Some properties of quantum chaos

W. D. Heiss, A. A. Kotz�

Sandro Wimberger

Hiroto Kubotani, Mikito Toda, Satoshi Adachi

Dynamical formation of entanglement is studied for quantum chaotic biparticle systems. We find that statistical properties of the Schmidt eigenvalues for strong chaos are well described by the random matrix theory of the Laguerre unitary ensemble. This implies that entanglement formation for quantum chaos has universal properties, and does not depend on specific aspects of the systems.

P. Lebœuf

Yongda Li

The quantum information is a new interdisciplinary science in the 21st century, and it has become a research field which attracts strongly much attention in the world. Recently, the study of the quantum computer is in the ascendant. In the process of finding a scheme for quantum computation, quantum chaos aroused much attention. It has been shown that it is possible to induce quantum chaos when running quantum computer and consequently it may destroy the operational condition of the quantum computer. The relationship between quantum entanglement and quantum chaos has already been investigated, and the spin squeezing is regarded as another classical quantum property indeed, then is there a natural relationship between quantum chaos and spin squeezing? In this paper a very typical QKT model in the quantum chaos has been discussed,and the properties of spin squeezing in the quantum chaotic system has been studied. The relation between spin squeezing parameters and chaotic parameter in the two different definitions is worked out by numerical calculation. The stronger that the regular regions are than chaotic ones, which are chosen firstly, in the classical phase space, the stronger the spin system which the initial states locate at the centre of elliptical regions as a result. If the initial states are chosen another condition, the contrary result is obtained naturally. It indicates the spin squeezing is very sensitive to the classical chaos and the classical chaos suppresses the spin squeezing. It is interesting that the definition by Wineland is more sensitive than the one by Kitagawa and Ueda, consequently a conclusion, which the quantum chaos can be described by spin squeezing, is acquired.

Andi Gu, Yihui Quek, Susanne F. Yelin +2 more

Quantum chaos is a quantum many-body phenomenon that is associated with a number of intricate properties, such as level repulsion in energy spectra or distinct scalings of out-of-time ordered correlation functions. In this work, we introduce a novel class of "pseudochaotic" quantum Hamiltonians that fundamentally challenges the conventional understanding of quantum chaos and its relationship to computational complexity. Our ensemble is computationally indistinguishable from the Gaussian unitary ensemble (GUE) of strongly-interacting Hamiltonians, widely considered to be a quintessential model for quantum chaos. Surprisingly, despite this effective indistinguishability, our Hamiltonians lack all conventional signatures of chaos: it exhibits Poissonian level statistics, low operator complexity, and weak scrambling properties. This stark contrast between efficient computational indistinguishability and traditional chaos indicators calls into question fundamental assumptions about the nature of quantum chaos. We, furthermore, give an efficient quantum algorithm to simulate Hamiltonians from our ensemble, even though simulating Hamiltonians from the true GUE is known to require exponential time. Our work establishes fundamental limitations on Hamiltonian learning and testing protocols and derives stronger bounds on entanglement and magic state distillation. These results reveal a surprising separation between computational and information-theoretic perspectives on quantum chaos, opening new avenues for research at the intersection of quantum chaos, computational complexity, and quantum information. Above all, it challenges conventional notions of what it fundamentally means to actually observe complex quantum systems.