scholarly journals Joint measurability structures realizable with qubit measurements: Incompatibility via marginal surgery

2020 ◽  
Vol 2 (4) ◽  
Author(s):  
Nikola Andrejic ◽  
Ravi Kunjwal
Keyword(s):  
Joint Measurability

scholarly journals Joint measurability and temporal steering

2015 ◽  
Vol 32 (4) ◽  
pp. A34 ◽  
Author(s):  
H. S. Karthik ◽  
J. Prabhu Tej ◽  
A. R. Usha Devi ◽  
A. K. Rajagopal
Keyword(s):  
Joint Measurability

scholarly journals Joint measurability of POVM measurement assemblages and applications

2020 ◽  
Vol 50 (7) ◽  
pp. 070001
Author(s):  
XIAO Shu ◽  
CAO HuaiXin ◽  
YU XueQing
Keyword(s):  
Joint Measurability

scholarly journals Exploring Multipartite Steering Effect Using Bell Operators

Entropy ◽  
2019 ◽  
Vol 22 (1) ◽  
pp. 19
Author(s):  
Li-Yi Hsu ◽  
Shoichi Kawamoto
Keyword(s):  
Quantum Correlation ◽  
Numerical Results ◽  
Quantum Network ◽  
Joint Measurability ◽  
Einstein Podolsky Rosen ◽  
Bell Nonlocality ◽  
The One ◽  
Necessary And Sufficient ◽  
Qubit States ◽  
Epr Steering

While Bell operators are exploited in detecting Bell nonlocality and entanglement classification, we demonstrate their usefulness in exploring Einstein–Podolsky–Rosen (EPR) steering, which represents the quantum correlation intermediate between entanglement and Bell nonlocality. We propose a task function that detects steerability of multi-qubit states in bipartite scenarios. A novel necessary and sufficient steering criterion is based on the superposition of the recursive Bell operators which are often employed for detecting Bell nonlocality. Utilizing the task function we can (i) reveal the one-to-one mapping relation between joint measurability and unsteerability, (ii) geometrically depict and compare the entanglement classification and the steering criteria and propose a geometrical measure, and (iii) compare the EPR steering with Bell nonlocality using an alternative task function. We extend the result to detect EPR steering for multi-qutrit cases and some numerical results are illustrated as examples. Finally, the steering criteria in a star-shaped quantum network is studied to see how the result is applied to a genuine multipartite steering case.

scholarly journals One-to-One Mapping between Steering and Joint Measurability Problems

2015 ◽  
Vol 115 (23) ◽  
Author(s):  
Roope Uola ◽  
Costantino Budroni ◽  
Otfried Gühne ◽  
Juha-Pekka Pellonpää
Keyword(s):  
Joint Measurability ◽  
One To One

scholarly journals Notes on Joint Measurability of Quantum Observables

2008 ◽  
Vol 38 (12) ◽  
pp. 1133-1147 ◽  
Author(s):  
Teiko Heinosaari ◽  
Daniel Reitzner ◽  
Peter Stano
Keyword(s):  
Joint Measurability ◽  
Quantum Observables

scholarly journals Quantum steerability based on joint measurability

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
Zhihua Chen ◽  
Xiangjun Ye ◽  
Shao-Ming Fei
Keyword(s):  
Joint Measurability

scholarly journals Approximate joint measurements of qubit observables

2008 ◽  
Vol 8 (8&9) ◽  
pp. 797-818
Author(s):  
P. Busch ◽  
T. Heinosaari
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Quantum Information Processing ◽  
Uncertainty Relations ◽  
Joint Measurement ◽  
Joint Measurability ◽  
Heisenberg Type

Joint measurements of qubit observables have recently been studied in conjunction with quantum information processing tasks such as cloning. Considerations of such joint measurements have until now been restricted to a certain class of observables that can be characterized by a form of covariance. Here we investigate conditions for the joint measurability of arbitrary pairs of qubit observables. For pairs of noncommuting sharp qubit observables, a notion of approximate joint measurement is introduced. Optimal approximate joint measurements are shown to lie in the class of covariant joint measurements. The marginal observables found to be optimal approximators are generally not among the coarse-grainings of the observables to be approximated. This yields scope for the improvement of existing joint measurement schemes. Both the quality of the approximations and the intrinsic unsharpness of the approximators are shown to be subject to Heisenberg-type uncertainty relations.

scholarly journals Uncertainty relations: An operational approach to the error-disturbance tradeoff

Quantum ◽  
2017 ◽  
Vol 1 ◽  
pp. 20 ◽  
Author(s):  
Joseph M. Renes ◽  
Volkher B. Scholz ◽  
Stefan Huber
Keyword(s):  
Quantum Theory ◽  
Uncertainty Relation ◽  
Uncertainty Relations ◽  
Actual Measurement ◽  
Quantum Uncertainty ◽  
Joint Measurability ◽  
Finite Dimensional ◽  
Wave Particle Duality ◽  
Heisenberg Type ◽  
Conceptual Difficulties

The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous measurements, and comparing the values of unmeasured observables is not necessarily meaningful according to quantum theory. To overcome these conceptual difficulties, we take a different approach and define error and disturbance in an operational manner. In particular, we formulate both in terms of the probability that one can successfully distinguish the actual measurement device from the relevant hypothetical ideal by any experimental test whatsoever. This definition itself does not rely on the formalism of quantum theory, avoiding many of the conceptual difficulties of usual definitions. We then derive new Heisenberg-type uncertainty relations for both joint measurability and the error-disturbance tradeoff for arbitrary observables of finite-dimensional systems, as well as for the case of position and momentum. Our relations may be directly applied in information processing settings, for example to infer that devices which can faithfully transmit information regarding one observable do not leak any information about conjugate observables to the environment. We also show that Englert's wave-particle duality relation [PRL 77, 2154 (1996)] can be viewed as an error-disturbance uncertainty relation.

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