Simulation of quantum optics by coherent state decomposition

We introduce a framework for simulating quantum optics by decomposing the system into a finite rank (number of terms) superposition of coherent states. This allows us to define a resource theory, where linear optical operations are 'free' (i.e., do not increase the rank), and the simulation complexity for an $m$-mode system scales quadratically in $m$, in stark contrast to the Hilbert space dimension. We outline this approach explicitly in the Fock basis, relevant in particular for Boson sampling, where the simulation time (space) complexity for computing output amplitudes, to arbitrary accuracy, scales as $O(m^2 2^n)$ ($O(m2^n)$), for $n$ photons distributed amongst $m$ modes. We additionally demonstrate that linear optical simulations with the $n$ photons initially in the same mode scales efficiently, as $O(m^2 n)$. This paradigm provides a practical notion of 'non-classicality', i.e., the classical resources required for simulation. Moreover, by making connections to the stellar rank formalism, we show this comes from two independent contributions, the number of single-photon additions, and the amount of squeezing.Comment: 24+9 pages. 6 figures. V2: Improvements to main text and additional reference

Scrambling of Algebras in Open Quantum Systems

Many quantitative approaches to the dynamical scrambling of information in quantum systems involve the study of out-of-time-ordered correlators (OTOCs). In this paper, we introduce an algebraic OTOC ($\mathcal{A}$-OTOC) that allows us to study information scrambling of generalized quantum subsystems under quantum channels. For closed quantum systems, this algebraic framework was recently employed to unify quantum information-theoretic notions of operator entanglement, coherence-generating power, and Loschmidt echo. The main focus of this work is to provide a natural generalization of these techniques to open quantum systems. We first show that, for unitary dynamics, the $\mathcal{A}$-OTOC quantifies a generalized notion of information scrambling, namely between a subalgebra of observables and its commutant. For open quantum systems, on the other hand, we find a competition between the global environmental decoherence and the local scrambling of information. We illustrate this interplay by analytically studying various illustrative examples of algebras and quantum channels. To complement our analytical results, we perform numerical simulations of two paradigmatic systems: the PXP model and the Heisenberg XXX model, under dephasing. Our numerical results reveal connections with many-body scars and the stability of decoherence-free subspaces.Comment: v3: minor typos correcte

Information Scrambling over Bipartitions: Equilibration, Entropy Production, and Typicality

In recent years, the out-of-time-order correlator (OTOC) has emerged as a diagnostic tool for information scrambling in quantum many-body systems. Here, we present exact analytical results for the OTOC for a typical pair of random local operators supported over two regions of a bipartition. Quite remarkably, we show that this "bipartite OTOC" is equal to the operator entanglement of the evolution and we determine its interplay with entangling power. Furthermore, we compute long-time averages of the OTOC and reveal their connection with eigenstate entanglement. For Hamiltonian systems, we uncover a hierarchy of constraints over the structure of the spectrum and elucidate how this affects the equilibration value of the OTOC. Finally, we provide operational significance to this bipartite OTOC by unraveling intimate connections with average entropy production and scrambling of information at the level of quantum channels.Comment: v3: minor additions, close to published versio

Quantum coherence as a signature of chaos

We establish a rigorous connection between quantum coherence and quantum chaos by employing coherence measures originating from the resource theory framework as a diagnostic tool for quantum chaos. We quantify this connection at two different levels: quantum states and quantum channels. At the level of states, we show how several well-studied quantifiers of chaos are, in fact, quantum coherence measures in disguise (or closely related to them). We further this connection for all quantum coherence measures by using tools from majorization theory. Then, we numerically study the coherence of chaotic-vs-integrable eigenstates and find excellent agreement with random matrix theory in the bulk of the spectrum. At the level of channels, we show that the coherence-generating power (CGP) -- a measure of how much coherence a dynamical process generates on average -- emerges as a subpart of the out-of-time-ordered correlator (OTOC), a measure of information scrambling in many-body systems. Via numerical simulations of the (nonintegrable) transverse-field Ising model, we show that the OTOC and CGP capture quantum recurrences in quantitatively the same way. Moreover, using random matrix theory, we analytically characterize the CGP-OTOC connection for the Haar and Gaussian ensembles. In closing, we remark on how our coherence-based signatures of chaos relate to other diagnostics, namely the Loschmidt echo, OTOC, and the Spectral Form Factor.Comment: close to published versio