arXiv subjects

Yoshihito Kuno

Publications and source records attributed to Yoshihito Kuno.

At least 19 recordsLinked to original sources

arXiv2026

Hierarchy of mixed symmetry protected topological states in extended cluster states under subsystem decoherence

We study the effect of subsystem decoherence to an extended cluster state which is a symmetry protected topological (SPT) phase. The model includes many subsystem $Z_2$ symmetries. We report that subsystem decoherence induces local charge fluctuations, leading to a mixed SPT state in the unaffected subsystems. If we start from the extended cluster state, hierarchical mixed-state SPT phases emerge in response to step-by-step subsystem decoherences. These mixed-state SPT phases keep strong symmetries the symmetry of which is protecting symmetries for the initial cluster SPT. Moreover, these SPTs can be characterized by Rényi-2 string orders. Then, as the subsystems are progressively decohered, the hierarchy of mixed-state SPT phases terminates in a $Z_2$ strong-to-weak spontaneous symmetry breaking (SWSSB) state on the final remaining subsystem, where a long-range entangled state appears, namely a glassy Greenberger-Horne-Zeilinger (GHZ) state. Our work demonstrates that decoherence is not merely a destructive process, but can induce and organize series of nontrivial mixed-states. This reveals a systematic route from mixed-state SPT order to SWSSB with the glassy GHZ-type long-range entanglement.

quant-ph↗

arXiv2026

Decohered color code and emerging mixed toric code by anyon proliferation: Topological entanglement negativity perspective

We study how the color code under decoherence gives rise to an intrinsic mixed-state topological order (imTO), which has no counterpart in pure ground states of local gapped Hamiltonians. For decoherence induced by XX-type operators on red links of the honeycomb lattice, we show that the resulting mixed state inherits half of the topological properties of the color code, including anyon content, logical operators, and topological entanglement structure. Using a gauging procedure for mixed stabilizer states, we identify the emergent phase as closely related to a single toric code. We characterize this phase by topological entanglement negativity (TEN) and perform efficient stabilizer-formalism simulations. While the pure color code has ${\rm TEN} = 2 \ln 2$, the maximally decohered state has ${\rm TEN} = \ln 2$, indicating emergence of a single toric code. By tuning the decoherence strength, we find a smooth crossover in TEN accompanied by a pronounced, nearly system-size-independent peak in its variance. We further show that the negativity exhibits characteristic scaling only for subsystem partitions commensurate with the triangular lattice of the emergent toric code. Our results demonstrate that negativity-based quantities provide powerful probes of mixed-state topological order generated by decoherence.

quant-ph↗

arXiv2026

Continuous Reset-Induced Phase Transition in Measurement-Free Random Quantum Circuits

We study a random unitary quantum circuit with only reset channels, which has high feasibility for real quantum devices. In particular, we investigate the many-body statistical physics properties, "reset-induced" entanglement phase transitions comparing the classical statistical picture in the large "$d$" limit of qudits. In the property of the reset-induced phase transition the parameter of qudit $d$ is essential. That is, the transition properties induced by the reset channel significantly depend on $d$. We numerically elucidate this statement employing efficient stabilizer circuit simulations for $d=2$. Specifically, large fluctuations are observed near the critical point, indicating that the reset-induced phase transition is continuous. We obtain clear data collapses, consistent with a second-order mixed phase transition. This behavior differs from expectations based on the classical statistical mapping in the large-$d$ limit.

quant-ph↗

arXiv2026

Measurement-only circuit of perturbed toric code on triangular lattice: Topological entanglement, 1-form symmetry and logical qubits

