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arXiv:2307.07485 · Physical Review A

Generating entanglement by quantum resetting

Manas Kulkarni, Satya N. Majumdar

Published Dec 13, 2023• 21 citations
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Abstract

We consider a closed quantum system subjected to stochastic Poissonian resetting with rate $r$ to its initial state. Resetting drives the system to a nonequilibrium stationary state (NESS) with a mixed density matrix which has both classical and quantum correlations. We provide a general framework to study these NESS correlations for a closed quantum system with a general Hamiltonian $H$. We then apply this framework to a simple model of a pair of ferromagnetically coupled spins, starting from state $\ensuremath{\mid}\ensuremath{\downarrow}\ensuremath{\downarrow}\ensuremath{\rangle}$ and resetting to the same state with rate $r$. We compute exactly the NESS density matrix of the full system. This then provides access to three basic observables, namely, (i) the von Neumann entropy of a subsystem, (ii) the fidelity between the NESS and the initial density matrix, and (iii) the concurrence in the NESS (that provides a measure of the quantum entanglement in a mixed state), as a function of the two parameters: the resetting rate and the interaction strength. One of our main conclusions is that a nonzero resetting rate and a nonzero interaction strength generate quantum entanglement in the NESS (quantified by a nonzero concurrence) and moreover this concurrence can be maximized by appropriately choosing the two parameters. Our results show that quantum resetting provides a simple and effective mechanism to enhance entanglement between two parts of an interacting quantum system.

