Scrambling of algebras in open quantum systems

Faidon, Andreadakis,; Anand, Namit; Zanardi, Paolo

doi:10.1103/physreva.107.042217

Cited by 15 publications

(3 citation statements)

References 67 publications

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“…Hilbert space delocalization is tied to non-equilibrium processes in quantum mechanics and, hence, pivotal in our understanding of quantum foundations [ 1 ], quantum technologies [ 2 , 3 ], and condensed matter theory [ 4 , 5 , 6 ]. Being intimately connected to the resource theories of quantum coherence and entanglement [ 7 , 8 ], Hilbert space delocalization provides a valuable tool for the characterization of quantum phases of matter [ 9 , 10 , 11 , 12 , 13 , 14 ], quantum chaos and thermalization [ 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ], and their violations in non-ergodic systems—including monitored systems [ 23 , 24 , 25 , 26 , 27 , 28 ] and disorder-induced localization [ 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 ].…”

Section: Introductionmentioning

confidence: 99%

Hilbert Space Delocalization under Random Unitary Circuits

Turkeshi,

Sierant

2024

Entropy

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The unitary dynamics of a quantum system initialized in a selected basis state yield, generically, a state that is a superposition of all the basis states. This process, associated with the quantum information scrambling and intimately tied to the resource theory of coherence, may be viewed as a gradual delocalization of the system’s state in the Hilbert space. This work analyzes the Hilbert space delocalization under the dynamics of random quantum circuits, which serve as a minimal model of the chaotic dynamics of quantum many-body systems. We employ analytical methods based on the replica trick and Weingarten calculus to investigate the time evolution of the participation entropies which quantify the Hilbert space delocalization. We demonstrate that the participation entropies approach, up to a fixed accuracy, their long-time saturation value in times that scale logarithmically with the system size. Exact numerical simulations and tensor network techniques corroborate our findings.

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Section: Introductionmentioning

confidence: 99%

Hilbert Space Delocalization under Random Unitary Circuits

Turkeshi,

Sierant

2024

Entropy

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“…Exploring quantum chaos and OTOC in OQSs is an ongoing area of research. Several techniques have been developed to address this issue [109][110][111][112][113][114]. To this end, we use the adjoint form of the GKSL master equation [89,90] to study the operator evolution in time, which is then used to calculate the OTOC.…”

Section: Introductionmentioning

confidence: 99%

Quantum chaos in the Dicke model and its variants

Tiwari,

Banerjee

2023

Proc. R. Soc. A.

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Recently, the out-of-time-ordered correlator (OTOC) has gained much attention as an indicator of quantum chaos. In the semi-classical limit, its exponential growth rate resembles the classical Lyapunov exponent. The quantum–classical correspondence has been supported for the one-body chaotic systems as well as realistic systems with interactions, as in the Dicke model, a model of multi-two-level atoms and cavity field interactions. To this end, we calculate the OTOC for different variations of the Dicke model in an open quantum system setting. The connection between the superradiant phase transition of the Dicke model and the OTOC is studied. Further, we establish a relation between the OTOC and the second-order coherence function. This becomes important for the experimental studies of the OTOC and quantum chaos in the models of quantum optics.

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“…Despite the significant attention that scrambling dynamics has received in the literature [16][17][18][19][20][21][22][23], curiously, little is known about the quantum-to-classical transition in the context of scrambling. Only recently have several studies begun to unravel the interplay between decoherence and scrambling [23][24][25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Pointer States and Quantum Darwinism with Two-Body Interactions

Duruisseau,

Touil,

Deffner

2023

Entropy

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Quantum Darwinism explains the emergence of classical objectivity within a quantum universe. However, to date, most research on quantum Darwinism has focused on specific models and their stationary properties. To further our understanding of the quantum-to-classical transition, it appears desirable to identify the general criteria a Hamiltonian has to fulfill to support classical reality. To this end, we categorize all N-qubit models with two-body interactions, and show that only those with separable interaction of the system and environment can support a pointer basis. We further demonstrate that “perfect” quantum Darwinism can only emerge if there are no intra-environmental interactions. Our analysis is complemented by solving the ensuing dynamics. We find that in systems exhibiting information scrambling, the dynamical emergence of classical objectivity directly competes with the non-local spread of quantum correlations. Our rigorous findings are illustrated through the numerical analysis of four representative models.

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Scrambling of algebras in open quantum systems

Cited by 15 publications

References 67 publications

Hilbert Space Delocalization under Random Unitary Circuits

Hilbert Space Delocalization under Random Unitary Circuits

Quantum chaos in the Dicke model and its variants

Pointer States and Quantum Darwinism with Two-Body Interactions

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