Relativity and Quantum Entanglement

Yun Cao, Dong Wang, Xiao‐Gang Fan +3 more

Abstract Quantum entanglement is regarded as one of the core concepts, which is used to describe the non-classical correlation between subsystems, and entropic uncertainty relation plays a vital role in quantum precision measurement. It is well known that entanglement of formation can be expressed by von Neumann entropy of subsystems for arbitrary pure states. An interesting question is naturally raised: is there any intrinsic correlation between the entropic uncertainty relation and quantum entanglement? Or if the relation can be applied to estimate the entanglement. In this work, we focus on exploring the complementary relation between quantum entanglement and the entropic uncertainty relation. The results show that there exists an inequality relation between both of them for an arbitrary two-qubit system, and specifically the larger uncertainty will induce the weaker entanglement of the probed system, and vice versa. Besides, we use randomly generated states as illustrations to verify our results. Therefore, we claim that our observations might offer and support the validity of using the entropy uncertainty relation to estimate quantum entanglement.

Pasqualini, Matías Daniel

The metaphysics of quantum entanglement has been a subject of interest among philosophers of physics in recent decades. Entanglement is commonly described as a relation that does not depend on the intrinsic properties of its relata. This feature has led some authors to propose that the quantum reality is fundamentally relational and/or holistic. Moreover, it has been employed to support various influential metaphysical perspectives within the metaphysics of science, including structuralism, monism, and, recently, coherentism. This paper advocates a non-reductionist approach to internal relations, drawing on Fine’s analysis of propositions involving essential properties. Assuming the pervasiveness of quantum entanglement, it is argued that treating it as an internal relation is the most compelling option. Under this interpretation, entanglement can be accommodated within different metaphysical frameworks: (1) as a fundamental internal relation, it aligns with structuralism; (2) as a derivative internal relation, it is compatible with monism; and (3) as a relation of dependence, it supports coherentism.

James Tan

Xiao-yan Dong, H.W. Chen, Zhou, L.

This work aims to understand the monogamy of quantum entanglement from a geometrical point of view. By regarding quantum entanglement as a geometrical structure on the state space of quantum systems and attributing all entanglement related properties as emergent from this geometry of entanglement, we assume there exists a genuine general monogamous relation of quantum entanglement w.r.t. a correspondent genuine entanglement measure Q* which possesses an underlying geometrical origin. We speculate that the monogamous relations w.r.t. an entanglement measure Q can be understood by comparing the different dimension dependencies of the measure Q and Q*. We gave evidences of our conjecture by readdressing two observed properties of the monogamy relations from this geometrical standpoint. Besides the phenomenal explanation of the monogamy of entanglement, we also discussed a fibre bundle structure based candidate solution for the geometry of entanglement and explained how this idea is related to the ER=EPR conjecture and other interesting quantum information processing problems including monogamy of entanglement, entanglement distillation, bound entanglement and activation, and entanglement catalyst.