Many-Body Chern Number from Statistical Correlations of Randomized Measurements

Entanglement is a key feature of many-body quantum systems. Measuring the entropy of different partitions of a quantum system provides a way to probe its entanglement structure. Here, we present and experimentally demonstrate a protocol for measuring the second-order Rényi entropy based on statistical correlations between randomized measurements. Our experiments, carried out with a trapped-ion quantum simulator with partition sizes of up to 10 qubits, prove the overall coherent character of the system dynamics and reveal the growth of entanglement between its parts, in both the absence and presence of disorder. Our protocol represents a universal tool for probing and characterizing engineered quantum systems in the laboratory, which is applicable to arbitrary quantum states of up to several tens of qubits.

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Statistical correlations between locally randomized measurements: A toolbox for probing entanglement in many-body quantum states

Physical Review A ◽

10.1103/physreva.99.052323 ◽

2019 ◽

Vol 99 (5) ◽

Cited By ~ 17

Author(s):

A. Elben ◽

B. Vermersch ◽

C. F. Roos ◽

P. Zoller

Keyword(s):

Quantum States ◽

Many Body ◽

Statistical Correlations

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Static and Dynamic Statistical Correlations in Water: Comparison of Classical Ab Initio Molecular Dynamics at Elevated Temperature With Path Integral Simulations at Ambient Temperature

10.33774/chemrxiv-2021-c603x-v2 ◽

2022 ◽

Author(s):

Chenghan Li ◽

Francesco Paesani ◽

Gregory A. Voth

Keyword(s):

Molecular Dynamics ◽

Elevated Temperature ◽

Ambient Temperature ◽

Ab Initio ◽

Density Functional ◽

Ab Initio Molecular Dynamics ◽

Many Body ◽

Statistical Correlations ◽

Higher Temperature ◽

The Many

It is a common practice in ab initio molecular dynamics (AIMD) simulations of water to use an elevated temperature to overcome the over-structuring and slow diffusion predicted by most current density functional theory (DFT) models. The simulation results obtained in this distinct thermodynamic state are then compared with experimental data at ambient temperature based on the rationale that a higher temperature effectively recovers nuclear quantum effects (NQEs) that are missing in the classical AIMD simulations. In this work, we systematically examine the foundation of this assumption for several DFT models as well as for the many-body MB-pol model. We find for the cases studied that a higher temperature does not correctly mimic NQEs at room temperature, which is especially manifest in significantly different three-molecule correlations as well as hydrogen bond dynamics. In many of these cases, the effects of NQEs are the opposite of the effects of carrying out the simulations at an elevated temperature.

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Universal Relation among the Many-Body Chern Number, Rotation Symmetry, and Filling

Physical Review Letters ◽

10.1103/physrevlett.120.096601 ◽

2018 ◽

Vol 120 (9) ◽

Cited By ~ 10

Author(s):

Akishi Matsugatani ◽

Yuri Ishiguro ◽

Ken Shiozaki ◽

Haruki Watanabe

Keyword(s):

Chern Number ◽

Universal Relation ◽

Many Body ◽

Rotation Symmetry ◽

The Many

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Many-Body Chern Number without Integration

Physical Review Letters ◽

10.1103/physrevlett.122.146601 ◽

2019 ◽

Vol 122 (14) ◽

Cited By ~ 15

Author(s):

Koji Kudo ◽

Haruki Watanabe ◽

Toshikaze Kariyado ◽

Yasuhiro Hatsugai

Keyword(s):

Chern Number ◽

Many Body

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FINITE TEMPERATURE APPROACH TO QUANTUM PHASE TRANSITIONS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127410025855 ◽

2010 ◽

Vol 20 (02) ◽

pp. 397-401

Author(s):

A. PLASTINO ◽

E. M. F. CURADO

Keyword(s):

Phase Transitions ◽

Statistical Mechanics ◽

Excited States ◽

Finite Temperature ◽

Quantum Phase Transitions ◽

Quantum Phase ◽

Many Body ◽

Statistical Correlations ◽

Many Body Systems

We show how ordinary, finite-temperature tools of Statistical Mechanics can be used to detect quantum phase transitions in many-body systems. In particular, statistical correlations exhibit a quite idiosyncratic behavior at the critical interaction-strengths. Moreover, what one may call "soft quantum phase-transitions" (crossings of excited states) are characterized by the rather special way of vanishing that these correlations adopt.

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