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The Uncertainty Principle in the Presence of Quantum Memory

Joseph M. Renes, Mario Berta, Matthias Christandl +2 more

Bulletin of the American Physical SocietyMar 19, 20100 citations

Experimental investigation of the uncertainty principle in the presence of quantum memory and its application to witnessing entanglement

Robert Prevedel, Deny R. Hamel, Roger Colbeck +2 more

arXiv:1012.0332Nature PhysicsJul 24, 2011274 citations

Entropic Uncertainty Principle and Information Exclusion Principle for multiple measurements in the presence of quantum memory

Jun Zhang, Yang Zhang, Chang‐shui Yu

The Heisenberg uncertainty principle shows that no one can specify the values of the non-commuting canonically conjugated variables simultaneously. However, the uncertainty relation is usually applied to two incompatible measurements. We present tighter bounds on both entropic uncertainty relation and information exclusion principle for multiple measurements in the presence of quantum memory. As applications, three incompatible measurements on Werner state and Horodecki's bound entangled state are investigated in details.The Heisenberg uncertainty principle shows that no one can specify the values of the non-commuting canonically conjugated variables simultaneously. However, the uncertainty relation is usually applied to two incompatible measurements. We present tighter bounds on both entropic uncertainty relation and information exclusion principle for multiple measurements in the presence of quantum memory. As applications, three incompatible measurements on Werner state and Horodecki's bound entangled state are investigated in details.

arXiv:1509.05973Sep 20, 20150 citations

Improved uncertainty relation in the presence of quantum memory

Yunlong Xiao, Naihuan Jing, Shao-Ming Fei +1 more

Abstract Berta et al ’s uncertainty principle in the presence of quantum memory (Berta et al 2010 Nat. Phys . 6 659 ) reveals uncertainties with quantum side information between the observables. In the recent important work of Coles and Piani (2014 Phys. Rev . A 89 022112 ), the entropic sum is controlled by the first and second maximum overlaps between the two projective measurements. We generalize the entropic uncertainty relation in the presence of quantum memory and find the exact dependence on all d largest overlaps between two measurements on any d -dimensional Hilbert space. Our bound is rigorously shown to be strictly tighter than previous entropic bounds in the presence of quantum memory, which have potential applications to quantum cryptography with entanglement witnesses and quantum key distributions.Abstract Berta et al ’s uncertainty principle in the presence of quantum memory (Berta et al 2010 Nat. Phys . 6 659 ) reveals uncertainties with quantum side information between the observables. In the recent important work of Coles and Piani (2014 Phys. Rev . A 89 022112 ), the entropic sum is controlled by the first and second maximum overlaps between the two projective measurements. We generalize the entropic uncertainty relation in the presence of quantum memory and find the exact dependence on all d largest overlaps between two measurements on any d -dimensional Hilbert space. Our bound is rigorously shown to be strictly tighter than previous entropic bounds in the presence of quantum memory, which have potential applications to quantum cryptography with entanglement witnesses and quantum key distributions.

arXiv:1604.04944Journal of Physics A Mathematical and TheoreticalNov 16, 201628 citations

Uncertainty under quantum measures and quantum memory

Yunlong Xiao, Naihuan Jing, Xianqing Li‐Jost

arXiv:1702.04497Quantum Information ProcessingMar 7, 201715 citations

Uncertainty Principle in the Light of Quantum Information Science

Saptarshi Sahoo, Amit Kumar Mandal, Nirmalya Misra +1 more

Algorithms for intelligent systemsJan 1, 20220 citations

The uncertainty principle in the presence of quantum memory

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