arXiv subjects

Xiaozhou Feng

Publications and source records attributed to Xiaozhou Feng.

12 recordsLinked to original sources

arXiv2026

Quantum resource localizability transitions in deep thermalization

We investigate how quantum resource constraints affect deep thermalization, the emergence of universal local wavefunction distributions from partial measurements of a quantum many-body state. Quantum resources, such as non-stabilizerness (magic), coherence, asymmetry, imaginarity, and non-Gaussianity, are essential for quantum information processing, and constraints on their global abundance can reshape these emergent distributions. To address this question, we develop a unified framework for deep thermalization within general quantum resource theories (QRTs). Our central result is that QRTs fall into two classes: ``smoothly localizable'' (SL) QRTs, where the resource content of local post-measurement states changes continuously with the global resource density, set by the initial state and measurement basis, yielding continuously tunable wavefunction distributions; and ``threshold localizable'' (TL) QRTs, where the local resource content jumps discontinuously from minimal to near-maximal past a critical global resource threshold, producing a sharp transition between a resourceless, ``deep-ergodicity breaking'' distribution and a resourceful, maximally random one. We trace this SL-TL dichotomy to an information-theoretic mechanism, block sharpening: by viewing each QRT as coherence between blocks in Hilbert space, we show that the local resource content depends on the measurement's ability to collapse an initial superposition into a single resourceless block. Our theory is analytically tractable and quantitatively predicts the phase boundaries across all studied QRTs, which we validate with extensive numerical simulations. Finally, we highlight two consequences: a novel magic transition in zero-rate quantum error-correcting codes--previously believed to occur only at finite rates--and new implications for quantum resource certification protocols based on post-measurement state ensembles.

quant-ph↗

arXiv2025

Pseudoentanglement from tensor networks

Pseudoentangled states are defined by their ability to hide their entanglement structure: they are indistinguishable from random states to any observer with polynomial resources, yet can have much less entanglement than random states. Existing constructions of pseudoentanglement based on phase- and/or subset-states are limited in the entanglement structures they can hide: e.g., the states may have low entanglement on a single cut, on all cuts at once, or on local cuts in one dimension. Here we introduce new constructions of pseudoentangled states based on (pseudo)random tensor networks that affords much more flexibility in the achievable entanglement structures. We illustrate our construction with the simplest example of a matrix product state, realizable as a staircase circuit of pseudorandom unitary gates, which exhibits pseudo-area-law scaling of entanglement in one dimension. We then generalize our construction to arbitrary tensor network structures that admit an isometric realization. A notable application of this result is the construction of pseudoentangled `holographic' states whose entanglement entropy obeys a Ryu-Takayanagi `minimum-cut' formula, answering a question posed in [Aaronson et al., arXiv:2211.00747].

quant-ph↗

arXiv2025

Hardness of observing strong-to-weak symmetry breaking

Spontaneous symmetry breaking (SSB) is the cornerstone of our understanding of quantum phases of matter. Recent works have generalized this concept to the domain of mixed states in open quantum systems, where symmetries can be realized in two distinct ways dubbed strong and weak. Novel intrinsically mixed phases of quantum matter can then be defined by the spontaneous breaking of strong symmetry down to weak symmetry. However, proposed order parameters for strong-to-weak SSB (based on mixed-state fidelities or purities) seem to require exponentially many copies of the state, raising the question: is it possible to efficiently detect strong-to-weak SSB in general? Here we answer this question negatively in the paradigmatic cases of $Z_2$ and $U(1)$ symmetries. We construct ensembles of pseudorandom mixed states that do not break the strong symmetry, yet are computationally indistinguishable from states that do. This rules out the existence of efficient state-agnostic protocols to detect strong-to-weak SSB.

quant-ph↗

arXiv2025

Charge and Spin Sharpening Transitions on Dynamical Quantum Trees

The dynamics of monitored systems can exhibit a measurement-induced phase transition (MIPT) between entangling and disentangling phases, tuned by the measurement rate. When the dynamics obeys a continuous symmetry, the entangling phase further splits into a fuzzy phase and a sharp phase based on the scaling of fluctuations of the symmetry charge. While the sharpening transition for Abelian symmetries is well understood analytically, no such understanding exists for the non- Abelian case. In this work, building on a recent analytical solution of the MIPT on tree-like circuit architectures (where qubits are repatedly added or removed from the system in a recursive pattern), we study entanglement and sharpening transitions in monitored dynamical quantum trees obeying U (1) and SU (2) symmetries. The recursive structure of tree tensor networks enables powerful analytical and numerical methods to determine the phase diagrams in both cases. In the U (1) case, we analytically derive a Fisher-KPP-like differential equation that allows us to locate the critical point and identify its properties. We find that the entanglement/purification and sharpening transitions generically occur at distinct measurement rates. In the SU (2) case, we find that the fuzzy phase is generic, and a sharp phase is possible only in the limit of maximal measurement rate. In this limit, we analytically solve the boundaries separating the fuzzy and sharp phases, and find them to be in agreement with exact numerical simulations.

