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arXiv:1808.06379 · Physical Review A

Dynamical stability of composite quantum particles: When entanglement is enough and when interaction is needed

Zakarya Lasmar, Adam S. Sajna, Su‐Yong Lee, Paweł Kurzyński

Published Dec 5, 2018• 3 citations
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Abstract

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.

DOI
10.1103/physreva.98.062105

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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.
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We explore in this paper ways to qualify and quantify the quantum entanglement E(M)E(M)E(M) between two macroscopic objects by way of model studies. Knowing that a macroscopic object is a composite, how does one determine E(M)E(M)E(M) in terms of the entanglements between its micro-constituents E(μ)E(μ)E(μ)? We assert that the notion of `levels of structure', the coupling strength between constituents in different levels, and the use of collective variables in each level are all pertinent factors. We consider two types of coupling, each constituent particle is coupled to only one other particle (1-to-1) versus it coupled to all particles (1-to-all). In the 1-1 case with pairwise interactions of equal strength, the entanglement is independent of the number of constituent particles NNN in the macroscopic object. In the 1-to-all case the relative coordinates are decoupled and the center of mass (CoM) coupling scales with NNN. We provide a proof of the conditions whereby the CoM variable decouples, a cause for the special role the CoM variable plays in the entanglement between the two such macroscopic objects. This qualitative behavior is largely not affected by fluctuations in the interaction strength. We also analyzed the entanglement pattern of 4 coupled oscillators in two pairs, representing the two objects A and B (or two adjacent levels of structure), each with two constituents. By assigning different coupling strengths we can investigate the interplay of inter-level entanglement with intra- level interactions. From the entanglement dynamics of the 4-oscillator system with varying coupling strength we see the entanglement between constituents meeting sudden death while the CoM variables may sustain over longer times. This offers another way to determine under what conditions quantum entanglement between macroscopic objects can persist.
Since quantum feedback is based on classically accessible measurement results, it can provide fundamental insights into the dynamics of quantum systems by making available classical information on the evolution of system properties and on the conditional forces acting on the system. In this paper, the feedback-induced interaction dynamics between a pair of quantum systems is analyzed. It is pointed out that any interaction Hamiltonian can be simulated by local feedback if the levels of decoherence are sufficiently high. The boundary between genuine entanglement generating quantum interactions and non-entangling classical interactions is identified and the nature of the information exchange between two quantum systems during an interaction is discussed.
Figuring out the physical rationale behind natural selection of quantum theory is one of the most acclaimed quests in quantum foundational research. This pursuit has inspired several axiomatic initiatives to derive a mathematical formulation of the theory by identifying the general structure of state and effect space of individual systems as well as specifying their composition rules. This generic framework can allow several consistent composition rules for a multipartite system even when state and effect cones of individual subsystems are assumed to be quantum. Nevertheless, for any bipartite system, none of these compositions allows beyond quantum spacelike correlations. In this Letter, we show that such bipartite compositions can admit stronger-than-quantum correlations in the timelike domain and, hence, indicates pragmatically distinct roles carried out by state and effect cones. We discuss consequences of such correlations in a communication task, which accordingly opens up a possibility of testing the actual composition between elementary quanta.