scholarly journals Optimal observables for minimum-error state discrimination in general probabilistic theories

2010 ◽  
Vol 51 (9) ◽  
pp. 093505 ◽  
Author(s):  
Koji Nuida ◽  
Gen Kimura ◽  
Takayuki Miyadera
Keyword(s):  
Minimum Error ◽  
State Discrimination ◽  
Error State ◽  
General Probabilistic Theories ◽  
Probabilistic Theories

scholarly journals Spooky action-at-a-distance in general probabilistic theories

2012 ◽  
Vol 376 (45) ◽  
pp. 2926-2930 ◽  
Author(s):  
Giacomo Mauro DʼAriano ◽  
Franco Manessi ◽  
Paolo Perinotti
Keyword(s):  
Action At A Distance ◽  
General Probabilistic Theories ◽  
Probabilistic Theories

scholarly journals Entropy, majorization and thermodynamics in general probabilistic theories

2015 ◽  
Vol 195 ◽  
pp. 43-58 ◽  
Author(s):  
Howard Barnum ◽  
Jonathan Barrett ◽  
Marius Krumm ◽  
Markus P. Müller
Keyword(s):  
General Probabilistic Theories ◽  
Probabilistic Theories

scholarly journals Simulability of observables in general probabilistic theories

2018 ◽  
Vol 97 (6) ◽  
Author(s):  
Sergey N. Filippov ◽  
Teiko Heinosaari ◽  
Leevi Leppäjärvi
Keyword(s):  
General Probabilistic Theories ◽  
Probabilistic Theories

Minimum guesswork discrimination between quantum states

2015 ◽  
Vol 15 (9&10) ◽  
pp. 737-758
Author(s):  
Weien Chen ◽  
Yongzhi Cao ◽  
Hanpin Wang ◽  
Yuan Feng
Keyword(s):  
Error Probability ◽  
Sufficient Conditions ◽  
Optimization Criterion ◽  
Quantum States ◽  
Actual State ◽  
Information Theoretic ◽  
Minimum Error ◽  
State Discrimination ◽  
Semidefinite Programming Problem ◽  
Necessary And Sufficient

Error probability is a popular and well-studied optimization criterion in discriminating non-orthogonal quantum states. It captures the threat from an adversary who can only query the actual state once. However, when the adversary is able to use a brute-force strategy to query the state, discrimination measurement with minimum error probability does not necessarily minimize the number of queries to get the actual state. In light of this, we take Massey's guesswork as the underlying optimization criterion and study the problem of minimum guesswork discrimination. We show that this problem can be reduced to a semidefinite programming problem. Necessary and sufficient conditions when a measurement achieves minimum guesswork are presented. We also reveal the relation between minimum guesswork and minimum error probability. We show that the two criteria generally disagree with each other, except for the special case with two states. Both upper and lower information-theoretic bounds on minimum guesswork are given. For geometrically uniform quantum states, we provide sufficient conditions when a measurement achieves minimum guesswork. Moreover, we give the necessary and sufficient condition under which making no measurement at all would be the optimal strategy.

Sign in / Sign up

Export Citation Format

Share Document