scholarly journals Minimum-error state discrimination constrained by the no-signaling principle

2010 ◽  
Vol 51 (2) ◽  
pp. 022202 ◽  
Author(s):  
Won-Young Hwang ◽  
Joonwoo Bae
Keyword(s):  
Minimum Error ◽  
State Discrimination ◽  
No Signaling ◽  
Error State

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.

scholarly journals Operational relevance of resource theories of quantum measurements

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 133 ◽  
Author(s):  
Michał Oszmaniec ◽  
Tanmoy Biswas
Keyword(s):  
Quantum Measurements ◽  
Relative Advantage ◽  
Minimal Amount ◽  
Geometric Quantity ◽  
Free Objects ◽  
State Discrimination ◽  
Operational Interpretation ◽  
Error State ◽  
Fixed Basis ◽  
Number Of Particles

For any resource theory it is essential to identify tasks for which resource objects offer advantage over free objects. We show that this identification can always be accomplished for resource theories of quantum measurements in which free objects form a convex subset of measurements on a given Hilbert space. To this aim we prove that every resourceful measurement offers advantage for some quantum state discrimination task. Moreover, we give an operational interpretation of robustness, which quantifies the minimal amount of noise that must be added to a measurement to make it free. Specifically, we show that this geometric quantity is related to the maximal relative advantage that a resourceful measurement offers in a class of minimal-error state discrimination (MESD) problems. Finally, we apply our results to two classes of free measurements: incoherent measurements (measurements that are diagonal in the fixed basis) and separable measurements (measurements whose effects are separable operators). For both of these scenarios we find, in the asymptotic setting in which the dimension or the number of particles increase to infinity, the maximal relative advantage that resourceful measurements offer for state discrimination tasks.

scholarly journals Almost minimum error discrimination of N-ary weak coherent states by Jaynes-Cummings Hamiltonian dynamics

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Min Namkung ◽  
Younghun Kwon
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Quantum State ◽  
Coherent States ◽  
Quantum Information Processing ◽  
Hamiltonian Dynamics ◽  
Quantum State Discrimination ◽  
Minimum Error ◽  
State Discrimination

AbstractQuantum state discrimination of coherent states has been one of important problems in quantum information processing. Recently, R. Han et al. showed that minimum error discrimination of two coherent states can be nearly done by using Jaynes-Cummings Hamiltonian. In this paper, based on the result of R. Han et al., we propose the methods where minimum error discrimination of more than two weak coherent states can be nearly performed. Specially, we construct models which can do almost minimum error discrimination of three and four coherent states. Our result can be applied to quantum information processing of various coherent states.

scholarly journals No-signaling bound on quantum state discrimination

2008 ◽  
Vol 77 (1) ◽  
Author(s):  
Sarah Croke ◽  
Erika Andersson ◽  
Stephen M. Barnett
Keyword(s):  
Quantum State ◽  
Quantum State Discrimination ◽  
State Discrimination ◽  
No Signaling
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