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arXiv:2306.06173 · Physical Review Research

Generation of scalable many-body Bell correlations in spin chains with short-range two-body interactions

Marcin Płodzień, Tomasz Wasak, Emilia Witkowska, Maciej Lewenstein, Jan Chwedeńczuk

Published Apr 15, 2024• 14 citations
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Abstract

Dynamical generation of strong and scalable quantum resources, like many-body entanglement and Bell correlations, in spin- 1/2 chains is possible with all-to-all interactions, either for constant interaction strength realizing one-axis twisting protocol or for power-law decaying potentials. We show, however, that such quantum resources can also be dynamically generated with a finite range of interactions. We identify a threshold range and indicate a threshold time when scalable quantum correlations appear. Finally, we show that the certification of generated states is accessible in modern quantum simulator platforms. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.023050

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Dynamical generation of strong and scalable quantum resources, like many-body entanglement and Bell correlations, in spin- 1/2 chains is possible with all-to-all interactions, either for constant interaction strength realizing one-axis twisting protocol or for power-law decaying potentials. We show, however, that such quantum resources can also be dynamically generated with a finite range of interactions. We identify a threshold range and indicate a threshold time when scalable quantum correlations appear. Finally, we show that the certification of generated states is accessible in modern quantum simulator platforms. Published by the American Physical Society 2024
Scalable quantum resources with short-range interacting spin-12\frac1221​ chains
The dynamical generation of quantum resources, such as many-body entanglement, Bell correlations or spin squeezing, can be achieved via one-axis twisting (OAT) dynamics, which require all-to-all couplings. However, current digital and analog quantum simulation platforms natively provide short-range or power-law couplings that decay too quickly for this purpose. We demonstrate that two spin-12\tfrac1221​ chain models -- a staggered nearest-neighbor XXX chain and a long-range XXZ chain -- develop an effective OAT nonlinearity when projected onto the symmetric sector. We show that these dynamics generate metrologically useful spin-squeezed states and Greenberger-Horne-Zeilinger coherences that ensure violation of many-body Bell inequalities. We confirm the accuracy of this mapping by comparing it to the exact dynamics and demonstrate that the generated correlations can be read out using a single probe qubit. The resulting dynamics can be simulated with analog and digital quantum simulators.
The standard way to generate many-body quantum correlations is via a dynamical protocol: an initial product state is transformed by interactions that generate nonclassical correlations at later times. Here, we show that many-body Bell correlations are inherently present in the eigenstates of a variety of spin-1/2 chains. In particular, we show that the eigenstates and thermal states of the collective Lipkin-Meshkov-Glick model possess many-body Bell correlations. We demonstrate that the Bell correlations present in the eigenstates of the Lipkin-Meshkov-Glick model can take on quantized values that change discontinuously with variations in the total magnetization. Finally, we show that these many-body Bell correlations persist even in the presence of both diagonal and off-diagonal disorder.
Long-range spin-spin interactions are known to generate nonequilibrium dynamics that can squeeze the collective spin of a quantum spin ensemble in a scalable manner, leading to states whose metrologically useful entanglement grows with system size. Here, we show theoretically that scalable squeezing can be produced in 2D U(1)-symmetric systems even by short-range interactions, i.e., interactions that at equilibrium do not lead to long-range order at finite temperatures, but rather to an extended Berezinskii-Kosterlitz-Thouless critical phase. If the initial state is a coherent spin state in the easy plane of interactions, whose energy corresponds to a thermal state in the critical Berezinskii-Kosterlitz-Thouless phase, the nonequilibrium dynamics exhibits critical slowing down, corresponding to a power-law decay of the collective magnetization in time. This slow decay protects scalable squeezing, whose scaling reveals in turn the decay exponent of the magnetization. Our results open the path to realizing massive entangled states of potential metrological interest in many relevant platforms of quantum simulation and information processing-such as Mott insulators of ultracold atoms, or superconducting circuits-characterized by short-range interactions in planar geometries.
The scalable production of multipartite entangled states in ensembles of qubits is a crucial function of quantum devices, as such states are an essential resource both for fundamental studies on entanglement, as well as for applied tasks. Here we focus on the U(1) symmetric Hamiltonians for qubits with dipolar interactions-a model realized in several state-of-the-art quantum simulation platforms for lattice spin models, including Rydberg-atom arrays with resonant interactions. Making use of exact and variational simulations, we theoretically show that the nonequilibrium dynamics generated by this Hamiltonian shares fundamental features with that of the one-axis-twisting model, namely, the simplest interacting collective-spin model with U(1) symmetry. The evolution governed by the dipolar Hamiltonian generates a cascade of multipartite entangled states-spin-squeezed states, Schrödinger's cat states, and multicomponent superpositions of coherent spin states. Investigating systems with up to N=144 qubits, we observe full scalability of the entanglement features of these states directly related to metrology, namely, scalable spin squeezing at an evolution time O(N^{1/3}) and Heisenberg scaling of sensitivity of the spin parity to global rotations for cat states reached at times O(N). Our results suggest that the native Hamiltonian dynamics of state-of-the-art quantum simulation platforms, such as Rydberg-atom arrays, can act as a robust source of multipartite entanglement.
Spin squeezing protocols successfully generate entangled many-body quantum states, the key pillars of the second quantum revolution. In our recent work [Phys. Rev. Lett. 129, 090403 (2022)] we showed that spin squeezing described by the one-axis twisting model can be generated in the Heisenberg spin-1/21/21/2 chain with periodic boundary conditions when accompanied by a position-dependent spin-flip coupling induced by a single laser field. In this work, we show analytically that the change in boundary conditions from the periodic to the open ones significantly modifies spin squeezing dynamics. A broad family of twisting models can be simulated by the system in the weak-coupling regime, including one- and two-axis twisting under specific conditions, providing the Heisenberg level of squeezing and acceleration of the dynamics. Our analytical findings are confirmed by full numerical simulations.
Bell correlations are among the most exotic of the phenomena through which quantum mechanics manifests itself. Their presence signals that the system may violate the postulates of local realism---conjectures once thought to be to be a non-negotiable property of the physical world. The importance of Bell correlations from this fundamental point of view is even further clarified by their applications, ranging from quantum cryptography to quantum metrology and quantum computing. It is therefore of growing interest to characterize the ``Bell content'' of complex, scalable many-body systems. Here, we perform a detailed analysis of the character and strength of many-body Bell correlations in interacting multiqubit systems with particle exchange symmetry. Such a configuration can be described by an effective Schr\"odinger-like equation, which allows precise analytical predictions. We show that in the vicinity of the quantum critical point, these correlations quickly become so strong that only a fraction of the qubits remain uncorrelated. We also identify the threshold temperature above which thermal fluctuations destroy Bell correlations. We hope that the approach presented here, due to its universality, will be useful for upcoming research on genuinely nonclassical Bell-correlated complex systems.