Operator delocalization in quantum networks

Kim, Joon-Ho; Murugan, Jeff; Ollé, Jan; Rosa, Dario

doi:10.1103/physreva.105.l010201

Cited by 53 publications

(17 citation statements)

References 25 publications

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“…The main topic of this work is the study of operator growth, which has been investigated from different angles in a number of recent works [26][27][28][29][30][31][32][33][34][35][36][37][38][39]. As the name suggests, operators in quantum systems tend to "grow" in the sense that they become more complicated as the system evolves in time, even if we start with some operator that is initially simple.…”

Section: Introductionmentioning

confidence: 99%

Probing the entanglement of operator growth

Patramanis

2021

Preprint

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In this work we probe the operator growth for systems with Lie symmetry using tools from quantum information. Namely, we investigate the Krylov complexity, entanglement negativity, von Neumann entropy and capacity of entanglement for systems with SU(1,1) and SU(2) symmetry. Our main tools are two-mode coherent states, whose properties allow us to study the operator growth and its entanglement structure for any system in a discrete series representation of the groups under consideration. Our results verify that the quantities of interest exhibit certain universal features in agreement with the universal operator growth hypothesis. Moreover, we illustrate the utility of this approach relying on symmetry as it significantly facilitates the calculation of quantities probing operator growth. In particular, we argue that the use of the Lanczos algorithm, which has been the most important tool in the study of operator growth so far, can be circumvented and all the essential information can be extracted directly from symmetry arguments.

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Section: Introductionmentioning

confidence: 99%

Probing the entanglement of operator growth

Patramanis

2021

Preprint

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“…Our approach to state complexity is related to the notion of Krylov operator complexity, which has been put forward in [46], and developed in [47][48][49][50][51][52][53][54][55][56][57][58][59][60][61], based on the Lanczos approach [13] to operator dynamics in manybody systems. This approach starts with a Hamiltonian H and a time-dependent operator O(t), determined by…”

Section: Relation To Krylov Complexitymentioning

confidence: 99%

“…In fact, however, Krylov operator complexity has a further ambiguity that is not present in our approach, arising from the choice of inner product. Starting with [46], recent literature [47][48][49][50][51][52][53][54][55][56][57][58][59][60][61] has mainly focused on the Wightman inner product…”

Section: Relation To Krylov Complexitymentioning

confidence: 99%

Quantum chaos and the complexity of spread of states

Balasubramanian,

Caputa,

Magan

et al. 2022

Preprint

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We propose a measure of quantum state complexity defined by minimizing the spread of the wavefunction over all choices of basis. Our measure is controlled by the "survival amplitude" for a state to remain unchanged, and can be efficiently computed in theories with discrete spectra. For continuous Hamiltonian evolution, it generalizes Krylov operator complexity to quantum states. We apply our methods to the harmonic and inverted oscillators, particles on group manifolds, the Schwarzian theory, the SYK model, and random matrix models. For time-evolved thermofield double states in chaotic systems our measure shows four regimes: a linear ramp up to a peak that is exponential in the entropy, followed by a slope down to a plateau. These regimes arise in the same physics producing the slope-dip-ramp-plateau structure of the Spectral Form Factor. Specifically, the complexity slope arises from spectral rigidity, distinguishing different random matrix ensembles.

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“…The two notions have attracted a lot of attentions in literature [3,4,5,6,7,8,9,10,11,12]. In particular, it was established in [10] that for general irreversible process, the two quantities enjoy a universal logarithmic relation to leading order at long times:…”

Section: Introductionmentioning

confidence: 99%

The growth of operator entropy in operator growth

Fan

2022

Preprint

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We study upper bounds on the growth of operator entropy S K in operator growth. Using uncertainty relation, we first prove a dispersion bound on the growth ratewhere b 1 is the first Lanczos coefficient and ∆S K is the variance of S K . However, for irreversible process, this bound generally turns out to be too loose at long times. We further find a tighter bound in the long time limit using a universal logarithmic relation between Krylov complexity and operator entropy. The new bound describes the long time behavior of operator entropy very well for physically interesting cases, such as chaotic systems and integrable models.

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Operator delocalization in quantum networks

Cited by 53 publications

References 25 publications

Probing the entanglement of operator growth

Probing the entanglement of operator growth

Quantum chaos and the complexity of spread of states

The growth of operator entropy in operator growth

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