Some Puzzles and Unresolved Issues About Quantum Entanglement

Abstract

Schrödinger (1935) averred that entanglement is the characteristic trait of quantum mechanics. The …rst part of this paper is simultaneously an exploration of Schrödinger's claim and an investigation into the distinction between mere entanglement and genuine quantum entanglement. The typical discussion of these matters in the philosophical literature neglects the structure of the algebra of observables, implicitly assuming a tensor product structure of the simple Type I factor algebras used in ordinary QM. This limitation is overcome by adopting the algebraic approach to quantum physics, which allows a uniform treatment of ordinary QM, relativistic QFT, and quantum statistical mechanics. The algebraic apparatus helps to distinguish several di¤erent criteria of quantum entanglement and to prove results about the relation of quantum entanglement to two additional ways of characterizing the classical vs. quantum divide, viz. abelian vs. non-abelian algebras of observables, and the ability vs. inability to interrogate the system without disturbing it. Schrödinger's claim is reassessed in the light of this discussion. The second part of the paper deals with the relativity-to-ambiguity threat: the entanglement of a state on a system algebra is entanglement of the state relative to a decomposition of the system algebra into subsystem algebras; a state may be entangled with respect to one decomposition but not another; hence, unless there is some principled way to choose a decomposition, entanglement is a radically ambiguous notion. The problem is illustrated in terms a Realist vs. Pragmatist debate, the former claiming that the decomposition must correspond to real as opposed to virtual subsystems, while the latter claims that the real vs. virtual distinction is bogus and that practical considerations can steer the choice of decomposition. This debate is applied to the fraught problem of measuring entanglement for indistinguishable particles. The paper ends with some (intentionally in ‡ammatory) remarks about claims in the philosophical literature that entanglement undermines the separability or independence of subsystems while promoting holism.

Quantum Bayesianism Assessed

“…16 Two agents, Ted and Alice interact with the system, with Ted making a measurement on particle 1 and Alice making a measurement on particle 2, their respective measurements being made at relatively spacelike positions. 17 If Ted measures spin along the z-axis then according to the collapse interpretation the singlet state collapses to j " 1 i j # 2 i or to j # 1 i j " 2 i according 16 This is an example of a quantum entangled state that violate the Bell inequalities. For an overview of the meaning and implications quantum entanglement see Earman (2015).…”

A Top-down View of the Classical Limit of Quantum Mechanics

“…Therefore, the concept of quantum correlations can also be generalized is such a way that it is also relativized to the subalgebras of the algebra of observables of the closed system (Bellomo et al 2014). This top-down view dissolves the so-called "puzzles" about quantum entanglement (Earman 2014), derived from the lack of a univocal criterion to introduce a decomposition into the closed system.…”

A pragmatist view of the metaphysics of entanglement

“…3 Today physicists regard it as a resource to be exploited in technological applications of quantum information and communication. But disputes continue on how to understand quantum theory, and (to echo the title of an important recent article) there still remain some puzzles and unresolved issues about quantum entanglement itself (see Earman [12]).…”

“…Much more could be said about how to de…ne entanglement of states of two or more systems in various forms of quantum theory that use di¤erent mathematical objects to represent quantum states of di¤erent types of system (see [12]). But it is time to ask what kind of gold metaphysicians have sought to extract from the mathematical ore of quantum entanglement.…”