state of the codes provides a way to discriminate the eigenstates correctly with the classical delayed information.

scholarly journals Quantum state discrimination

2009 ◽  
Vol 1 (2) ◽  
pp. 238 ◽  
Author(s):  
Stephen M. Barnett ◽  
Sarah Croke
Keyword(s):  
Quantum State ◽  
Quantum State Discrimination ◽  
State Discrimination

scholarly journals Quantum state discrimination and enhancement by noise

2014 ◽  
Vol 378 (30-31) ◽  
pp. 2128-2136 ◽  
Author(s):  
François Chapeau-Blondeau
Keyword(s):  
Quantum State ◽  
Quantum State Discrimination ◽  
State Discrimination

scholarly journals A general approach to physical realization of unambiguous quantum-state discrimination

2006 ◽  
Vol 356 (4-5) ◽  
pp. 306-311 ◽  
Author(s):  
Bing He ◽  
János A. Bergou
Keyword(s):  
Quantum State ◽  
Physical Realization ◽  
Quantum State Discrimination ◽  
State Discrimination
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