DOI
10.1103/physreva.108.062210

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We consider a closed quantum system subjected to stochastic Poissonian resetting with rate rrr to its initial state. Resetting drives the system to a nonequilibrium stationary state (NESS) with a mixed density matrix which has both classical and quantum correlations. We provide a general framework to study these NESS correlations for a closed quantum system with a general Hamiltonian HHH. We then apply this framework to a simple model of a pair of ferromagnetically coupled spins, starting from state \ensuremath∣\ensuremath↓\ensuremath↓\ensuremath⟩\ensuremath{\mid}\ensuremath{\downarrow}\ensuremath{\downarrow}\ensuremath{\rangle}\ensuremath∣\ensuremath↓\ensuremath↓\ensuremath⟩ and resetting to the same state with rate rrr. We compute exactly the NESS density matrix of the full system. This then provides access to three basic observables, namely, (i) the von Neumann entropy of a subsystem, (ii) the fidelity between the NESS and the initial density matrix, and (iii) the concurrence in the NESS (that provides a measure of the quantum entanglement in a mixed state), as a function of the two parameters: the resetting rate and the interaction strength. One of our main conclusions is that a nonzero resetting rate and a nonzero interaction strength generate quantum entanglement in the NESS (quantified by a nonzero concurrence) and moreover this concurrence can be maximized by appropriately choosing the two parameters. Our results show that quantum resetting provides a simple and effective mechanism to enhance entanglement between two parts of an interacting quantum system.
Stochastic resetting drives quantum systems into nonequilibrium stationary states unreachable under uninterrupted unitary evolution, and their entanglement depends on whether the reset history is resolved or averaged over. We study this interplay in the transverse-field Ising chain, deriving closed-form results for two qubits and evaluating chains of up to 12 qubits exactly. In the two-qubit system, these closed-form results show that phase matching between energy eigenstates produces resonances, and their visibility in the stationary state is determined by the symmetry of the reset state. Measurements on an IBM superconducting processor show the entropies evaluated before and after the reset average closely following noiseless predictions with no fitted parameter, while concurrence lies below prediction across most of the hardware measurements. The two diagnostics respond differently because they read different components of the same reconstructed state, and a depolarizing model captures the concurrence suppression with one fitted parameter. The difference between the two entropies, i. e., the Jensen gap of entanglement entropy, equals the Holevo information that a subsystem retains about the time since the last reset. With a Bell-state reset, this information grows with chain length across a half-chain cut over the sizes studied, without visible saturation at the smaller reset probabilities. Since reset times are sampled and recorded classically, the trajectory-averaged entropy, and with it the Jensen gap, is obtained without postselection, in contrast to monitored circuits, where trajectory-resolved entanglement requires sampling exponentially rare measurement records.
We study nonequilibrium dynamics of integrable and nonintegrable closed quantum systems whose unitary evolution is interrupted with stochastic resets, characterized by a reset rate rrr, that project the system to its initial state. We show that the steady-state density matrix of a nonintegrable system, averaged over the reset distribution, retains its off-diagonal elements for any finite rrr. Consequently a generic observable $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{O}$, whose expectation value receives a contribution from these off-diagonal elements, never thermalizes under such dynamics for any finite rrr. We demonstrate this phenomenon by exact numerical studies of experimentally realizable models of ultracold bosonic atoms in a tilted optical lattice. For integrable Dirac-like fermionic models driven periodically between such resets, the reset-averaged steady state is found to be described by a family of generalized Gibbs ensembles characterized by rrr. We also study the spread of particle density of a noninteracting one-dimensional fermionic chain, starting from an initial state where all fermions occupy the left half of the sample, while the right half is empty. When driven by resetting dynamics, the density profile approaches at long times to a nonequilibrium stationary profile that we compute exactly. We suggest concrete experiments that can possibly test our theory.
We investigate the dynamics of a noninteracting spin system, undergoing coherent Rabi oscillations, in the presence of stochastic resetting. We show that resetting generally induces long-range quantum and classical correlations both in the emergent dissipative dynamics and in the nonequilibrium stationary state. Moreover, for the case of conditional reset protocols---where the system is reinitialized to a state dependent on the outcome of a preceding measurement---we show that in the thermodynamic limit, the spin system can feature collective behavior which results in a phenomenology reminiscent of that occurring in nonequilibrium phase transitions. The discussed reset protocols can be implemented on quantum simulators and quantum devices that permit fast measurement and readout of macroscopic observables, such as the magnetization. Our approach does not require the control of coherent interactions and may therefore highlight a route towards a simple and robust creation of quantum correlations and collective nonequilibrium states, with potential applications in quantum enhanced metrology and sensing.
We show that quantum mechanical entanglement can prevail in noisy open quantum systems at high temperature and far from thermodynamical equilibrium, despite the deteriorating effect of decoherence. The system consists of a number NNN of interacting quantum particles, and can interact and exchange particles with some environments. The effect of decoherence is counteracted by a simple mechanism, where system particles are randomly reset to some standard initial state, e.g., by replacing them with particles from the environment. We present a master equation that describes this process, which we can solve analytically for small NNN. If we vary the interaction strength and the reset against decoherence rate, we find a threshold below which the equilibrium state is classically correlated and above which there is a parameter region with genuine entanglement.
We consider closed quantum many-body systems subject to stochastic resetting. This means that their unitary time evolution is interrupted by resets at randomly selected times. When a reset takes place, the system is reinitialized to a state chosen from a set of reset states conditionally on the outcome of a measurement taken immediately before resetting. We construct analytically the resulting nonequilibrium stationary state, thereby establishing an explicit connection between quantum quenches in closed systems and the emergent open system dynamics induced by stochastic resetting. We discuss as an application the paradigmatic transverse-field quantum Ising chain. We show that signatures of its ground-state quantum phase transition are visible in the steady state of the reset dynamics as a sharp crossover. Our findings show that a controlled stochastic resetting dynamics allows one to design nonequilibrium stationary states of quantum many-body systems, where uncontrolled dissipation and heating can be prevented. These states can thus be created on demand and exploited, e.g., as a resource for quantum enhanced sensing on quantum simulator platforms.
When a two-qubit system is initially maximally entangled, two independent decoherence channels, one per qubit, would greatly reduce the entanglement of the two-qubit system when it reaches its stationary state. We propose a method on how to minimize such a loss of entanglement in open quantum systems. We find that the quantum entanglement of general two-qubit systems with controllable parameters can be controlled by tuning both the single-qubit parameters and the two-qubit coupling strengths. Indeed, the maximum fidelity Fmax{F}_{\text{max}}Fmax​ between the stationary entangled state, ${\ensuremath{\rho}}_{\ensuremath{\infty}}$, and the maximally entangled state, ${\ensuremath{\rho}}_{m}$, can be about $2/3\ensuremath{\approx}\text{max}{\text{tr}({\ensuremath{\rho}}_{\ensuremath{\infty}}{\ensuremath{\rho}}_{m})}={F}_{\text{max}}$, corresponding to a maximum stationary concurrence, Cmax{C}_{\text{max}}Cmax​, of about $1/3\ensuremath{\approx}C({\ensuremath{\rho}}_{\ensuremath{\infty}})={C}_{\text{max}}$. This is significant because the quantum entanglement of the two-qubit system can be produced and kept, even for a long time. We apply our proposal to several types of two-qubit superconducting circuits and show how the entanglement of these two-qubit circuits can be optimized by varying experimentally controllable parameters.