arXiv subjects

Amir-Reza Negari

Publications and source records attributed to Amir-Reza Negari.

14 recordsLinked to original sources

arXiv2026

Long-range entangled criticality from coherent errors

We find that coherent error can induce a phase transition from the clean surface code phase into an extended long-range entangled critical regime with diverging Markov length. To demonstrate this, we establish two general results of independent interest. The first relates topology and quantum information to mixed-state entanglement: we show that when a noise channel acting on a topological code preserves a higher-form symmetry and nonzero coherent information, the noisy state for generic logical input is long-range entangled. The second generalizes the local recovery construction based on finite Markov length to any locally parameterized family, thus encompassing local Lindbladian evolution, coherent errors followed by syndrome dephasing, and thermal states. We apply these results to the honeycomb surface code, in which we find an extended long-range entangled critical regime that is a quasi-long-ranged counterpart of 1-form strong-to-weak spontaneous symmetry breaking. As a byproduct of these studies, we relate the conditional mutual information to conductance in a Majorana network model.

quant-ph↗

arXiv2026

Instability of Markov chains under infinitesimal coherent dissipation

Under local Lindbladian evolution, the growth of conditional mutual information and its associated Markov length scale is not limited by Lieb-Robinson bounds, yet it has been unclear how quickly the Markov length can increase. We show that an arbitrarily short, strictly local Lindbladian can generate infinite Markov length from a product state. We also construct strictly local Lindbladians that converge rapidly to steady states with algebraically decaying conditional mutual information. Despite their long-range conditional correlations, the states we construct are local reversibly connected to a product state by sublinear depth circuits. Thus infinite Markov length does not imply slow relaxation nor obstruct phase stability when suitably defined.

quant-ph↗

arXiv2026

Nonadditivity in fermionic quantum Shannon theory

We study collective state preparation and channel encoding in fermionic systems under parity superselection and composition governed by the canonical anticommutation relations. For a two-mode Gaussian state $τ$, we obtain the exact entanglement of formation, $E_{\mathrm F}^{\mathrm{phys}}(τ^{\otimes m})=\lceil m/2\rceil\log2$ for every $m\geq1$. Two copies have the same formation value as one, violating additivity and strong superadditivity, while regularization halves the single-copy value. For an associated Gaussian channel, we determine the minimum output entropy and Holevo information at every blocklength and prove nonadditivity of both. Together, these results give exact answers to the fermionic counterparts of the four additivity questions associated with Shor and Hastings. One physical use carries no classical information, whereas two uses transmit one bit perfectly. The unassisted classical and zero-error classical capacities both equal one half bit per mode. A sharp finite-block bound gives a strong converse: the decoding success probability vanishes at every rate above capacity. These optimizations cover all physical pure-state decompositions and channel inputs, with Gaussian ensembles and classical codes attaining the optima. The formation and minimum output entropy formulas hold for every Rényi order $α\in(0,\infty]$. We also determine the unassisted quantum and zero-error quantum capacities, both equal to one half logical qubit per mode, and prove a strong converse: entanglement fidelity vanishes at every rate above capacity. For a noisy Gaussian family, we determine the one- and two-copy formation values and prove strict nonadditivity at full rank. For $τ$, Bell violation under local parity-preserving measurements first appears at three copies.

quant-ph↗

arXiv2026

Entanglement of purification for Werner states: canonical purification and nonadditivity

We prove that the von Neumann entanglement of purification is nonadditive. For two-qubit Werner states $W(f)$ with singlet weight $1/64\le f\le1/4$, we show that canonical purification is globally optimal: its entanglement, also known as reflected entropy, gives the exact entanglement of purification. In contrast, the regularized entanglement of purification lies strictly below the reflected entropy for $0<f<f_\ast$, where $f_\ast\approx0.017$. Together, these results establish nonadditivity throughout $1/64\le f<f_\ast$. Our canonical-optimality proof generalizes the proof in [1], which established Rényi nonadditivity for $0\leα<1$ using classical two-qubit states. We thus resolve the additivity question at $α=1$. Remarkably, nonadditivity is again witnessed by separable states and no entanglement in the underlying states is required.