Measurement-only (quantum) circuit (MoC) gives possibility to realize the states with rich entanglements, topological orders and quantum memories. This work studies the MoC, in which the projective-measurement operators consist of stabilizers of the toric code and competitive local Pauli operators. The former correspond to terms of the toric code on a triangular lattice and the later to external magnetic and electric fields. We employ efficient numerical stabilizer algorithm to trace evolving states undergoing phase transitions. We elucidate the phase diagram of the MoC system with the observables such as, topological entanglement entropy (TEE), disorder parameters of 1-form symmetries and emergent logical operators. We clarify the locations of the phase transitions through the observation of the above quantities and obtain precise critical exponents to examine if the observables exhibit the critical behavior simultaneously under the MoC and transitions belong to the same universality class. In contrast to the TC Hamiltonian system and toric code MoC on a square lattice, the system on the triangular lattice is not self-dual nor bipartite, and then, coincidence by symmetries, such as critical behaviors across the TC and Higgs/confined phase, does not takes place. Then, the toric code MoC on the triangular lattice provides us a suitable playground to clarify the mutual relationship between the TEE, spontaneous symmetry breaking of the 1-form symmetries, and emergence of logical operators. Obtained results indicate that toric code MoC on the triangular lattice exhibits a few distinct phase transitions with different location and critical exponents, and some of them are closely related with the two-dimensional percolation transition.

quant-ph↗

arXiv2025

Edge bits in average symmetry protected topological mixed state

Edge bit in an average symmetry protected topological (ASPT) mixed state is studied. The state is protected by one strong $Z_2$ and one weak (average) $Z_2$ symmetries. As analogous objects of pure symmetry protected topological (SPT) states, the ASPT possesses edge bits. In particular, the analogous operator response exists, that is, symmetry fractionalization. The fractionalization preserves the presence of the ASPT in the bulk, and the fractionalized edge operators acting on the edge bits of the ASPT. %analogous to the ones in the pure SPTs. In this work, based on the cluster model and by employing Choi mapping, we discuss generic features of the edge bits and numerically clarify the behavior of the edge bits and their robustness for varying decoherence and perturbative interactions. By using an operator-space mutual information (OSMI), we track the flow of quantum correlations between the two edges. Remarkably, even in the ASPT regime, a finite portion of the initial edge-to-edge correlation survives.

quant-ph↗

arXiv2025

Mixed-state phase structure of gauge-Higgs subsystem codes under logical-preserving decoherence

Some of lattice-gauge-theory models, in particular gauge-Higgs model (GHM), can be regarded and work as a subsystem code. This work studies the effect of local-gauge-symmetric decoherence on the GHM from the perspective of the subsystem code. We clarify the global phase diagram of the subsystem code. In particular, the decoherence induces an unconventional critical mixed state, where the logical information is preserved but the rest of the system exhibits mixed state criticality. For a fixed point, the decohered subsystem code is understood by the ``gauging out" prescription. By mapping the GHM to the toric code subject to decoherence, we can understand the properties of the subsystem code. We further discuss and investigate the robustness of the logical space of the subsystem code. Although this kind of subsystem code can be produced by using any bulk mixed state in the GHM, its robustness is a subtle problem due to the mixed critical gauge qubits. We consider some specific unitary for examining the robustness of the stored quantum information. For dynamical unitary perturbations described by interactions between the logical qubit and gauge qubits, the deformation of the subsystem code drastically depends on the initial mixed state of the gauge qubits.

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arXiv2025

System-environmental entanglement in critical spin systems under $ZZ$-decoherence and its relation to strong and weak symmetries

Open quantum many-body systems exhibit nontrivial behavior under decoherence. In particular, system-environmental entanglement (SEE) is one of the efficient quantities for classifying mixed states subject to decoherence. In this work, we investigate the SEE of critical spin chains under nearest-neighbor $ZZ$-decoherence. We numerically show that the SEE exhibits a specific scaling law, in particular, its system-size-independent term (``$g$-function'') changes drastically its behavior in the vicinity of phase transition caused by decoherence. For the XXZ model in its gapless regime, a transition diagnosed by strong Rényi-2 correlations occurs as the strength of the decoherence increases. We determine the location of the phase transition by investigating the $g$-function that exhibits a sharp change in the critical region of the transition. Furthermore, we find that the value of the SEE is twice that of the system under single-site $Z$-decoherence, which was recently studied by conformal field theory. From the viewpoint of Rényi-2 Shannon entropy}, which is closely related to the SEE at the maximal decoherence, we clarify the origin of this $g$-function behavior.

