arXiv subjects

Leonardo A. Lessa

Publications and source records attributed to Leonardo A. Lessa.

10 recordsLinked to original sources

arXiv2026

Symmetry enforces entanglement at high temperatures

Many-body quantum systems with local interactions undergo ``sudden death of entanglement" at high temperatures, whereby thermal states become classical mixtures of product states. We investigate whether symmetry constraints can prevent this phenomenon. We prove that strongly symmetric thermal states (canonical ensemble) of generic Hamiltonians with on-site Abelian symmetries remain entangled with non-zero entanglement negativity at arbitrarily high temperatures, under mild conditions on the symmetry actions and the charge sector of the strong symmetry. Our results extend to weakly symmetric thermal states (Gibbs ensemble) under superselection rules, which restrict state decompositions to be symmetric. In particular, we show that fermionic Gibbs states evade sudden death of entanglement and have persistent fermionic negativity at high temperatures, proving along the way some existing conjectures about fermionic entanglement. These findings demonstrate that global symmetry correlations can preserve quantum entanglement despite thermal decoherence, providing new insights into the interplay between symmetry and quantum information in thermal equilibrium.

quant-ph↗

arXiv2026

Local Strong-to-Weak Spontaneous Symmetry Breaking

We propose a local notion of strong-to-weak spontaneous symmetry breaking (SW-SSB), through a local one-point fidelity correlator. Compared with the previous definition in terms of a two-point fidelity correlator, our local formulation offers two key advantages: (1) it is easier to detect in large systems: for a system of size $N$ and with ${\rm poly}(N)$ amount of resources, one can detect the local fidelity order up to volume scale $O(\log(N))$; and (2) the local SW-SSB order remains well defined in the thermodynamic limit, where the density matrix itself is not well defined. We show that key features of SW-SSB, including stability under finite-depth symmetric channels and long-range conditional mutual information, persist within this local framework. Our definition is conceptually analogous to local thermalization, as exemplified by pure states obeying the eigenstate thermalization hypothesis (ETH). For critical states, the local one-point fidelity correlator defines an interesting class of defect problems. We demonstrate the applicability of the local formulation through several concrete examples, and derive the universal scaling behavior of the local fidelity correlator in a range of critical systems, including ground states of conformal field theories as well as ballistic and diffusive free-fermion metals.

quant-ph↗

arXiv2026

Mixed-State Long-Range Entanglement from Dimensional Constraints

We present a new mechanism for long-range entanglement (LRE) in strongly symmetric many-body mixed states that does not rely on symmetry anomalies or long-range correlations. Our primary example is the maximally mixed state in the translation-invariant subspace on a one-dimensional ring. This state is LRE because translationally symmetric short-range entangled states span a subspace whose dimension grows only polynomially with system size, whereas the full translation-invariant subspace grows exponentially. We further discuss certain unconventional properties of this state, including logarithmically growing conditional mutual information, strong-to-weak spontaneous symmetry-breaking, and Rényi-index-dependent operator-space entanglement. We also construct a geometrically non-local Lindbladian to stabilize this state as the steady state. Our results identify dimensional mismatch as a novel route to LRE that is intrinsic to many-body mixed states.

quant-ph↗

arXiv2025

A Formalization of the Generalized Quantum Stein's Lemma in Lean

The Generalized Quantum Stein's Lemma is a theorem in quantum hypothesis testing that provides an operational meaning to the relative entropy within the context of quantum resource theories. Its original proof was found to have a gap, which led to a search for a corrected proof. We formalize the proof presented in [Hayashi and Yamasaki (2024)] in the Lean interactive theorem prover. This is the most technically demanding theorem in physics with a computer-verified proof to date, building with a variety of intermediate results from topology, analysis, and operator algebra. In the process, we rectified minor imprecisions in [HY24]'s proof that formalization forces us to confront, and refine a more precise definition of quantum resource theory. Formalizing this theorem has ensured that our Lean-QuantumInfo library, which otherwise has begun to encompass a variety of topics from quantum information, includes a robust foundation suitable for a larger collaborative program of formalizing quantum theory more broadly.

quant-ph↗

arXiv2025

Mixed-state phases from local reversibility

We propose a refined definition of mixed-state phase equivalence based on locally reversible channel circuits. We show that such circuits preserve topological degeneracy and the locality of all operators including both strong and weak symmetries. Under a locally reversible channel, weak unitary symmetries are locally dressed into channel symmetries, a new generalization of symmetry for open quantum systems. For abelian higher-form symmetries, we show the refined definition preserves anomalies and spontaneous breaking of such symmetries within a phase. As a primary example, a two-dimensional classical loop ensemble is trivial under the previously adopted definition of mixed-state phases. However, it has non-trivial topological degeneracy arising from a mutual anomaly between strong and weak 1-form symmetries, and our results show that it is not connected to a trivial state via locally reversible channel circuits.

quant-ph↗

arXiv2025

Higher-form anomaly and long-range entanglement of mixed states

In open quantum systems, we directly relate anomalies of higher-form symmetries to the long-range entanglement of any mixed state with such symmetries. First, we define equivalence classes of long-range entanglement in mixed states via stochastic local channels (SLCs), which effectively ``mod out'' any classical correlations and thus distinguish phases by differences in long-range quantum correlations only. It is then shown that strong symmetries of a mixed state and their anomalies (non-trivial braiding and self-statistics) are intrinsic features of the entire phase of matter. For that, a general procedure of symmetry pullback for strong symmetries is introduced, whereby symmetries of the output state of an SLC are dressed into symmetries of the input state, with their anomaly relation preserved. This allows us to prove that states in (2+1)-D with anomalous strong 1-form symmetries exhibit long-range bipartite entanglement, and to establish a lower bound for their topological entanglement of formation, a mixed-state generalization of topological entanglement entropy. For concreteness, we apply this formalism to the toric code under Pauli-X and Z dephasing noise, as well as under ZX decoherence, which gives rise to the recently discovered intrinsically mixed-state topological order. Finally, we conjecture a connection between higher-form anomalies and long-range multipartite entanglement for mixed states in higher dimensions.

