Quantum Contextual Advantage Depending on Nonzero Prior Probabilities in State Discrimination of Mixed Qubit States
Recently, Schmid and Spekkens studied the quantum contextuality in terms of state discrimination. By dealing with the minimum error discrimination of two quantum states with identical prior probabilities, they reported that quantum contextual advantage exists. Meanwhile, if one notes a striking obse...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-11-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/23/12/1583 |
| _version_ | 1797504910425587712 |
|---|---|
| author | Jaehee Shin Donghoon Ha Younghun Kwon |
| author_facet | Jaehee Shin Donghoon Ha Younghun Kwon |
| author_sort | Jaehee Shin |
| collection | DOAJ |
| description | Recently, Schmid and Spekkens studied the quantum contextuality in terms of state discrimination. By dealing with the minimum error discrimination of two quantum states with identical prior probabilities, they reported that quantum contextual advantage exists. Meanwhile, if one notes a striking observation that the selection of prior probability can affect the quantum properties of the system, it is necessary to verify whether the quantum contextual advantage depends on the prior probabilities of the given states. In this paper, we consider the minimum error discrimination of two states with arbitrary prior probabilities, in which both states are pure or mixed. We show that the quantum contextual advantage in state discrimination may depend on the prior probabilities of the given states. In particular, even though the quantum contextual advantage always exists in the state discrimination of two nonorthogonal <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="italic">pure</mi></semantics></math></inline-formula> states with nonzero prior probabilities, the quantum contextual advantage depends on prior probabilities in the state discrimination of two <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="italic">mixed</mi></semantics></math></inline-formula> states. |
| first_indexed | 2024-03-10T04:11:07Z |
| format | Article |
| id | doaj.art-63dabcbeb07e4b11b05bc8d678c75a18 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T04:11:07Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-63dabcbeb07e4b11b05bc8d678c75a182023-11-23T08:10:14ZengMDPI AGEntropy1099-43002021-11-012312158310.3390/e23121583Quantum Contextual Advantage Depending on Nonzero Prior Probabilities in State Discrimination of Mixed Qubit StatesJaehee Shin0Donghoon Ha1Younghun Kwon2Department of Applied Physics, Center for Bionano Intelligence Education and Research, Hanyang University (ERICA), Ansan 15588, KoreaDepartment of Applied Mathematics and Institute of Natural Sciences, Kyung Hee University, Yongin 17104, KoreaDepartment of Applied Physics, Center for Bionano Intelligence Education and Research, Hanyang University (ERICA), Ansan 15588, KoreaRecently, Schmid and Spekkens studied the quantum contextuality in terms of state discrimination. By dealing with the minimum error discrimination of two quantum states with identical prior probabilities, they reported that quantum contextual advantage exists. Meanwhile, if one notes a striking observation that the selection of prior probability can affect the quantum properties of the system, it is necessary to verify whether the quantum contextual advantage depends on the prior probabilities of the given states. In this paper, we consider the minimum error discrimination of two states with arbitrary prior probabilities, in which both states are pure or mixed. We show that the quantum contextual advantage in state discrimination may depend on the prior probabilities of the given states. In particular, even though the quantum contextual advantage always exists in the state discrimination of two nonorthogonal <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="italic">pure</mi></semantics></math></inline-formula> states with nonzero prior probabilities, the quantum contextual advantage depends on prior probabilities in the state discrimination of two <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="italic">mixed</mi></semantics></math></inline-formula> states.https://www.mdpi.com/1099-4300/23/12/1583contextualityontological modelminimum error discrimination |
| spellingShingle | Jaehee Shin Donghoon Ha Younghun Kwon Quantum Contextual Advantage Depending on Nonzero Prior Probabilities in State Discrimination of Mixed Qubit States Entropy contextuality ontological model minimum error discrimination |
| title | Quantum Contextual Advantage Depending on Nonzero Prior Probabilities in State Discrimination of Mixed Qubit States |
| title_full | Quantum Contextual Advantage Depending on Nonzero Prior Probabilities in State Discrimination of Mixed Qubit States |
| title_fullStr | Quantum Contextual Advantage Depending on Nonzero Prior Probabilities in State Discrimination of Mixed Qubit States |
| title_full_unstemmed | Quantum Contextual Advantage Depending on Nonzero Prior Probabilities in State Discrimination of Mixed Qubit States |
| title_short | Quantum Contextual Advantage Depending on Nonzero Prior Probabilities in State Discrimination of Mixed Qubit States |
| title_sort | quantum contextual advantage depending on nonzero prior probabilities in state discrimination of mixed qubit states |
| topic | contextuality ontological model minimum error discrimination |
| url | https://www.mdpi.com/1099-4300/23/12/1583 |
| work_keys_str_mv | AT jaeheeshin quantumcontextualadvantagedependingonnonzeropriorprobabilitiesinstatediscriminationofmixedqubitstates AT donghoonha quantumcontextualadvantagedependingonnonzeropriorprobabilitiesinstatediscriminationofmixedqubitstates AT younghunkwon quantumcontextualadvantagedependingonnonzeropriorprobabilitiesinstatediscriminationofmixedqubitstates |