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Simulating positive-operator-valued measures with projective measurements
- Publication Year :
- 2016
-
Abstract
- Standard projective measurements represent a subset of all possible measurements in quantum physics, defined by positive-operator-valued measures. We study what quantum measurements are projective simulable, that is, can be simulated by using projective measurements and classical randomness. We first prove that every measurement on a given quantum system can be realised by classical processing of projective measurements on the system plus an ancilla of the same dimension. Then, given a general measurement in dimension two or three, we show that deciding whether it is projective-simulable can be solved by means of semi-definite programming. We also establish conditions for the simulation of measurements using projective ones valid for any dimension. As an application of our formalism, we improve the range of visibilities for which two-qubit Werner states do not violate any Bell inequality for all measurements. From an implementation point of view, our work provides bounds on the amount of noise a measurement tolerates before losing any advantage over projective ones.<br />v2: 4 pages + 12.5 pages of appendices, 2 figures, updated references and narrative, computational appendix is available at https://github.com/peterwittek/ipython-notebooks/blob/master/Simulating_POVMs.ipynb, comments and suggestions are welcome
- Subjects :
- Semidefinite programming
Pure mathematics
Quantum Physics
General Physics and Astronomy
FOS: Physical sciences
White noise
Mathematical Physics (math-ph)
01 natural sciences
010305 fluids & plasmas
Subatomär fysik
Real projective line
Blocking set
Bell's theorem
Quantum mechanics
Subatomic Physics
0103 physical sciences
Quantum system
Projective test
010306 general physics
Quantum Physics (quant-ph)
Randomness
Mathematical Physics
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....6293e22a47d63121fc963422705a8bb9