quant-ph↗

arXiv2025

Dynamics of Pseudoentanglement

The dynamics of quantum entanglement plays a central role in explaining the emergence of thermal equilibrium in isolated many-body systems. However, entanglement is notoriously hard to measure. Recent works have introduced a notion of pseudoentanglement describing ensembles of many-body states that, while only weakly entangled, cannot be efficiently distinguished from states with much higher entanglement, such as random states in the Hilbert space. This prompts the question: how much entanglement is truly necessary to achieve thermal equilibrium in quantum systems? In this work we address this question by introducing random circuit models of quantum dynamics that, at late times, equilibrate to pseudoentangled ensembles -- a phenomenon we name ensemble pseudothermalization. These models replicate all the efficiently observable predictions of thermal equilibrium, while generating only a small (and tunable) amount of entanglement. We examine (i) how a pseudoentangled ensemble on a small subsystem spreads to the whole system as a function of time, and (ii) how a pseudoentangled ensemble can be generated from an initial product state. We map the above problems onto a family of classical Markov chains on subsets of the computational basis. The mixing times of such Markov chains are related to the time scales at which the states produced from the dynamics become indistinguishable from Haar-random states at the level of each statistical moment, or number of copies. Based on a combination of rigorous bounds and conjectures supported by numerics, we argue that each Markov chain's relaxation time and mixing time have different asymptotic behavior in the limit of large system size. This is a necessary condition for a cutoff phenomenon: an abrupt dynamical transition to equilibrium. We thus conjecture that our random circuits give rise to asymptotically sharp distinguishability transitions.

quant-ph↗

arXiv2025

Postselection-free experimental observation of the measurement-induced phase transition in circuits with universal gates

Monitored many-body systems can exhibit a phase transition between entangling and disentangling dynamical phases by tuning the strength of measurements made on the system as it evolves. This phenomenon is called the measurement-induced phase transition (MIPT). Understanding the properties of the MIPT is a prominent challenge for both theory and experiment at the intersection of many-body physics and quantum information. Realizing the MIPT experimentally is particularly challenging due to the postselection problem, which demands a number of experimental realizations that grows exponentially with the number of measurements made during the dynamics. Proposed approaches that circumvent the postselection problem typically rely on a classical decoding process that infers the final state based on the measurement record. But the complexity of this classical process generally also grows exponentially with the system size unless the dynamics is restricted to a fine-tuned set of unitary operators. In this work we overcome these difficulties. We construct a tree-shaped quantum circuit whose nodes are Haar-random unitary operators followed by weak measurements of tunable strength. For these circuits, we show that the MIPT can be detected without postselection using only a simple classical decoding process whose complexity grows linearly with the number of qubits. Our protocol exploits the recursive structure of tree circuits, which also enables a complete theoretical description of the MIPT, including an exact solution for its critical point and scaling behavior. We experimentally realize the MIPT on Quantinuum's H1-1 trapped-ion quantum computer and show that the experimental results are precisely described by theory. Our results close the gap between analytical theory and postselection-free experimental observation of the MIPT.

quant-ph↗

arXiv2024

Holographic Classical Shadow Tomography

We introduce "holographic shadows", a new class of randomized measurement schemes for classical shadow tomography that achieves the optimal scaling of sample complexity for learning geometrically local Pauli operators at any length scale, without the need for fine-tuning protocol parameters such as circuit depth or measurement rate. Our approach utilizes hierarchical quantum circuits, such as tree quantum circuits or holographic random tensor networks. Measurements within the holographic bulk correspond to measurements at different scales on the boundary (i.e. the physical system of interests), facilitating efficient quantum state estimation across observable at all scales. Considering the task of estimating string-like Pauli observables supported on contiguous intervals of $k$ sites in a 1D system, our method achieves an optimal sample complexity scaling of $\sim d^k\mathrm{poly}(k)$, with $d$ the local Hilbert space dimension. We present a holographic minimal cut framework to demonstrate the universality of this sample complexity scaling and validate it with numerical simulations, illustrating the efficacy of holographic shadows in enhancing quantum state learning capabilities.

