Details
| Original language | English |
|---|---|
| Article number | 180502 |
| Journal | Physical review letters |
| Volume | 126 |
| Issue number | 18 |
| Publication status | Published - 6 May 2021 |
| Externally published | Yes |
Abstract
We introduce sequential analysis in quantum information processing, by focusing on the fundamental task of quantum hypothesis testing. In particular, our goal is to discriminate between two arbitrary quantum states with a prescribed error threshold ϵ when copies of the states can be required on demand. We obtain ultimate lower bounds on the average number of copies needed to accomplish the task. We give a block-sampling strategy that allows us to achieve the lower bound for some classes of states. The bound is optimal in both the symmetric as well as the asymmetric setting in the sense that it requires the least mean number of copies out of all other procedures, including the ones that fix the number of copies ahead of time. For qubit states we derive explicit expressions for the minimum average number of copies and show that a sequential strategy based on fixed local measurements outperforms the best collective measurement on a predetermined number of copies. Whereas for general states the number of copies increases as log1/ϵ, for pure states sequential strategies require a finite average number of samples even in the case of perfect discrimination, i.e., ϵ=0.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- General Physics and Astronomy
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In: Physical review letters, Vol. 126, No. 18, 180502, 06.05.2021.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Quantum Sequential Hypothesis Testing
AU - Martínez Vargas, Esteban
AU - Hirche, Christoph
AU - Sentís, Gael
AU - Skotiniotis, Michalis
AU - Carrizo, Marta
AU - Muñoz-Tapia, Ramon
AU - Calsamiglia, John
N1 - Funding Information: We acknowledge financial support from the Spanish Agencia Estatal de Investigación, project PID2019–107609 GB-I00, from Secretaria d’Universitats i Recerca del Departament d’Empresa i Coneixement de la Generalitat de Catalunya, co-funded by the European Union Regional Development Fund within the ERDF Operational Program of Catalunya (project QuantumCat, ref. 001-P-001644), and Generalitat de Catalunya CIRIT 2017-SGR-1127. C. H. acknowledges financial support from the European Research Council (ERC Grant Agreement No. 81876), VILLUM FONDEN via the QMATH Centre of Excellence (Grant No. 10059) and the QuantERA ERA-NET Cofund in Quantum Technologies implemented within the European Union Horizon 2020 Programme (QuantAlgo project) via Innovation Fund Denmark, J. C. acknowledges from the QuantERA grant C’MON-QSENS!, via Spanish MICINN PCI2019-111869-2, EMV thanks financial support from CONACYT. J. C. also acknowledges support from ICREA Academia award.
PY - 2021/5/6
Y1 - 2021/5/6
N2 - We introduce sequential analysis in quantum information processing, by focusing on the fundamental task of quantum hypothesis testing. In particular, our goal is to discriminate between two arbitrary quantum states with a prescribed error threshold ϵ when copies of the states can be required on demand. We obtain ultimate lower bounds on the average number of copies needed to accomplish the task. We give a block-sampling strategy that allows us to achieve the lower bound for some classes of states. The bound is optimal in both the symmetric as well as the asymmetric setting in the sense that it requires the least mean number of copies out of all other procedures, including the ones that fix the number of copies ahead of time. For qubit states we derive explicit expressions for the minimum average number of copies and show that a sequential strategy based on fixed local measurements outperforms the best collective measurement on a predetermined number of copies. Whereas for general states the number of copies increases as log1/ϵ, for pure states sequential strategies require a finite average number of samples even in the case of perfect discrimination, i.e., ϵ=0.
AB - We introduce sequential analysis in quantum information processing, by focusing on the fundamental task of quantum hypothesis testing. In particular, our goal is to discriminate between two arbitrary quantum states with a prescribed error threshold ϵ when copies of the states can be required on demand. We obtain ultimate lower bounds on the average number of copies needed to accomplish the task. We give a block-sampling strategy that allows us to achieve the lower bound for some classes of states. The bound is optimal in both the symmetric as well as the asymmetric setting in the sense that it requires the least mean number of copies out of all other procedures, including the ones that fix the number of copies ahead of time. For qubit states we derive explicit expressions for the minimum average number of copies and show that a sequential strategy based on fixed local measurements outperforms the best collective measurement on a predetermined number of copies. Whereas for general states the number of copies increases as log1/ϵ, for pure states sequential strategies require a finite average number of samples even in the case of perfect discrimination, i.e., ϵ=0.
UR - http://www.scopus.com/inward/record.url?scp=85105712904&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.126.180502
DO - 10.1103/PhysRevLett.126.180502
M3 - Article
C2 - 34018787
AN - SCOPUS:85105712904
VL - 126
JO - Physical review letters
JF - Physical review letters
SN - 0031-9007
IS - 18
M1 - 180502
ER -