quant-ph↗

arXiv2026

Approximation theorems for fermionic Gaussian states

A recurring principle in many-body physics is that sufficiently distributed interactions or correlations lead to an effectively mean-field description. For fermionic Gaussian states, we establish a quantitative version of this principle directly at the level of Majorana covariance matrices. The main observation is that the admissibility condition for fermionic covariance matrices imposes a quantitative monogamy constraint on two-point correlations: a fixed region has only a bounded covariance budget to distribute among many disjoint regions. We use this principle in three directions. First, for quadratic fermionic Hamiltonians on finite simple graphs of high degree, we obtain product-state approximations to both the ground-state energy and the finite-temperature free energy, with error of order $D^{-1/2}$ for $D$-regular graphs. Second, we prove a finite fermionic Gaussian de Finetti theorem: a $k$-copy Gaussian state that is $n$-exchangeable under graded fermionic copy permutations is $O(k/n)$-close in trace norm to the product of its one-copy marginal. In particular, infinite exchangeability within the Gaussian class implies exact product structure. Third, for spatial fermionic Gaussian states with exponentially clustering mutual information, we prove that the conditional mutual information across a separating buffer decays as $O(r^{-1})$, and hence, by recoverability, the state admits an $O(r^{-1/2})$ trace-norm approximation by a recovered state. These results show that product and de Finetti approximations and recoverability estimates for fermionic Gaussian systems can all be derived directly from covariance-level structure.

quant-ph↗

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

Rényi Entanglement of Purification Is Non-additive

Entanglement of purification is a fundamental measure of total correlations whose additivity remains unresolved. We study its additivity for classical states on two qubits at different Rényi orders. For every $α\in[0,1)$, we prove nonadditivity within this family, witnessed by two copies of a single state. We first solve the one-copy optimization exactly for the entire family at every Rényi order. We then restrict the two-copy optimization to a natural finite set of purifications and exhibit one whose entropy is strictly below the product value. In contrast, for $α\in[2,\infty]$ we prove additivity under tensor products within this family. The interval $α\in[1,2)$, including the von Neumann case $α=1$, remains open, and we conjecture additivity there throughout the same family.

quant-ph↗

arXiv2026

Extendibility of Fermionic Gaussian States

We investigate $(k_1,k_2)$-extendibility of fermionic Gaussian states, a property central to quantum correlations and approximations of separability. We show that these states are $(k_1,k_2)$-extendible if and only if they admit a fermionic Gaussian extension, yielding a complete covariance-matrix characterization and a simple semidefinite program (SDP) whose size scales linearly with the number of modes. This provides necessary conditions for arbitrary fermionic states and is sufficient within the Gaussian setting. Our main result is a finite de Finetti--type theorem: we derive trace-norm bounds between $(k_1,k_2)$-extendible fermionic Gaussian states and separable states, improving previous exponential scaling to linear in the number of modes, with complementary relative entropy and squashed entanglement bounds. For two modes, upper and lower bounds match at order $1/\sqrt{k_1 k_2}$. Extendibility also provides operational support for one of the different notions of separability in fermionic systems. Finally, for fermionic Gaussian channels, we provide an SDP criterion for anti-degradability and show that entanglement-breaking channels coincide with replacement channels, implying no nontrivial entanglement-breaking fermionic Gaussian channels exist.

quant-ph↗

arXiv2026

Unlearnable phases of matter

We identify fundamental limitations in machine learning by demonstrating that non-trivial mixed-state phases of matter are computationally hard to learn. Focusing on unsupervised learning of distributions, we show that autoregressive neural networks fail to learn global properties of distributions characterized by locally indistinguishable (LI) states. We demonstrate that conditional mutual information (CMI) is a useful diagnostic for LI: we show that for classical distributions, long-range CMI of a state implies a spatially LI partner. By introducing a restricted statistical query model, we prove that nontrivial phases with long-range CMI, such as strong-to-weak spontaneous symmetry breaking phases, are hard to learn. We validate our claims by using recurrent, convolutional, and Transformer neural networks to learn the syndrome and physical distributions of toric/surface code under bit flip noise. Our findings suggest hardness of learning as a diagnostic tool for detecting mixed-state phases and transitions and error-correction thresholds, and they suggest CMI and more generally ``non-local Gibbsness'' as metrics for how hard a distribution is to learn.