quant-ph↗

arXiv2023

Measurement-induced phase transitions on dynamical quantum trees

Monitored many-body systems fall broadly into two dynamical phases, ``entangling'' or ``disentangling'', separated by a transition as a function of the rate at which measurements are made on the system. Producing an analytical theory of this measurement-induced transition is an outstanding challenge. Recent work made progress in the context of tree tensor networks, which can be related to all-to-all quantum circuit dynamics with forced (postselected) measurement outcomes. So far, however, there are no exact solutions for dynamics of spin-1/2 degrees of freedom (qubits) with ``real'' measurements, whose outcome probabilities are sampled according to the Born rule. Here we define dynamical processes for qubits, with real measurements, that have a tree-like spacetime interaction graph, either collapsing or expanding the system as a function of time. The former case yields an exactly solvable measurement transition. We explore these processes analytically and numerically, exploiting the recursive structure of the tree. We compare the case of ``real'' measurements with the case of ``forced'' measurements. Both cases show a transition at a nontrivial value of the measurement strength, with the real measurement case exhibiting a smaller entangling phase. Both exhibit exponential scaling of the entanglement near the transition, but they differ in the value of a critical exponent. An intriguing difference between the two cases is that the real measurement case lies at the boundary between two distinct types of critical scaling. On the basis of our results we propose a protocol for realizing a measurement phase transition experimentally via an expansion process.

cond-mat.stat-mech↗

arXiv2022

Exact solution for the filling-induced thermalization transition in a 1D fracton system

We study a random circuit model of constrained fracton dynamics, in which particles on a one-dimensional lattice undergo random local motion subject to both charge and dipole moment conservation. The configuration space of this system exhibits a continuous phase transition between a weakly fragmented ("thermalizing") phase and a strongly fragmented ("nonthermalizing") phase as a function of the number density of particles. Here, by mapping to two different problems in combinatorics, we identify an exact solution for the critical density $n_c$. Specifically, when evolution proceeds by operators that act on $\ell$ contiguous sites, the critical density is given by $n_c = 1/(\ell -2)$. We identify the critical scaling near the transition, and we show that there is a universal value of the correlation length exponent $ν= 2$. We confirm our theoretical results with numeric simulations. In the thermalizing phase the dynamical exponent is subdiffusive: $z=4$, while at the critical point it increases to $z_c \gtrsim 6$.

cond-mat.stat-mech↗

arXiv2022

Hilbert space fragmentation produces a "fracton Casimir effect"

Fracton systems exhibit restricted mobility of their excitations due to the presence of higher-order conservation laws. Here we study the time evolution of a one-dimensional fracton system with charge and dipole moment conservation using a random unitary circuit description. Previous work has shown that when the random unitary operators act on four or more sites, an arbitrary initial state eventually thermalizes via a universal subdiffusive dynamics. In contrast, a system evolving under three-site gates fails to thermalize due to strong "fragmentation" of the Hilbert space. Here we show that three-site gate dynamics causes a given initial state to evolve toward a highly nonthermal state on a time scale consistent with Brownian diffusion. Strikingly, the dynamics produces an effective attraction between isolated fractons or between a single fracton and the boundaries of the system, in analogy with the Casimir effect in quantum electrodynamics. We show how this attraction can be understood by exact mapping to a simple classical statistical mechanics problem, which we solve exactly for the case of an initial state with either one or two fractons.

quant-ph↗

arXiv2021

Large enhancement of thermopower at low magnetic field in compensated semimetals

The thermoelectric properties of conductors with low electron density can be altered significantly by an applied magnetic field. For example, recent work has shown that Dirac/Weyl semimetals with a single pocket of carriers can exhibit a large enhancement of thermopower when subjected to a sufficiently large field that the system reaches the extreme quantum limit, in which only a single Landau level is occupied. Here we study the magnetothermoelectric properties of compensated semimetals, for which pockets of electron- and hole-type carriers coexist at the Fermi level. We show that, when the compensation is nearly complete, such systems exhibit a huge enhancement of thermopower starting at a much smaller magnetic field, such that $ω_cτ> 1$, and the stringent conditions associated with the extreme quantum limit are not necessary. We discuss our results in light of recent measurements on the compensated Weyl semimetal tantalum phosphide, in which an enormous magnetothermoelectric effect was observed. We also calculate the Nernst coefficient of compensated semimetals, and show that it exhibits a maximum value with increasing magnetic field that is much larger than in the single band case. In the dissipationless limit, where the Hall angle is large, the thermoelectric response can be described in terms of quantum Hall edge states, and we use this description to generalize previous results to the multi-band case.

cond-mat.mes-hall↗

arXiv2020

Distinct magneto-Raman signatures of spin-flip phase transitions in CrI3

The discovery of 2-dimensional (2D) materials, such as CrI3, that retain magnetic ordering at monolayer thickness has resulted in a surge of research in 2D magnetism from both pure and applied perspectives. Here, we report a magneto-Raman spectroscopy study on multilayered CrI3, focusing on two new features in the spectra which appear at temperatures below the magnetic ordering temperature and were previously assigned to high frequency magnons. We observe a striking evolution of the Raman spectra with increasing magnetic field in which clear, sudden changes in intensities of the modes are attributed to the interlayer ordering changing from antiferromagnetic to ferromagnetic at a critical magnetic field. Our work highlights the sensitivity of the Raman modes to weak interlayer spin ordering in CrI3. In addition, we theoretically examine potential origins for the new modes, which we deduce are unlikely single magnons.

cond-mat.mes-hall↗