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arXiv:1902.08574 · Physical Review A

Spin-entanglement wave in a coarse-grained optical lattice

Pedro Silva Correia, Fernando de Melo

Published Aug 26, 2019• 11 citations

Abstract

In the present article, we explore a suitable coarse-graining channel as a tool to describe effective entanglement spreading in a coarse-grained spin chain with different degrees of resolution. Comparing it with the experimental realizations performed with ultracold atoms, our results suggest that even if we are not able to fully resolve the system, entanglement can still be detected for some coarse-graining levels. Furthermore, we show that it is possible to have some information about the ``microscopic'' entanglement, even if we only have access to the system's coarse-grained description. We show that the amount of entanglement decays exponentially with the lack of system resolution. The lack of experimental resolution might thus lead to an effective classical description.

DOI: 10.1103/physreva.100.022334

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In the present article, we explore a suitable coarse-graining channel as a tool to describe effective entanglement spreading in a coarse-grained spin chain with different degrees of resolution. Comparing it with the experimental realizations performed with ultracold atoms, our results suggest that even if we are not able to fully resolve the system, entanglement can still be detected for some coarse-graining levels. Furthermore, we show that it is possible to have some information about the ``microscopic'' entanglement, even if we only have access to the system's coarse-grained description. We show that the amount of entanglement decays exponentially with the lack of system resolution. The lack of experimental resolution might thus lead to an effective classical description.

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1/2 \mathit{XX}

chain, obtaining a blurred picture of the entanglement generation and propagation in the system. By construction, both maps are simply related via a partial trace, which allows us to concentrate on the properties of the former. We fully characterize the fuzzy map, identifying its symmetries and invariant spaces. We show that the volume of the tomographically accessible states decreases at a double-exponential rate in the number of particles, imposing severe bounds on the ability to read and use information of a many-body quantum system.

We derive experimentally measurable lower bounds for the two-site entanglement of the spin-degrees of freedom of many-body systems with local particle-number fluctuations. Our method aims at enabling the spatially resolved detection of spin-entanglement in Hubbard systems using high-resolution imaging in optical lattices. A possible application is the observation of entanglement generation and spreading during spin impurity dynamics, for which we provide numerical simulations. More generally, the scheme can simplify the entanglement detection in ion chains, Rydberg atoms, or similar atomic systems.

A model of a quantum measurement process is presented: a system consisting of a qubit in a superposition interacts with a measuring apparatus consisting of a

N

qubit state. Looking at the emerging, effective description of the apparatus given by the action of a coarse-graining channel, we have been able to recover information about the superposition coefficients of the system. We have also been able to visualize the death of quantum correlations between system and apparatus and the death of quantum coherences in the apparatus' effective state, in the limit of a strong coarse-graining action---a situation akin to decoherence, although it is not necessary to evoke any interaction with the surrounding environment.

Abstract Shedding a new light in the coarse-graining scenario, in this contribution we came up with different necessary and sufficient conditions for the existence of a well-defined coarse-grained state. For doing so, we had to break apart with the usual quantum channels perspective and assume a more decision-theoretical posture. Broadly speaking, we reinterpret the coarse-graining problem in the language of quantum state pooling, and by making an extensive use of the conditional quantum states toolkit, we have been able to derive more tangible conditions for the emergence of a compatible effective coarse-grained state.