quant-ph↗

arXiv2025

Succession of Ising criticality and its threshold in critical quantum Ising model subject to symmetric decoherence

We investigate a mixed state quantum criticality in the Ising model under $X+ZZ$ decoherence. In the doubled Hilbert space formalism, the decohered state resides on the self-dual critical line of the quantum Ashkin-Teller (qAT) model, as a result of the specific choice of the decoherence channel. On the other hand, since the mixed state under $X+ZZ$ decoherence satisfies the Kramers-Wannier self-duality in a weak sense, the Ising criticality of the pure state can be partially preserved in the mixed system. By making use of the combination of the doubled Hilbert space formalism and matrix product states, we carry out extensive numerical study to elucidate the mixed state criticality. We find that under decoherence up to moderate strength, the mixed states on the critical line have properties of the Ising CFT, where $c=1/2$, $η=0.25$ and, $ν=1$. These values of the central charge and critical exponents contrast with the ones in the $c=1$ orbifold boson CFT describing the critical state of the qAT model. In addition, we also observe the threshold of the mixed Ising CFT. The strong decoherence washes out the remnant Ising criticality and induces strong-to-weak spontaneous symmetry breaking.

quant-ph↗

arXiv2025

Disordered purification phase transition in hybrid random circuits

Noise is inevitable in realistic quantum circuits. It arises randomly in space. Inspired by spatial non-uniformity of the noise, we investigate the effects of spatial modulation on purification phase transitions in a hybrid random Clifford circuit. As an efficient observable for extracting quantum entanglement in mixed states, we employ many-body negativity. The behavior of the many-body negativity well characterizes the presence of the purification phase transitions and its criticality. We find the effect of spatial non-uniformity in measurement probability on purification phase transition. The criticality of the purification phase transition changes from that of uniform probability, which is elucidated from the argument of the Harris criterion. The critical correlation length exponent $ν$ changes from $ν< 2$ for uniform probability to $ν> 2$ for spatially modulated probability. We further investigate a setting where two-site random Clifford gate becomes spatially (quasi-)modulated. We find that the modulation induces a phase transition, leading to a different pure phase where a short-range quantum entanglement remains.

quant-ph↗

arXiv2025

Rényi and Shannon mutual information in critical and decohered critical system

We investigate a critical many-body system by introducing a Rényi generalized mutual information, connecting between Rényi mutual information and Rényi Shannon mutual information. This Rényi generalized mutual information can offer more experimentally accessible alternative than the conventional entanglement entropy. As a critical many-body state, we focus on the critical transverse-field Ising model (TFIM) described by the Ising conformal field theory (CFT). We show that even if we modify the non-selective projective measurement assumed in Rényi Shannon mutual information by replacing the measurement into decoherence by environment, the Rényi generalized Shannon mutual information maintains the CFT properties such as subsystem CFT scaling law and its central charge observed through both the conventional Rényi Shannon mutual information and Rényi mutual information. Furthermore, we apply a local decoherence to the critical ground state of the TFIM and numerically observe the Rényi generalized mutual information by changing the parameter controlling environment effect (corresponding to the strength of measurement) in the Rényi generalized mutual information and the strength of the decoherence to which the entire system subjects. We find that Rényi-$2$ type central charge connected to the central charge is fairly robust, indicating the strong robustness of the Ising CFT properties against local decoherence by environment.

quant-ph↗

arXiv2025

Rényi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions

Discovering and classifying non-trivial mixed states and mixed state phase transitions are some of the most important current issues in condensed matter and quantum information. In this study, we investigate some non-trivial mixed states and phase transitions between them by using the second Rényi conditional mutual information (CMI). The CMI can measure mixed state ``gap'', estimated by the exponential decay rate of the second Rényi CMI under a tripartition of system, which provides the second Rényi version of the Markov length. We introduce an efficient numerical scheme for the calculation of the second Rényi CMI based on the doubled Hilbert space formalism, and study the classification of non-trivial mixed states and the emergence of mixed state phase transitions for (i) the cluster model under odd-site local $Z$ decoherence and (ii) transverse field Ising model under both $ZZ$ and $X$ decoherence. The second Rényi CMI is a powerful measure to study non-trivial mixed ``gapped" quantum matters and mixed phase transitions. In addition to this, the present study shows that the second Rényi CMI exhibits specific behavior for the transition to strong-to-weak spontaneous symmetry breaking mixed phase.

