Information scrambling versus quantum revival through the lens of operator entanglement

Abstract

In this paper, we look for signatures of quantum revivals in two-dimensional conformal field theories (2d CFTs) on a spatially compact manifold by using operator entanglement. It is believed that thermalization does not occur on spatially compact manifolds as the quantum state returns to its initial state which is a phenomenon known as quantum revival. We find that in CFTs such as the free fermion CFT, the operator mutual information exhibits quantum revival in accordance with the relativistic propagation of quasiparticles while in holographic CFTs, the operator mutual information does not exhibit this revival and the quasiparticle picture breaks down. Furthermore, by computing the tripartite operator mutual information, we find that the information scrambling ability of holographic CFTs can be weakened by the finite size effect. We propose a modification of an effective model known as the line tension picture to explain the entanglement dynamics due to the strong scrambling effect and find a close relationship between this model and the wormhole (Einstein-Rosen Bridge) in the holographic bulk dual.

Entanglement dynamics of the non-unitary holographic channel

“…As the simplest example, we assume that the spatial direction is homogeneous and infinite, and no projective measurement is performed. These assumptions can be relaxed to allow for a compact space as well as the presence of spatial inhomogeneity [53].…”

“…We expect that the effect of the projective measurement on the unitary time evolution will depend on the degree of information scrambling generated by the dynamics. The dynamics of the unitary time evolution in the 2d free fermion can be described by relativistic propagation of quasi-particles [20,24]. It would be interesting to study how this effective picture is modified when a finite-size projective measurement is included in the quantum circuit.…”

“…In nonscrambling quantum mechanical systems such as a 2d free fermion theory, the entanglement dynamics is known to be described by the relativistic propagation of localized objects called quasiparticles [20]. In systems where strong information scrambling is present, such as holographic CFTs which are CFTs that possess a gravitational dual, it is described by the growth in time of a codimension-2 object [20][21][22][23][24]. For example, in 2d holographic CFTs, it is a one-dimensional object, and the effective model is called the line tension picture.…”

Quantum Information Scrambling in Non-Markovian Open Quantum System

“…As shown in Figure 4 a, TLN is non-negative without baths for this initial state, implying that quantum information is not scrambled. The reason quantum information is not scrambled for this initial state in the unitary case is that there is only one excitation for this initial state; thus, there are few quasi-particles [ 97 ], which confines the dynamics and hence constrains the amount of entanglement that can emerge. Accordingly, quantum information is stored mostly in bipartite partitions and cannot spread properly over many degrees of freedom.…”

Hayden-Preskill Recovery in Hamiltonian Systems

“…The unitary dynamics leading to the Hayden-Preskill recovery is referred to as information scrambling [1]. A huge number of studies aiming to characterize information scrambling were performed from different perspectives, such as entanglement generation [2,4], operator mutual information (OMI) [19,[36][37][38], and out-of-time-ordered correlators (OTOCs) [26,39,40].…”