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Triple measurements uncertainty and the distinguishment between the separable and entangled states

Minyi Huang, Ray‐Kuang Lee

Abstract Uncertainty and entanglement are both profound and key concepts in quantum theory. For three observables, recent works have revealed the tightest uncertainty constants for both product and summation forms. In this work, we give an alternative proof of the uncertainty relations, as well as a physical interpretation of the uncertainty constants. Our results show that such relations are intimately connected with the distinguishment between separable and entangled states. The uncertainty constant is a critical point whether such a condition of entanglement detection is valid.Abstract Uncertainty and entanglement are both profound and key concepts in quantum theory. For three observables, recent works have revealed the tightest uncertainty constants for both product and summation forms. In this work, we give an alternative proof of the uncertainty relations, as well as a physical interpretation of the uncertainty constants. Our results show that such relations are intimately connected with the distinguishment between separable and entangled states. The uncertainty constant is a critical point whether such a condition of entanglement detection is valid.

Laser PhysicsFeb 26, 20260 citations

Generalized uncertainty relations and efficient measurements in quantum systems

V. P. Belavkin

arXiv:quant-ph/0412030Theoretical and Mathematical PhysicsMar 1, 197658 citations

Uncertainty relations in the theory of open quantum systems

Аурелиан Исар

Romanian Journal of PhysicsJan 1, 20030 citations

Experimental test of the majorization uncertainty relation with mixed states

Shuang Wang, Fang-Xia Meng, Hui Wang +1 more

The uncertainty relation lies at the heart of quantum theory and behaves as a non-classical constraint on the indeterminacies of incompatible observables in a system. In the literature, many experiments have been devoted to the test of the uncertainty relations which mainly focus on the pure states. In this work we test the novel majorization uncertainty relations of three incompatible observables using a series of mixed states with adjustable mixing degrees, and compare the compactness of various entropy uncertainty relations. The experimental results confirm that for general mixed quantum system, the majorization uncertainty relation tends to be the tightest constraint on uncertainty, and indicate that the entropy uncertainty relation obtained from the majorization uncertainty relation is the optimal one. Our experimental setup provides an easy means for preparing mixed states, and based on this simple optical elements can be utilized to realize the required quantum states.The uncertainty relation lies at the heart of quantum theory and behaves as a non-classical constraint on the indeterminacies of incompatible observables in a system. In the literature, many experiments have been devoted to the test of the uncertainty relations which mainly focus on the pure states. In this work we test the novel majorization uncertainty relations of three incompatible observables using a series of mixed states with adjustable mixing degrees, and compare the compactness of various entropy uncertainty relations. The experimental results confirm that for general mixed quantum system, the majorization uncertainty relation tends to be the tightest constraint on uncertainty, and indicate that the entropy uncertainty relation obtained from the majorization uncertainty relation is the optimal one. Our experimental setup provides an easy means for preparing mixed states, and based on this simple optical elements can be utilized to realize the required quantum states.

arXiv:2104.02848Physics Letters AMar 31, 20221 citation

Triple measurements uncertainty and the distinguishment between the separable and entangled states

Minyi Huang, Ray-Kuang Lee

Uncertainty and entanglement are both profound and key concepts in quantum theory. For three observables, the tightest uncertainty constants for both product and summation forms are revealed. In this work, we give an alternative proof for three observables, also with a physical interpretation of the uncertainty constants. Our results show that such constants are intimately connected with the distinguishment between separable and entangled states.

quant-pharXiv:2512.18374Dec 23, 20250 citations

States of minimal uncertainty and maximal information for position and momentum observables in quantum theory

PEKKA J. LAHTI

Reports on Mathematical PhysicsJun 1, 19869 citations

Signifying quantum uncertainty relations by optimal observable sets and the tightest uncertainty constants

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