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arXiv:2009.12451 · Physical Review A

Emergent dynamics from entangled mixed states

Andrea Valdés-Hernández, C. G. Maglione, A. P. Majtey, Angel Ricardo Plastino

Published Nov 20, 2020• 3 citations
arXivHTMLPDF

Abstract

Entanglement is at the core of quantum physics, playing a central role in quantum phenomena involving composite systems. According to the timeless picture of quantum dynamics, entanglement may also be essential for understanding the very origins of dynamical evolution and the flow of time. Within this point of view, the Universe is regarded as a bipartite entity comprising a clock $C$ and a system $R$ (or ``rest of the Universe'') jointly described by a global stationary state, and the dynamical evolution of $R$ is construed as an emergent phenomena arising from the entanglement between $C$ and $R$. In spite of substantial recent efforts, many aspects of this approach remain unexplored, particularly those involving mixed states. In the present contribution we investigate the timeless picture of quantum dynamics for mixed states of the clock-system composite, focusing on quantitative relations linking the clock-system entanglement with the emerging dynamical evolution experienced by the system.

DOI
10.1103/physreva.102.052417

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Abstract Dynamical evolution can be reconstructed within stationary, closed quantum systems by employing the Page-Wootters “timeless approach”. When conditioning upon the state of a “clock” subsystem, the rest of the system regains its time dependence. This mechanism, involving entanglement between the above subsystems has gained much attention during the last few years. After a brief introduction to the topic we will elaborate on a few recent results: The derivation of new time-energy uncertainty relations, emergence of non-Hermitian dynamics when utilizing non-inertial quantum clocks and dynamical nonlocality in quantum time.
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We investigate the emergent time scenario in quantum cosmology based on the Page–Wotters approach. Using a quantum cosmological model with a qubit clock, it is demonstrated how the entanglement between the qubit clock and the geometry derives emergence of a time parameter, which defines evolution of the timeless quantum state of the universe. We show that the universe wave function conditioned by a qubit clock obeys the standard Schrödinger equation and the Fisher information for the clock state, which quantifies entanglement between the universe and the clock, and contributes as a negative energy density.