相关论文: Universal relation for operator complexity

For statistical systems that violate one of the four Shannon-Khinchin axioms, entropy takes a more general form than the Boltzmann-Gibbs entropy. The framework of superstatistics allows one to formulate a maximum entropy principle with…

Starting from an arbitrary endomorphism $\alpha$ of a unital C*-algebra $A$ we construct a bigger C*-algebra $B$ and extend $\alpha$ onto $B$ in such a way that the extended endomorphism $\alpha$ has a unital kernel and a hereditary range,…

Stochastic entropy production, which quantifies the difference between the probabilities of trajectories of a stochastic dynamics and its time reversals, has a central role in nonequilibrium thermodynamics. In the theory of probability, the…

We investigate operator growth in a Brownian spin Sachdev--Ye--Kitaev (SYK) model with random all-to-all interactions, focusing on the full operator-size distribution. For Hamiltonians containing interactions of order two up to $L$, we…

We numerically analyze the complexity of unitary time-evolution and precursor operators in one- and two-qubit systems using the framework of Nielsen complexity geometry. We find that, as expected, the complexities of unitary time evolution…

The purpose of this paper is to present a universal approach to the study of controllability/observability problems for infinite dimensional systems governed by some stochastic/deterministic partial differential equations. The crucial…

The operator space entanglement entropy, or simply 'operator entanglement' (OE), is an indicator of the complexity of quantum operators and of their approximability by Matrix Product Operators (MPO). We study the OE of the density matrix of…

Strong subadditivity goes beyond the tensored subsystem and commuting operator models. As previously noted by Petz and later by Araki and Moriya, two subalgebras of observables satisfy a generalized SSA-like inequality if they form a…

How can we define complexity in dS space from microscopic principles? Based on recent developments pointing towards a correspondence between a pair of double-scaled Sachdev-Ye-Kitaev (DSSYK) models/ 2D Liouville-de Sitter (LdS$_2$) field…

Wave functions of bounded quantum systems with time-independent potentials, being almost periodic functions, cannot have time asymptotics as in classical chaos. However, bounded quantum systems with time-dependent interactions, as used in…

One of the fundamental manifestations of classical chaos is exponential sensitivity to initial conditions that is, two trajectories starting from nearly identical initial states diverge exponentially over time. This behavior is quantified…

In this work, we investigate the impact of conserved charges on the dynamics of spread complexity of quantum states. Building on the notion of symmetry-resolved Krylov complexity [1], we extend the framework to general quantum states and…

In this work, we explore in detail, the time evolution of Krylov complexity. We demonstrate, through analytical computations, that in finite many-body systems, while ramp and plateau are two generic features of Krylov complexity, the manner…

We discuss the universal scaling laws of order parameter fluctuations in any system in which the second-order critical behaviour can be identified. These scaling laws can be derived rigorously for equilibrium systems when combined with the…

Operator scrambling is a crucial ingredient of quantum chaos. Specifically, in the quantum chaotic system, a simple operator can become increasingly complicated under unitary time evolution. This can be diagnosed by various measures such as…

The unitary evolution can be represented by a finite product of exponential operators. It leads to a perturbative expression of the density operator of a close system. Based on the perturbative expression scheme, we present a entanglement…

A way to pose the entropic uncertainty principle for trace-preserving super-operators is presented. It is based on the notion of extremal unraveling of a super-operator. For given input state, different effects of each unraveling result in…

We study the time evolution of the excess value of capacity of entanglement between a locally excited state and ground state in free, massless fermionic theory and free Yang-Mills theory in four spacetime dimensions. Capacity has…

Operator learning is reshaping scientific computing by amortizing inference across infinite families of problems. While neural operators (NOs) are increasingly well understood for regression, far less is known for classification and its…

In this paper we study Krylov complexity in the presence of single and multiple operators in the DSSYK model, where we can use the analytical techniques coming from chord diagrammatics. One of the results we obtain is that it showcases the…