quant-ph↗

arXiv2024

Symmetry enforced entanglement in maximally mixed states

Entanglement in quantum many-body systems is typically fragile to interactions with the environment. Generic unital quantum channels, for example, have the maximally mixed state with no entanglement as their unique steady state. However, we find that for a unital quantum channel that is `strongly symmetric', i.e. it preserves a global on-site symmetry, the maximally mixed steady state in certain symmetry sectors can be highly entangled. For a given symmetry, we analyze the entanglement and correlations of the maximally mixed state in the invariant sector (MMIS), and show that the entanglement of formation and distillation are exactly computable and equal for any bipartition. For all Abelian symmetries, the MMIS is separable, and for all non-Abelian symmetries, the MMIS is entangled. Remarkably, for non-Abelian continuous symmetries described by compact semisimple Lie groups (e.g. $SU(2)$), the bipartite entanglement of formation for the MMIS scales logarithmically $\sim \log N$ with the number of qudits $N$.

quant-ph↗

arXiv2024

Mixed-state quantum anomaly and multipartite entanglement

Quantum entanglement measures of many-body states have been increasingly useful to characterize phases of matter. Here we explore a surprising connection between mixed state entanglement and 't Hooft anomaly. More specifically, we consider lattice systems in $d$ space dimensions with anomalous symmetry $G$ where the anomaly is characterized by an invariant in the group cohomology $H^{d+2}(G,U(1))$. We show that any mixed state $ρ$ that is strongly symmetric under $G$, in the sense that $Gρ\proptoρ$, is necessarily $(d+2)$-nonseparable, i.e. is not the mixture of tensor products of $d+2$ states in the Hilbert space. Furthermore, such states cannot be prepared from any $(d+2)$-separable states using finite-depth local quantum channels, so the nonseparability is long-ranged in nature. We provide proof of these results in $d\leq1$, and plausibility arguments in $d>1$. The anomaly-nonseparability connection thus allows us to generate simple examples of mixed states with nontrivial long-ranged multipartite entanglement. In particular, in $d=1$ we found an example of intrinsically mixed quantum phase, in the sense that states in this phase cannot be two-way connected to any pure state through finite-depth local quantum channels. We also analyze mixed anomaly involving both strong and weak symmetries, including systems constrained by the Lieb-Schultz-Mattis type of anomaly. We find that, while strong-weak mixed anomaly in general does not constrain quantum entanglement, it does constrain long-range correlations of mixed states in nontrivial ways. Namely, such states are not symmetrically invertible and not gapped Markovian, generalizing familiar properties of anomalous pure states.

cond-mat.str-el↗

arXiv2024

Strong-to-Weak Spontaneous Symmetry Breaking in Mixed Quantum States

Symmetry in mixed quantum states can manifest in two distinct forms: strong symmetry, where each individual pure state in the quantum ensemble is symmetric with the same charge, and weak symmetry, which applies only to the entire ensemble. This paper explores a novel type of spontaneous symmetry breaking (SSB) where a strong symmetry is broken to a weak one. While the SSB of a weak symmetry is measured by the long-ranged two-point correlation function, the strong-to-weak SSB (SW-SSB) is measured by the fidelity correlator. We prove that SW-SSB is a universal property of mixed-state quantum phases, in the sense that the phenomenon of SW-SSB is robust against symmetric low-depth local quantum channels. We also show that the symmetry breaking is "spontaneous" in the sense that the effect of a local symmetry-breaking measurement cannot be recovered locally. We argue that a thermal state at a nonzero temperature in the canonical ensemble (with fixed symmetry charge) should have spontaneously broken strong symmetry. Additionally, we study non-thermal scenarios where decoherence induces SW-SSB, leading to phase transitions described by classical statistical models with bond randomness. In particular, the SW-SSB transition of a decohered Ising model can be viewed as the "ungauged" version of the celebrated toric code decodability transition. We confirm that, in the decohered Ising model, the SW-SSB transition defined by the fidelity correlator is the only physical transition in terms of channel recoverability. We also comment on other (inequivalent) definitions of SW-SSB, through correlation functions with higher Renyi indices.

quant-ph↗

arXiv2023

Measurement as a shortcut to long-range entangled quantum matter

The preparation of long-range entangled states using unitary circuits is limited by Lieb-Robinson bounds, but circuits with projective measurements and feedback (``adaptive circuits'') can evade such restrictions. We introduce three classes of local adaptive circuits that enable low-depth preparation of long-range entangled quantum matter characterized by gapped topological orders and conformal field theories (CFTs). The three classes are inspired by distinct physical insights, including tensor-network constructions, multiscale entanglement renormalization ansatz (MERA), and parton constructions. A large class of topological orders, including chiral topological order, can be prepared in constant depth or time, and one-dimensional CFT states and non-abelian topological orders with both solvable and non-solvable groups can be prepared in depth scaling logarithmically with system size. We also build on a recently discovered correspondence between symmetry-protected topological phases and long-range entanglement to derive efficient protocols for preparing symmetry-enriched topological order and arbitrary CSS (Calderbank-Shor-Steane) codes. Our work illustrates the practical and conceptual versatility of measurement for state preparation.

cond-mat.str-el↗