quant-ph↗

arXiv2025

Topological pump and its plateau transitions of $N$-leg spin ladder

A topological pump on an $N\textrm{-}$leg spin ladder is discussed by introducing spatial clusterization whose adiabatic limit is a set of $2N\textrm{-}$site staircase clusters. We set a pump path in the parameter space that connects two different symmetry protected topological phases. By introducing a symmetry breaking staggered magnetic field, the system is always gapped during the pump. In the topological pump {thus obtained}, the bulk Chern number is given by the number of the critical points enclosed by the pump path. Plateau transitions characterized by the Chern number are demonstrated associated with deformation of the pump path. We find that there are $N$ critical points enclosed by the pump path for the $N\textrm{-}$leg ladder. The ground state phase diagram without symmetry breaking terms is numerically investigated by using the quantized Berry phase. We also discuss the physical picture of edge states in the diagonal boundary, and numerically demonstrate the bulk-edge correspondence for $N=2,3$ cases.

cond-mat.stat-mech↗

arXiv2025

Strong-to-weak spontaneous symmetry breaking and average symmetry protected topological order in the doubled Hilbert space

Discovering and categorizing quantum orders in mixed many-body systems are currently one of the most important problems. Target model in this study is an extended version of the cluster model in one dimension with $Z_2\otimes Z_2$ symmetry, and we investigate effects of decoherence applied to the ground state of the model, focusing on the symmetry aspect. By using a scheme that we propose, a strong symmetry protected topological (SPT) mixed state and double average SPT (ASPT) state are constructed through the pure gapless SPT order and the domain-wall duality. Among them, the double ASPT is categorized by coexisting orders, i.e., a strong-to-weak spontaneous symmetry breaking and ASPT defined by the remaining weak and strong symmetries. We make use of the doubled Hilbert space formalism for the construction scheme. We numerically demonstrate the emergence of the two mixed SPT states and find that a phase transition occurs between them tuned by the strength of decoherence. Finally, we discuss the coexistence of SPT and SWSSB in the double SPT state from the view point of symmetrically invertible property, and comment on the classification of ASPT proposed recently. Suitable multiple-decoherence channel applied to SPT states gives a broad possibility to induce rich ASPTs, possessing non-trivial internal entanglement properties from the view of doubled Hilbert space formalism.

quant-ph↗

arXiv2025

Intrinsic mixed state topological order in a stabilizer system under stochastic decoherence: Strong-to-weak spontaneous symmetry breaking from percolation point of view

Discovering quantum orders in mixed many-body systems is an ongoing issue. Very recently, the notion of an intrinsic mixed state topologically-ordered (IMTO) state was proposed. As a concrete example, we observe the emergence of IMTO by studying the toric code system under stochastic maximal decoherence by $ZX$-diagonal type projective measurement without monitoring. We study how the toric code state changes to an IMTO state at the level of the averaged quantum trajectories. This phase transition is understood from the viewpoint of spontaneous symmetry breaking (SSB) of 1-form weak symmetry, that is, the IMTO is characterized by the symmetry restoration from the SSB, which comes from the proliferation of anyons. To understand the emergent IMTO, order and disorder parameters of 1-form symmetry are numerically studied by stabilizer simulation. The present study clarifies the existence of two distinct microscopic string operators for the fermionic anyons, that leads to distinct fermionic strong and weak 1-form symmetries, and also the obtained critical exponents indicate strong relation between IMTO and percolation.

quant-ph↗

arXiv2025

Strong and weak symmetries and their spontaneous symmetry breaking in mixed states emerging from the quantum Ising model under multiple decoherence

