Abstract Observable scattering processes entail emission-absorption of soft photons. As these degrees of freedom go undetected, some information is lost. Whether some of this information can be recovered in the observation of the hard particles, depends of the actual pattern of the scrambling of information. We compute the information scrambling of electron and soft photon scattering by the tripartite mutual information in terms of the 2-Renyi entropy, and find a finite amount of scrambling is present. We show that scrambling is a byproduct of decoherence achieved by the scattering system in its interaction with the environment, due to the emission-absorption of soft photons in fully unitary processes.
Abstract Observable scattering processes entail emission-absorption of soft photons. As these degrees of freedom go undetected, some information is lost. Whether some of this information can be recovered in the observation of the hard particles, depends of the actual pattern of the scrambling of information. We compute the information scrambling of electron and soft photon scattering by the tripartite mutual information in terms of the 2-Renyi entropy, and find a finite amount of scrambling is present. We show that scrambling is a byproduct of decoherence achieved by the scattering system in its interaction with the environment, due to the emission-absorption of soft photons in fully unitary processes.
Abstract Quantum information scrambling (QIS), from the perspective of quantum information theory, is generally understood as local non-retrievability of information evolved through some dynamical process, and is often quantified via entropic quantities such as the tripartite information. We argue that this approach comes with a number of issues, in large part due to its reliance on quantum mutual informations, which do not faithfully quantify correlations directly retrievable via measurements, and in part due to the specific methodology used to compute tripartite informations of the studied dynamics. We show that these issues can be overcome by using accessible mutual informations, defining corresponding ‘accessible tripartite informations’, and provide explicit examples of dynamics whose scrambling properties are not properly quantified by the standard tripartite information. Our results lay the groundwork for a more profound understanding of what QIS represents, and reveal a number of promising, as of yet unexplored, venues for further research.
How quantum information is scrambled in the global degrees of freedom of nonequilibrium many-body systems is a key question to understand local thermalization. A consequence of scrambling is that in the scaling limit the mutual information between two intervals vanishes at all times, i.e., it does not exhibit a peak at intermediate times. Here we investigate the mutual information scrambling after a quantum quench in both integrable and nonintegrable one-dimensional systems. We study the mutual information between two intervals of finite length as a function of their distance. In integrable systems, the mutual information exhibits an algebraic decay with the distance between the intervals, signaling weak scrambling. This behavior may be qualitatively understood within the quasiparticle picture for the entanglement spreading. In the scaling limit of large intervals, times, and distances between the intervals, with their ratios fixed, this predicts a decay exponent equal to 1/2. Away from the scaling limit, the power-law behavior persists, but with a larger (and model-dependent) exponent. For nonintegrable models, a much faster decay is observed, which can be attributed to the finite lifetime of the quasiparticles: unsurprisingly, nonintegrable models are better scramblers.
In this paper, we investigate the dynamics of a spin chain whose two end spins interact with two independent non-Markovian baths by using the non-Markovian quantum state diffusion (QSD) equation approach. Specifically, two issues about information scrambling in an open quantum system are addressed. The first issue is that tripartite mutual information (TMI) can quantify information scrambling properly via its negative value in a closed system, whether it is still suitable to indicate information scrambling in an open quantum system. We find that negative TMI is not a suitable quantifier of information scrambling in an open quantum system in some cases, while negative tripartite logarithmic negativity (TLN) is an appropriate one. The second one is that up to now almost all information scrambling in open quantum systems reported were focus on a Markovian environment, while the effect of a non-Markovian environment on information scrambling is still elusive. Our results show that the memory effect of an environment will be beneficial to information scrambling. Moreover, it is found that the environment is generally detrimental for information scrambling in the long-term, while in some cases it will be helpful for information scrambling in the short-term.
Abstract Scrambling is a process by which the state of a quantum system is effectively randomized due to the global entanglement that “hides” initially localized quantum information. Closely related notions include quantum chaos and thermalization. Such phenomena play key roles in the study of quantum gravity, many-body physics, quantum statistical mechanics, quantum information etc. Scrambling can exhibit different complexities depending on the degree of randomness it produces. For example, notice that the complete randomization implies scrambling, but the converse does not hold; in fact, there is a significant complexity gap between them. In this work, we lay the mathematical foundations of studying randomness complexities beyond scrambling by entanglement properties. We do so by analyzing the generalized (in particular Rényi) entanglement entropies of designs, i.e. ensembles of unitary channels or pure states that mimic the uniformly random distribution (given by the Haar measure) up to certain moments. A main collective conclusion is that the Rényi entanglement entropies averaged over designs of the same order are almost maximal. This links the orders of entropy and design, and therefore suggests Rényi entanglement entropies as diagnostics of the randomness complexity of corresponding designs. Such complexities form a hierarchy between information scrambling and Haar randomness. As a strong separation result, we prove the existence of (state) 2-designs such that the Rényi entanglement entropies of higher orders can be bounded away from the maximum. However, we also show that the min entanglement entropy is maximized by designs of order only logarithmic in the dimension of the system. In other words, logarithmic-designs already achieve the complexity of Haar in terms of entanglement, which we also call max-scrambling. This result leads to a generalization of the fast scrambling conjecture, that max-scrambling can be achieved by physical dynamics in time roughly linear in the number of degrees of freedom. This paper is an extended version of Phys. Rev. Lett. 120 (2018) 130502 [1].
Abstract Quantum information scrambling refers to the loss of local recoverability of quantum information, which has found widespread attention from high energy physics to quantum computing. In the present analysis we propose a possible starting point for the development of a comprehensive framework for the thermodynamics of scrambling. To this end, we prove that the growth of entanglement as quantified by the mutual information is lower bounded by the time-dependent change of out-of-time-ordered correlator. We further show that the rate of increase of the mutual information can be upper bounded by the sum of local entropy productions, and the exchange entropy arising from the flow of information between separate partitions of a quantum system. Our results are illustrated for the ion trap system, that was recently used to verify information scrambling in an experiment, and for the Sachdev–Ye–Kitaev model.
A bstract In closed quantum many-body systems, initially localized information spreads throughout the system and becomes highly complex. This phenomenon, known as information scrambling, is closely related to entropy growth and quantum thermalization. Recent studies have shown that dissipation in open systems can hinder information scrambling, driving the system into a dissipative phase when the system-bath coupling is strong. However, the signature of this scrambling transition in entropy dynamics remains unexplored. In this work, we unveil a novel phenomenon in open quantum systems, termed entropy accumulation, which occurs exclusively within the scrambling phase. By generalizing the study of perturbative Page curve in closed systems, we consider a setup in which a probe is weakly coupled to a system that is already interacting with a bath. We calculate the increase in the second Rényi entropy induced by an external impulse on the system, after tracing out the probe. Despite the system-probe coupling being weak, the entropy continues to increase and eventually saturates at a finite value due to operator growth. In contrast, the entropy increase is limited by the coupling strength in the dissipative phase. The theoretical prediction is derived from both general arguments and explicit examples using generalized Boltzmann equations or SYK solvable models. Our results offer new insights into the intriguing relationship between entropy dynamics and information scrambling in open quantum systems.