cond-mat.dis-nn↗

arXiv2026

Critical non-equilibrium phases from noisy topological memories

We demonstrate the existence of an extended non-equilibrium critical phase, characterized by sub-exponential decay of conditional mutual information (CMI), in the surface code subject to heralded random Pauli measurement channels. By mapping the resulting mixed state to the ensemble of completely packed loops on a square lattice, we relate the extended phase to the Goldstone phase of the loop model. In particular, CMI is controlled by the characteristic length scale of loops, and we use analytic results of the latter to establish polylogarithmic decay of CMI in the critical phase. We find that the critical phase retains partial logical information that can be recovered by a global decoder, but not by any quasi-local decoder. To demonstrate this, we introduce a diagnostic called punctured coherent information which provides a necessary condition for quasi-local decoding.

quant-ph↗

arXiv2025

Spacetime Markov length: a diagnostic for fault tolerance via mixed-state phases

We establish a correspondence between the fault-tolerance of local stabilizer codes experiencing measurement and physical errors and the mixed-state phases of decohered resource states in one higher dimension. Drawing from recent developments in mixed-state phases of matter, this motivates a diagnostic of fault-tolerance, which we refer to as the spacetime Markov length. This is a length scale determined by the decay of the (classical) conditional mutual information of repeated syndrome measurement outcomes in spacetime. The diagnostic is independent of the decoder, and its divergence signals the intrinsic breakdown of fault tolerance. As a byproduct, we find that decoherence may be useful for exposing transitions from higher-form symmetry-protected topological phases driven by both incoherent and coherent perturbations.

quant-ph↗

arXiv2024

Measurement-induced phase transitions in the toric code

We show how distinct phases of matter can be generated by performing random single-qubit measurements on a subsystem of toric code. Using a parton construction, such measurements map to random Gaussian tensor networks, and in particular, random Pauli measurements map to a classical loop model in which watermelon correlators precisely determine measurement-induced entanglement. Measuring all but a 1d boundary of qubits realizes hybrid circuits involving unitary gates and projective measurements in 1+1 dimensions. We find that varying the probabilities of different Pauli measurements can drive transitions in the un-measured boundary between phases with different orders and entanglement scaling, corresponding to short and long loop phases in the classical model. Furthermore, by utilizing single-site boundary unitaries conditioned on the bulk measurement outcomes, we generate mixed state ordered phases and transitions that can be experimentally diagnosed via linear observables. This demonstrates how parton constructions provide a natural framework for measurement-based quantum computing setups to produce and manipulate phases of matter.

quant-ph↗

arXiv2022

Chiral Ising Gross-Neveu criticality of a single Dirac cone: A quantum Monte Carlo study

We perform large-scale quantum Monte Carlo simulations of SLAC fermions on a two-dimensional square lattice at half filling with a single Dirac cone with $N=2$ spinor components and repulsive on-site interactions. Despite the presence of a sign problem, we accurately identify the critical interaction strength $U_c = 7.28 \pm 0.02$ in units of the hopping amplitude, for a continuous quantum phase transition between a paramagnetic Dirac semimetal and a ferromagnetic insulator. Using finite-size scaling, we extract the critical exponents for the corresponding $N=2$ chiral Ising Gross-Neveu universality class: the inverse correlation length exponent $ν^{-1} = 1.19 \pm 0.03$, the order parameter anomalous dimension $η_ϕ = 0.31 \pm 0.01$, and the fermion anomalous dimension $η_ψ = 0.136 \pm 0.005$.

cond-mat.str-el↗

arXiv2021

An Amelioration for the Sign Problem: Adiabatic Quantum Monte Carlo

We introduce the adiabatic quantum Monte Carlo (AQMC) method, where we gradually crank up the interaction strength, as an amelioration of the sign problem. It is motivated by the adiabatic theorem and will approach the true ground-state if the evolution time is long enough. We demonstrate that the AQMC enhances the average sign exponentially such that low enough temperatures can be accessed and ground-state properties probed. It is a controlled approximation that satisfies the variational theorem and provides an upper bound for the ground-state energy. We first benchmark the AQMC vis-à-vis the undoped Hubbard model on the square lattice which is known to be sign-problem-free within the conventional quantum Monte Carlo formalism. Next, we test the AQMC against the density-matrix-renormalization-group approach for the doped four-leg ladder Hubbard model and demonstrate its remarkable accuracy. As a nontrivial example, we apply our method to the Hubbard model at $p=1/8$ doping for a $16\times 8$ system and discuss its ground-state properties. We finally utilize our method and demonstrate the emergence of $U(1)_2\sim SU(2)_1$ topological order in a strongly correlated Chern insulator.

cond-mat.str-el↗