arXiv subjects

Raz Firanko

Publications and source records attributed to Raz Firanko.

4 recordsLinked to original sources

arXiv2026

A Unified Framework for Locally Stable Phases

We propose a unifying framework for characterizing pure and mixed state phases of matter across equilibrium, non equilibrium, and metastable regimes. We introduce the concept of locally stable states, defined by the operational property that any local operation (including post selection) can be reversed by a local channel. We prove that local stability is equivalent to a state being short range correlated, defined by the decay of both correlations and conditional mutual information. We demonstrate that these properties are invariant under locally reversible channels, thus defining locally stable phases. Furthermore, we prove that local stability implies both the decay of a family of nonlinear correlators, including the fidelity correlator, and the decay of correlations in the canonical purification, thus bridging the gap between mixed and pure states. Along the way, we establish two results which may be of independent interest: we show that post-selection on locally stable (short range correlated) states can be implemented via local channels and that quantum Markov chains can be characterized by the local computability of nonlinear observables.

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arXiv2025

Area laws and tensor networks for maximally mixed ground states

We show an area law in the mutual information for the maximally-mixed state $Ω$ in the ground space of general Hamiltonians, which is independent of the underlying ground space degeneracy. Our result assumes the existence of a `good' approximation to the ground state projector (a good AGSP), a crucial ingredient in previous area-law proofs. Such approximations have been explicitly derived for 1D gapped local Hamiltonians and 2D frustration-free locally-gapped Hamiltonians. As a corollary, we show that in 1D gapped local Hamiltonians, for any $\varepsilon>0$ and any bi-partition $L\cup L^c$ of the system, \begin{align*} \mathrm I_{\max}^\varepsilon (L:L^c)_Ω \le \mathrm O \big( \log (|L|\log(d))+\log(1/\varepsilon)\big), \end{align*} where $|L|$ represents the number of sites in $L$, $d$ is the dimension of a site and $ \mathrm I_{\max}^\varepsilon (L:L^c)_Ω $ represents the $\varepsilon$-\emph{smoothed maximum mutual information} with respect to the $L:L^c$ partition in $Ω$. From this bound we then conclude $\mathrm I (L:L^c)_Ω \le \mathrm O\big(\log(|L|\log(d))\big)$ -- an area law for the mutual information in 1D systems with a logarithmic correction. In addition, we show that $Ω$ can be approximated in trace norm up to $\varepsilon$ with a state of Schmidt rank of at most $\mathrm{poly}(|L|/\varepsilon)$, leading to a good MPO approximation for $Ω$ with polynomial bond dimension. Similar corollaries are derived for the mutual information of 2D frustration-free and locally-gapped local Hamiltonians.

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arXiv2025

Local quantum channels giving rise to quasi-local Gibbs states

We study the steady-state properties of quantum channels with local Kraus operators. We consider a large family that consists of general ergodic 1-local (non-interacting) terms and general 2-local (interacting) terms. Physically, a repeated application of these channels can be seen as a simple model for the thermalization process of a many-body system. We study its steady state perturbatively, by interpolating between the 1-local and 2-local channels with a perturbation parameter $ε$. We prove that under very general conditions, these states are Gibbs states of a quasi-local Hamiltonian. Expanding this Hamiltonian as a series in $ε$, we show that the $k$'th order term corresponds to a $(k+1)$-local interaction term in the Hamiltonian, which follows the same interaction graph as the Kraus channel. We also prove a complementary result suggesting the existence of an interaction strength threshold, under which the total weight of the high-order terms in the Hamiltonian decays exponentially fast. For sufficiently small $ε$, this implies both exponential decay of local correlation functions and a classical algorithm for computing expectation value of local observables in such steady states. Finally, we present numerical simulations of various channels that support our theoretical results.

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arXiv2023

Area law for steady states of detailed-balance local Lindbladians

We study steady-states of quantum Markovian processes whose evolution is described by local Lindbladians. We assume that the Lindbladian is gapped and satisfies quantum detailed balance with respect to a unique full-rank steady state $σ$. We show that under mild assumptions on the Lindbladian terms, which can be checked efficiently, the Lindbladian can be mapped to a local Hamiltonian on a doubled Hilbert space that has the same spectrum, and a ground state that is the vectorization of $σ^{1/2}$. Consequently, we can use Hamiltonian complexity tools to study the steady states of such open systems. In particular, we show an area-law in the mutual information for the steady state of such 1D systems, together with a tensor-network representation that can be found efficiently.

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