The study of state revivals has long advanced our understanding of dynamical systems. We introduce a resource theory framework to study the use of state revivals in quantum information. In this theory, a state is said to contain no amount of resource if it experiences perfect revivals under some unitary evolution. All other states are said to be resourceful. The resource, which we dub ``nonrevivals,'' quantifies a state's inability to experience revivals. We use our framework to understand revivals in quantum many-body scarred systems and their applications. In particular, we show that quantum many-body scarred dynamics can produce revivals in the Hayden-Preskill decoding protocol and can also be used to recover damaged quantum information. We also use our resource theory to bound information scrambling. Our theory establishes a framework to study information retrieval and its applications in quantum many-body physics.
The study of state revivals has long advanced our understanding of dynamical systems. We introduce a resource theory framework to study the use of state revivals in quantum information. In this theory, a state is said to contain no amount of resource if it experiences perfect revivals under some unitary evolution. All other states are said to be resourceful. The resource, which we dub ``nonrevivals,'' quantifies a state's inability to experience revivals. We use our framework to understand revivals in quantum many-body scarred systems and their applications. In particular, we show that quantum many-body scarred dynamics can produce revivals in the Hayden-Preskill decoding protocol and can also be used to recover damaged quantum information. We also use our resource theory to bound information scrambling. Our theory establishes a framework to study information retrieval and its applications in quantum many-body physics.
Quantum many-body scarring is a recently discovered weak ergodicity-breaking phenomenon in quantum many-body systems. It was first seen in experiments with Rydberg atom array simulators, and characterized by nonthermalizing periodic revivals of certain initial-state configurations. Here, the authors extend our understanding of the physical origins of this phenomenon by showing through an explicit construction that scars can arise through the presence of entangled virtual degrees of freedom undergoing periodic dynamics. This demonstrates a novel analytic scenario, whereby intrinsically entangled states can exhibit periodic revivals in an otherwise chaotic many-body system, enriching the phenomenology of quantum many-body scarring.
We derive general rigorous results relating revivals in the dynamics of quantum many-body systems to the entanglement properties of energy eigenstates. For a D-dimensional lattice system of N sites initialized in a low-entangled and short-range correlated state, our results show that a perfect revival of the state after a time of at most O(poly(N)) implies the existence of at least O(N/log2D(N)) ``quantum many-body scars'': energy eigenstates with energies placed in an equally spaced ladder and with R\'enyi entanglement entropy of at most $O(log(N))+O(|\ensuremath{\partial}A|)$ for any region A of the lattice. This shows that quantum many-body scars are a necessary consequence of revivals, independent of particularities of the Hamiltonian leading to them. We also present results for approximate revivals and for revivals of expectation values of observables and prove that the duration of revivals of states has to become vanishingly short with increasing system size.
Quantum chaos has become a cornerstone of physics through its many applications. One trademark of quantum chaotic systems is the spread of local quantum information, which physicists call scrambling. In this work, we introduce a mathematical definition of scrambling and a resource theory to measure it. We also describe two applications of this theory. First, we use our resource theory to provide a bound on magic, a potential source of quantum computational advantage, which can be efficiently measured in experiment. Second, we also show that scrambling resources bound the success of Yoshida's black hole decoding protocol.
Quantum many-body scars (QMBSs) are a novel paradigm for the violation of the eigenstate thermalization hypothesis—Hamiltonians of these systems exhibit mid-spectrum eigenstates that are equidistant in energy and which possess low entanglement and evade thermalization for long times. We present a novel approach to understanding the anomalous dynamical behavior in these systems. Specifically, we postulate that QMBS Hamiltonians H can generically be partitioned into a set of terms O a which do not commute over the entire Hilbert space, but commute to all orders within the subspace of scar states. All states in the scar subspace thus evolve according to a “broken unitary” U s ( t ) = ∏ a e − i O a t , where H = ∑ a O a , which provides a simple interpretation of the anomalous dynamical features exhibited by quantum scars; they evolve in time according to a simpler unitary operator allowing for revivals. It is found that the observed dynamical decoupling is often a direct consequence of simple local conditions, which when satisfied lead to recurring aspects of QMBSs, including equidistant eigenvalues, many-body revivals, and sub-volume-law entanglement entropy. Two classes of scar models emerge in this picture—those with a finite set of O a , as pertaining of, for instance, scars in the AKLT model, and those with an extensive set of such operators, such as eta pairing scar states in the Hubbard model. Besides discussing how many well-known scar models fit into the above picture, we show how the broken unitary formalism captures many known scar construction methods, known in the literature and generalizes others such as quasiparticles matrix product state (MPS) based methods, and the Shiraishi-Mori approach. Published by the American Physical Society 2024
Abstract Quantum many-body scars (QMBSs) are atypical eigenstates in otherwise nonintegrable systems that weakly break ergodicity, exhibiting nonthermal dynamics and long-lived periodic revivals. However, implementing QMBS in non-Hermitian systems remains a significant challenge, as it demands a deep understanding of the influence of exceptional points (EPs) on quantum many-body dynamics, especially higher-order EPs. Here, we use single-photon interference to demonstrate that experimentally controlled non-Hermitian dissipation stabilizes and enhances scarred dynamics, realizing nearly perfect, high-fidelity revival. These ideas can be exemplified in quantum systems that support scarred dynamics. In the non-Hermitian regime, symmetry-promoted exceptional points confine the dynamics to robust nonthermal subspaces, enabling high-fidelity scarred revivals over an extended parameter range. These results establish non-Hermitian quantum engineering as a versatile strategy for creating and sustaining perfect quantum scars, offering pathways for quantum-enhanced metrology, coherent state preparation, and fault-tolerant quantum information processing.
The recent discovery of persistent revivals in the Rydberg-atom quantum simulator has revealed a weakly ergodicity-breaking mechanism dubbed quantum many-body scars, which are a set of nonthermal states embedded in otherwise thermal spectra. Until now, such a mechanism has been mainly studied in Hermitian systems. Here, we establish the non-Hermitian quantum many-body scars and systematically characterize their nature from dynamic revivals, entanglement entropy, physical observables, and energy level statistics. Notably, we find the non-Hermitian quantum many-body scars exhibit significantly enhanced coherent revival dynamics when approaching the exceptional point. The signatures of non-Hermitian scars switch from the real-energy axis to the imaginary-energy axis after a real-to-complex spectrum transition driven by increasing non-Hermiticity, where an exceptional point and a quantum tricritical point emerge simultaneously. We further examine the stability of non-Hermitian quantum many-body scars against external fields, reveal the non-Hermitian quantum criticality and eventually set up the whole phase diagram. The possible connection to the open quantum many-body systems is also explored. Our findings offer insights for realizing long-lived coherent states in non-Hermitian many-body systems.