Some Puzzles and Unresolved Issues About Quantum Entanglement
- 356 Downloads
Schrödinger (Proc Camb Philos Soc 31:555–563, 1935) averred that entanglement is the characteristic trait of quantum mechanics. The first 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 Quantum Mechanics (QM). This limitation is overcome by adopting the algebraic approach to quantum physics, which allows a uniform treatment of ordinary QM, relativistic quantum field theory, and quantum statistical mechanics. The algebraic apparatus helps to distinguish several different criteria of quantum entanglement and to prove results about the relation of quantum entanglement to two additional ways of characterizing the classical versus quantum divide, viz. abelian versus non-abelian algebras of observables, and the ability versus 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 versus Pragmatist debate, the former claiming that the decomposition must correspond to real as opposed to virtual subsystems, while the latter claims that the real versus 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 inflammatory) remarks about claims in the philosophical literature that entanglement undermines the separability or independence of subsystems while promoting holism.
I am grateful to an anonymous referee for suggestions that led to improvements of a earlier version of this article.
- d’Espagnat, B. (1971). Conceptual foundations of quantum mechanics. Menlo Park, CA: W. A. Benjamin.Google Scholar
- Giddings, J. R., & Fisher, A. J. (2002). Describing mixed spin-space entanglement of pure states of indistinguishable particles using occupation-number basis. Physical Review A, 66, 032305-1–11.Google Scholar
- Healey, R. (2008). Holism and nonseparability in physics. In Stanford encyclopedia of philosophy. URL: http://plato.stanford.edu/entries/physics-holism/.
- Horuzhy, S. S. (1990). Introduction to algebraic quantum field theory. Dordrecht: Kluwer Academic.Google Scholar
- Howard, D. (1989). Holism, separability, and the metaphysical implications of the Bell Experiments. In J. Cushing & E. McMullin (Eds.), Philosophical consequences of quantum theory: Reflections on Bell’s theorem (pp. 224–253). Notre Dame, IN: University of Nature Dame Press.Google Scholar
- Li, N., & Luo, S. (2008). Classical states versus separable states. Physical Review A, 78, 024303-1–4.Google Scholar
- Li, Y. S., Zeng, B., Liu, X. S., & Long, G. L. (2001). Entanglement in a two-identical-particle system. Physical Review A, 64, 054302-1–4.Google Scholar
- Luo, S. (2008). Using measurement-induced disturbance to characterize correlations as classical or quantum. Physical Review A, 77, 022301-1–5.Google Scholar
- Ollivier, H., & Zurek, H. (2002). Quantum discord: A measure of quantumness of correlations. Physical Review Letters, 88, 017901-1–4.Google Scholar
- Paškauskas, R., & You, L. (2001). Quantum correlation in two-boson wave functions. Physical Review A, 64, 042310-1–4.Google Scholar
- Plastino, A. R., Manzano, D., & Dehesa, J. S. (2005). Separability criteria and entanglement measures for pure states of N identical particles. European, Physics Letters, 86, 2005-p1–2005-p5.Google Scholar
- Schlosshauer, M. (2007). Decoherence and the quantum-to-classical transition. Berlin: Springer.Google Scholar
- Schrödinger, E. (1935). Discussion of probability relations between separated systems. Proceedings of the Cambridge Philosophical Society, 31, 555–563; 32 (1936), 446–451.Google Scholar
- Sunder, V. (1986). An invitation to von Neumann algebras. Berlin: Springer.Google Scholar
- Valente, G. (2013). Local disentanglement in relativistic quantum field theory. Pre-print.Google Scholar
- Winsberg, E., & Fine, A. (2003). Quantum life: Interaction, entanglement, and separation. Journal of Philosophy, C, 80–97.Google Scholar