Complexity from the reduced density matrix: a new diagnostic for chaos

Bhattacharyya, Arpan; Haque, S. Shajidul; Kim, Eugene H.

doi:10.1007/jhep10(2021)028

Cited by 36 publications

(24 citation statements)

References 70 publications

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“…• Recently in [123][124][125] Circuit Complexity has been explored in continuous variable system and open quantum systems, similarly techniques and analysis can be done with study of Circuit Complexity in context of cosmological perturbations.…”

Section: Future Prospectsmentioning

confidence: 99%

Causality Constraint on Circuit Complexity from $COSMOEFT$

Choudhury¹,

Mukherjee²,

Pandey³

et al. 2021

Preprint

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In this article, we investigate the physical implications of the causality constraint via effective sound speed cs(≤ 1) on Quantum Circuit Complexity(QCC) in the framework of Cosmological Effective Field Theory (COSMOEFT) using the two-mode squeezed quantum states. This COS-MOEFT setup is constructed using the Stückelberg trick with the help of the lowest dimensional operators, which are broken under time diffeomorphism. In this setup, we consider only the contribution from two derivative terms in the background quasi de Sitter metric. Next, we compute the relevant measures of circuit complexity and their cosmological evolution for different cs by following two different approaches, Nielsen's and Covariance matrix method. Using this setup, we also compute the Von-Neumann and Rényi entropy, which finally establishes an underlying connecting relationship between the entanglement entropy and circuit complexity. Essentially, we study the behaviour of the circuit complexity measures and entanglement entropy with respect to the scale factor and cs and find various interesting unexplored features within the window, 0.024 ≤ cs ≤ 1, which is supported by both causality and cosmological observation. Finally, we also comment on the connection between the circuit complexity, entanglement entropy and equilibrium temperature for different cs lying within the mentioned window.

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Section: Future Prospectsmentioning

confidence: 99%

Causality Constraint on Circuit Complexity from $COSMOEFT$

Choudhury¹,

Mukherjee²,

Pandey³

et al. 2021

Preprint

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“…Once again we have denoted the extra copy of H as H anc to distinguish it from the original. In that sense, this process of operator-state mapping is a special case of the purification discussed above [49]. The most important difference is that the state |O in (2) associated to the operator Ô is unique, there are no free parameters introduced in the mapping.…”

Section: Complexity For a Density Matrixmentioning

confidence: 99%

“…In this section, we will investigate the circuit complexity for our open quantum system by applying operator-state mapping [49]. Considering explicitly the system's density matrix (Eq.…”

Section: Complexity By Operator-state Mappingmentioning

confidence: 99%

Complexity for Open Quantum System

Bhattacharyya,

Hanif,

Haque

et al. 2021

Preprint

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We study the complexity for an open quantum system. Our system is a harmonic oscillator coupled to a one-dimensional massless scalar field, which acts as the bath. Specifically, we consider the reduced density matrix by tracing out the bath degrees of freedom for both regular and inverted oscillator and computed the complexity of purification (COP) and complexity by using the operator-state mapping. We found that when the oscillator is regular the COP saturates quickly for both underdamped and overdamped oscillators.Interestingly, when the oscillator is underdamped, we discover a kink like behaviour for the saturation value of COP with varying damping coefficient. For the inverted oscillator, we found a linear growth of COP with time for all values of bath-system interaction. However, when the interaction is increased the slope of the linear growth decreases, implying that the unstable nature of the system can be regulated by the bath.

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“…One of the most striking questions is whether it is possible to use quantum information tools to describe quantum chaos [12][13][14][15][16][17][18], such as circuit complexity [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. Recent works have shown that circuit complexity can indeed detect quantum chaos [35][36][37]. In particular, it was found that chaotic behavior can be characterized by the complexity of bidirectional evolution.…”

Section: Introductionmentioning

confidence: 99%

“…Note that the complexity here increases linearly with time and hence has no upper bound. However, the complexity calculated by different methods in Ref [37]. has an upper bound.…”

mentioning

confidence: 99%

Chaos and Complexity for Inverted Harmonic Oscillators

Qu,

Chen,

Liu

2021

Preprint

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We investigate the circuit complexity and Loschmidt echo for the (inverted) harmonic oscillators. Focusing on the chaotic behaviors under the perturbation, we analytically derive the Lyapunov exponent and scrambling time of the inverted harmonic oscillators. We show that the circuit complexity and Loschmidt echo exhibit qualitatively similar behaviors, particularly the consistent Lyapunov exponent.

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Complexity from the reduced density matrix: a new diagnostic for chaos

Cited by 36 publications

References 70 publications

Causality Constraint on Circuit Complexity from $COSMOEFT$

Causality Constraint on Circuit Complexity from $COSMOEFT$

Complexity for Open Quantum System

Chaos and Complexity for Inverted Harmonic Oscillators

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