The Bell inequalities and the joint measurement of incompatible observables

1992 ◽  
Vol 5 (6) ◽  
pp. 527-534 ◽  
Author(s):  
W. M. de Muynck ◽  
W. De Baere ◽  
H. Martens
Keyword(s):  
Bell Inequalities ◽  
Joint Measurement ◽  
Incompatible Observables

Joint measurement of incompatible observables and the bell inequalities

1989 ◽  
Vol 142 (4-5) ◽  
pp. 187-190 ◽  
Author(s):  
Willem M. De Muynck ◽  
Hans Martens
Keyword(s):  
Bell Inequalities ◽  
Joint Measurement ◽  
Incompatible Observables

On the joint measurement of incompatible observables in quantum mechanics

1983 ◽  
Vol 98 (1-2) ◽  
pp. 1-4 ◽  
Author(s):  
W.M. De Muynck ◽  
J.M.V.A. Koelman
Keyword(s):  
Quantum Mechanics ◽  
Joint Measurement ◽  
Incompatible Observables

scholarly journals Bilocal Bell Inequalities Violated by the Quantum Elegant Joint Measurement

2021 ◽  
Vol 126 (22) ◽  
Author(s):  
Armin Tavakoli ◽  
Nicolas Gisin ◽  
Cyril Branciard
Keyword(s):  
Bell Inequalities ◽  
Joint Measurement

scholarly journals Experimental investigation of joint measurement uncertainty relations for three incompatible observables at a single-spin level

2020 ◽  
Vol 28 (18) ◽  
pp. 25949
Author(s):  
K. Rehan ◽  
T. P. Xiong ◽  
L.-L. Yan ◽  
F. Zhou ◽  
J. W. Zhang ◽  
...  
Keyword(s):  
Experimental Investigation ◽  
Measurement Uncertainty ◽  
Uncertainty Relations ◽  
Joint Measurement ◽  
Single Spin ◽  
Spin Level ◽  
Incompatible Observables

Neutron interferometry and the joint measurement of incompatible observables

1990 ◽  
Vol 42 (9) ◽  
pp. 5079-5085 ◽  
Author(s):  
Willem M. de Muynck ◽  
Hans Martens
Keyword(s):  
Neutron Interferometry ◽  
Joint Measurement ◽  
Incompatible Observables

scholarly journals Theory and experiment for resource-efficient joint weak-measurement

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 599
Author(s):  
Aldo C. Martinez-Becerril ◽  
Gabriel Bussières ◽  
Davor Curic ◽  
Lambert Giner ◽  
Raphael A. Abrahao ◽  
...  
Keyword(s):  
Quantum Physics ◽  
Weak Measurement ◽  
Photon Polarization ◽  
Joint Measurement ◽  
Heisenberg Uncertainty Principle ◽  
Expectation Value ◽  
Heisenberg Uncertainty ◽  
Fundamental Limitation ◽  
Measured Particle ◽  
Incompatible Observables

Incompatible observables underlie pillars of quantum physics such as contextuality and entanglement. The Heisenberg uncertainty principle is a fundamental limitation on the measurement of the product of incompatible observables, a 'joint' measurement. However, recently a method using weak measurement has experimentally demonstrated joint measurement. This method [Lundeen, J. S., and Bamber, C. Phys. Rev. Lett. 108, 070402, 2012] delivers the standard expectation value of the product of observables, even if they are incompatible. A drawback of this method is that it requires coupling each observable to a distinct degree of freedom (DOF), i.e., a disjoint Hilbert space. Typically, this 'read-out' system is an unused internal DOF of the measured particle. Unfortunately, one quickly runs out of internal DOFs, which limits the number of observables and types of measurements one can make. To address this limitation, we propose and experimentally demonstrate a technique to perform a joint weak-measurement of two incompatible observables using only one DOF as a read-out system. We apply our scheme to directly measure the density matrix of photon polarization states.

scholarly journals Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments

2021 ◽  
Vol 7 (7) ◽  
pp. eabc3847
Author(s):  
Armin Tavakoli ◽  
Máté Farkas ◽  
Denis Rosset ◽  
Jean-Daniel Bancal ◽  
Jedrzej Kaniewski
Keyword(s):  
Quantum Key Distribution ◽  
Random Number ◽  
Random Number Generation ◽  
Bell Inequalities ◽  
Extremal Point ◽  
Optimal Rate ◽  
Quantum Nonlocality ◽  
Space Structures ◽  
Mutually Unbiased Bases ◽  
Practical Relevance

Mutually unbiased bases (MUBs) and symmetric informationally complete projectors (SICs) are crucial to many conceptual and practical aspects of quantum theory. Here, we develop their role in quantum nonlocality by (i) introducing families of Bell inequalities that are maximally violated by d-dimensional MUBs and SICs, respectively, (ii) proving device-independent certification of natural operational notions of MUBs and SICs, and (iii) using MUBs and SICs to develop optimal-rate and nearly optimal-rate protocols for device-independent quantum key distribution and device-independent quantum random number generation, respectively. Moreover, we also present the first example of an extremal point of the quantum set of correlations that admits physically inequivalent quantum realizations. Our results elaborately demonstrate the foundational and practical relevance of the two most important discrete Hilbert space structures to the field of quantum nonlocality.

scholarly journals Symmetrized persistency of Bell correlations for Dicke states and GHZ-based mixtures

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Marcin Wieśniak
Keyword(s):  
Communication Complexity ◽  
Quantum Communication ◽  
Bell Inequality ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
Complexity Reduction ◽  
Main Difficulty ◽  
Quantum Communication Complexity ◽  
Number Of Particles ◽  
Dicke States

AbstractQuantum correlations, in particular those, which enable to violate a Bell inequality, open a way to advantage in certain communication tasks. However, the main difficulty in harnessing quantumness is its fragility to, e.g, noise or loss of particles. We study the persistency of Bell correlations of GHZ based mixtures and Dicke states. For the former, we consider quantum communication complexity reduction (QCCR) scheme, and propose new Bell inequalities (BIs), which can be used in that scheme for higher persistency in the limit of large number of particles N. In case of Dicke states, we show that persistency can reach 0.482N, significantly more than reported in previous studies.

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