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arXiv:2206.04994 · Journal of Physics G Nuclear and Particle Physics

Neutrinos, mixed bosons, quantum reference frames and entanglement

Antonio Capolupo, Aniello Quaranta

Published Mar 22, 2023• 5 citations
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Abstract

Abstract We discuss the relevance of quantum reference frames in the description of mixed particle states. We show that the notion of a rest frame for mixed particles, which is classically ill-defined, can be introduced in the context of quantum frames. We discuss the possible implications, displaying a new form of frame-dependent entanglement that characterizes reactions involving mixed particles, and suggest a possible route to extract observables related to such an entanglement.

DOI
10.1088/1361-6471/acc679

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Abstract We discuss the relevance of quantum reference frames in the description of mixed particle states. We show that the notion of a rest frame for mixed particles, which is classically ill-defined, can be introduced in the context of quantum frames. We discuss the possible implications, displaying a new form of frame-dependent entanglement that characterizes reactions involving mixed particles, and suggest a possible route to extract observables related to such an entanglement.
In this paper, we discuss the concept of transformations among reference frames (classical or quantum). Usually transformations among classical reference frames have sharply defined parameters; geometrically they can be considered as pure states in the parameters’ space, and they form a group. It is however possible that the distributions in the parameters’ space are mixed states; such states form a semigroup. Similarly, transformations among quantum reference frames can be either pure or mixed. This gives rise to interesting consequences: the state of a system can be pure with respect to a reference frame and mixed with respect to another; we concretely discuss this in the framework of Galilei transformations in 1+1 dimensions. In particular, if the state of a reference frame with respect to another frame is thermal at some temperature, a quantum particle in the pure (improper) rest state with respect to the first frame will appear in a thermal state with a related nonzero temperature with respect to the other. This can also be discussed in relation to the time/energy uncertainty relation.
In physics, every observation is made with respect to a frame of reference. Although reference frames are usually not considered as degrees of freedom, in all practical situations it is a physical system which constitutes a reference frame. Can a quantum system be considered as a reference frame and, if so, which description would it give of the world? Here, we introduce a general method to quantise reference frame transformations, which generalises the usual reference frame transformation to a "superposition of coordinate transformations". We describe states, measurement, and dynamical evolution in different quantum reference frames, without appealing to an external, absolute reference frame, and find that entanglement and superposition are frame-dependent features. The transformation also leads to a generalisation of the notion of covariance of dynamical physical laws, to an extension of the weak equivalence principle, and to the possibility of defining the rest frame of a quantum system.
We find a necessary condition for subsystems to become entangled after a quantum reference frame transformation. We then distinguish between subsystems that admit separable descriptions relative to a quantum reference frame, and those that do not. On the one hand, we show that separable descriptions maximize the entanglement internal to the subsystem, and relate our results with the conservation of entanglement and coherence under quantum reference frame transformations. On the other hand, systems that do not admit a separable description relative to any subsystem display a form of entanglement that is genuine to the quantum reference frame formalism.