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Physical Review A

Collective dynamics of N -partite quantum systems: The role of entanglement, classical correlations, and interaction

Adam S. Sajna, Paweł Kurzyński

Published Jan 10, 2022• 0 citations
Publisher

Abstract

Entanglement between two noninteracting particles can give rise to their joint motion. This suggests that entanglement may be a kind of resource to activate collective behavior in multipartite systems. However, here we argue that entanglement is neither a necessary nor a sufficient condition for a multipartite collective dynamics. We consider an $N$-partite scenario and show that a genuinely multipartite entangled noninteracting system can move collectively. Nevertheless, at the same time any $M$-partite ($1<M<N$) subsystem, which also moves collectively, is classically correlated. Moreover, since there is no interaction, such a subsystem would behave the same way if the remaining $N\ensuremath{-}M$ particles were removed. This proves that entanglement is not necessary for a collective motion. Next, we introduce external potentials and show that some collective dynamical properties cannot be observed unless an interaction between the particles is turned on.

DOI
10.1103/physreva.105.012206

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Entanglement between two noninteracting particles can give rise to their joint motion. This suggests that entanglement may be a kind of resource to activate collective behavior in multipartite systems. However, here we argue that entanglement is neither a necessary nor a sufficient condition for a multipartite collective dynamics. We consider an NNN-partite scenario and show that a genuinely multipartite entangled noninteracting system can move collectively. Nevertheless, at the same time any MMM-partite (1<M<N1<M<N1<M<N) subsystem, which also moves collectively, is classically correlated. Moreover, since there is no interaction, such a subsystem would behave the same way if the remaining N\ensuremath−MN\ensuremath{-}MN\ensuremath−M particles were removed. This proves that entanglement is not necessary for a collective motion. Next, we introduce external potentials and show that some collective dynamical properties cannot be observed unless an interaction between the particles is turned on.
We consider an evolution of two elementary quantum particles and ask the question: under what conditions does such a system behaves as a single object? It is obvious that if the attraction between the particles is stronger than any other force acting on them the whole system behaves as one. However, recent insight from the quantum information theory suggests that in bipartite systems it is not attraction per se that is responsible for the composite nature, but the entanglement between the parts. Since entanglement can be present between the subsystems that interacted in the past, but do not interact anymore, it is natural to ask when such an entangled pair behaves as a single object. We show that there are situations when entanglement is enough to observe single-particle behavior. However, due to the no-signaling condition, in general an interaction, or a post-selective measurement, is necessary for a complex collective behavior.
Nonclassical correlations between measurement results make entanglement the essence of quantum physics and the main resource for quantum information applications. Surprisingly, there are n-particle states which do not exhibit n-partite correlations at all but still are genuinely n-partite entangled. We introduce a general construction principle for such states, implement them in a multiphoton experiment and analyze their properties in detail. Remarkably, even without multipartite correlations, these states do violate Bell inequalities showing that there is no classical, i.e., local realistic model describing their properties.
Quantum entanglement manifests itself in non-local correlations between the constituents of a system. In its simplest realization, a measurement on one subsystem is affected by a prior measurement on its partner, irrespective of their separation. For multiple parties, purely collective types of entanglement exist but their detection, even theoretically, remains an outstanding open question. Here, we argue that all forms of multipartite entanglement entirely disappear during the typical evolution of a physical state as it heats up, evolves in time in a large family of dynamical protocols, or as its parts become separated. We focus on the generic case where the system interacts with an environment. These results mainly follow from the geometry of the entanglement-free continent in the space of physical states, and hold in great generality. We illustrate these phenomena with a frustrated molecular quantum magnet in and out of equilibrium, and a quantum spin chain. In contrast, if the particles are fermions, such as electrons, another notion of entanglement exists that protects bipartite quantum correlations. However, genuinely collective fermionic entanglement disappears during typical evolution, thus sharing the same fate as in bosonic systems. These findings provide fundamental knowledge about the structure of entanglement in quantum matter and architectures, paving the way for its manipulation.
We propose a measure for genuine multipartite correlations suited for the study of dynamics in open quantum systems. This measure is contextual in the sense that it depends on how information is read from the environment. It is used to study an interacting collective system of atoms undergoing phase transitions as external parameters are varied. We show that the steady state of the system can have a significant degree of genuine multipartite quantum and classical correlations and that the proposed measure can serve as a witness of critical behavior in quantum systems.
We study the dynamics of genuine multipartite entanglement for quantum systems upto four qubits interacting with general collective dephasing process. Using a computable entanglement monotone for multipartite systems, we observe the feature of freezing dynamics of genuine entanglement for three and four qubits entangled states. We compare the dynamics with that of random states and find that most states exibit this feature. We then study the effects of collective dephasing on genuine nonlocality and find out that although quantum states remain genuinely entangled yet their genuine nonlocality is lost in a finite time. We show the sensitivity of asymptotic states being genuinely entangled by mixing white noise.
This thesis contributes to the theory of entanglement dynamics, that is, the behaviour of entanglement in systems that are evolving with time. Progressively more complex multipartite systems are considered, starting with low-dimensional tripartite systems, whose entanglement dynamics can nonetheless display surprising properties, progressing through larger networks of interacting particles, and finishing with infinitely large lattice models. Firstly, what is perhaps the most basic question in entanglement dynamics is considered: what resources are necessary in order to create entanglement