2015/05/16 by H. S. Karthik, Karthik, H. S., A. R. Usha Devi +3
Computer Science · Mathematics · Physics and Astronomy · #Joint probability distribution #Mathematical analysis #Mathematics #Observable #Operator (biology) #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Qubit #Statistical Mechanics and Entropy #Statistical physics #Statistics #Upper and lower bounds #quant-ph
paper · pdf · doi:10.48550/arxiv.1505.04246
RevTeX, 8 pages, No figures. Based on the work presented in the "Discussion Meeting on Quantum Measurements"(DMQM2014) held at Bangalore during 22-24 October, 2014
arxiv created 2015/05/16 · openalex publication_date 2015/05/16 · arxiv updated 2015/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We give an overview of joint unsharp measurements of non-commuting observables using positive operator valued measures (POVMs). We exemplify the role played by joint measurability of POVMs in entropic uncertainty relation for Alice's pair of non-commuting observables in the presence of Bob's entangled quantum memory. We show that Bob should record the outcomes of incompatible (non-jointly measurable) POVMs in his quantum memory so as to beat the entropic uncertainty bound. In other words, in addition to the presence of entangled Alice-Bob state, implementing incompatible POVMs at Bob's end is necessary to beat the uncertainty bound and hence, predict the outcomes of non-commuting observables with improved precision. We also explore the implications of joint measurability to \em validate a moment matrix constructed from average pairwise correlations of three dichotomic non-commuting qubit observables. We prove that a classically acceptable moment matrix -- which ascertains the existence of a legitimate joint probability distribution for the outcomes of all the three dichotomic observables -- could be realized if and only if compatible POVMs are employed.