Discovering and categorizing quantum orders in mixed many-body systems are currently one of the most important problems. Specific types of decoherence applied to typical quantum many-body states can induce a novel kind of mixed state accompanying characteristic symmetry orders, which has no counterparts in pure many-body states. We study phenomena generated by interplay between two types of decoherence applied to the one-dimensional transverse field Ising model (TFIM). We show that in the doubled Hilbert space formalism, the decoherence can be described by filtering operation applied to matrix product states (MPS) defined in the doubled Hilbert system. The filtering operation induces specific deformation of the MPS, which approximates the ground state of a certain parent Hamiltonian in the doubled Hilbert space. In the present case, such a parent Hamiltonian is the quantum Ashkin-Teller model, having a rich phase diagram with a critical lines and quantum phase transitions. By investigating the deformed MPS, we find various types of mixed states emergent from the ground states of the TFIM, and clarify phase transitions between them. In that study, strong and weak $Z_2$ symmetries play an important role, for which we introduce efficient order parameters, such as Rényi-2 correlators, entanglement entropy, etc., in the doubled Hilbert space.

quant-ph↗

arXiv2024

Topological domain-wall pump with $\mathbb{Z}_2$ spontaneous symmetry breaking

A domain-wall pump by an extended cluster model of $S=1/2$ spins is proposed with local $U(1)$ gauge invariance. Its snapshot ground state is gapped and doubly degenerated due to $\mathbb{Z}_2$ invariance, which is broken by an infinitesimal boundary magnetic field. The ground state associated with the spontaneous symmetry breaking (SSB) is still symmetry-protected with additional spatial inversion that is characterized by the $\mathbb{Z}_2$ Berry phase. We investigate the topological domain-wall pump with/without boundaries. The topological pump associated with the inversion symmetry-breaking path induces a non-trivial Chern number of bulk and a singular behavior of edge states of the domain-wall. Generalization to the multi-spin interaction is also explicitly given.

cond-mat.str-el↗

arXiv2024

Strong-to-weak symmetry breaking states in stochastic dephasing stabilizer circuits

Discovering mixed state quantum orders is an on-going issue. Recently, it has been recognized that there are (at least) two kinds of symmetries in the mixed state; strong and weak symmetries. Under symmetry-respective decoherence, spontaneous strong-to-weak symmetry breaking (SSSB) can occur. This work provides a scheme to describe SSSB and other decoherence phenomena in the mixed state by employing the stabilizer formalism and the efficient numerical algorithm of Clifford circuits. We present two systematic numerical studies.In a two-dimensional (2D) circuit with a stochastic Ising type decoherence, an SSSB phase transition is clearly observed and its criticality is elucidated by the numerical methods. In particular, we calculate Rényi-2 correlations and estimate critical exponents of the SSSB transition. For the second system, we introduce an idea of subgroup SSSB. As an example, we study a system with symmetry-protected-topological (SPT) order provided by both one-form and zero-form symmetries, and observe how the system evolves under decoherence. After displaying numerical results, we show that viewpoint of percolation is quite useful to understand the SSSB transition, which is applicable for a wide range of decohered states. Finally, we comment on SSSB of one-form-symmetry exemplifying toric code.

quant-ph↗

arXiv2024

Hierarchy of emergent cluster states by measurement from symmetry-protected-topological states with large symmetry to subsystem cat state

We propose {\it measurement-producing hierarchy} emerging among correlated states by sequential subsystem projective measurements. We start from symmetry-protected-topological (SPT) cluster states with a large symmetry and apply sequential subsystem projective measurements to them and find that generalized cluster SPT states with a reduced symmetry appear in the subsystem of the unmeasured sites. That prescription finally produces Greenberger-Home-Zeilinger states with long-range order in the subsystem composed of periodic unmeasured sites of the original lattice. The symmetry-reduction hierarchical structure from a general large symmetric SPT cluster state is clearly captured by the measurement update flow in the efficient algorithm of stabilizer formalism. This approach is useful not only for the analytical search for the measured state but also for numerical simulation with a large system size. We also numerically verify the symmetry-reduction hierarchy by sequential subsystem projective measurements applied to large systems and large symmetric cluster SPT states.

cond-mat.stat-mech↗