研究発表

A quantum channel described by a CPTP map generally turns a pure quantum state into a mixed state, which can be viewed as development of system-environment entanglement. We study a phase transition in the system-environment Renyi entanglement entropy (EE) when the XXZ chain with open boundary conditions is subject to continuous density measurements. We show that the EE exhibits a volume law followed by a subleading logarithmic term; the coefficient of the latter changes from 0 to 1/4 as a function of the measurement strength. We also study the expectation value of a certain twist operator in the doubled Hilbert space formalism, that is expected to detect the phase transition. We compare our results with previous results for the periodic boundary condition as well as the boundary renormalization group analysis.

We study how quantum measurements can transform quantum phases in spin ladder systems through an entanglement swapping protocol. Consecutive Bell measurements are performed between the legs of two independent ladders, followed by uniform post-selection of the measurement outcomes. We analyze the resulting phase realized in the unmeasured outer legs. Our analysis is based on topological indices protected by the D_2=Z_2×Z_2 spin rotational symmetry as well as the lattice translation symmetry. We find that these indices remain unchanged through the measurement process, leading to a nontrivial inheritance rule. Namely, the output state is topological if only one of the ladders is initially topological, while it becomes trivial if both are. To illustrate this, we explicitly construct post-measurement states using matrix product states (MPS), in which the rung singlet (trivial) and Haldane (SPT) phases are represented by a product of singlets and a valence bond solid state, respectively. The MPS results are consistent with the index characterization and further reveal that the correlation length increases after measurement, indicating enhanced fluctuations. Finally, we perform a field-theoretical analysis using bosonization. By identifying the locking positions of bosonic fields associated with string order parameters, we determine the resulting phase and confirm consistency with both the index argument and MPS analysis. Interestingly, the post-measurement correlation length is approximately equal to the sum of those before measurement.

A quantum channel described by a CPTP map generally turns a pure quantum state into a mixed state, which can be viewed as development of system-environment entanglement. We study a phase transition in the system-environment Renyi entanglement entropy (EE) when the XXZ chain with open boundary conditions is subject to continuous density measurements. We show that the EE exhibits a volume law followed by a subleading logarithmic term; the coefficient of the latter changes from 0 to 1/4 as a function of the measurement strength. We also study the expectation value of a certain twist operator in the doubled Hilbert space formalism, that is expected to detect the phase transition. We compare our results with previous results for the periodic boundary condition as well as the boundary renormalization group analysis. All the work are done by the numerical calculation.

Quantum operations that involve measurements generally turn a pure quantum state into a mixed state, which can be viewed as development of system-environment entanglement. We study a phase transition in the system-environment Renyi entanglement entropy (EE) when a Tomonaga-Luttinger liquid (TLL) is subject to continuous density measurements [1,2]. We show that the EE exhibits a volume law followed by a universal subleading constant or logarithmic term for periodic and open boundary conditions, respectively. We develop a field-theoretical description to relate the universal constant to the effective boundary degeneracy g in boundary conformal field theory. We show that the universal constant is determined by the TLL parameter K and exhibits a phase transition as a function of the measurement strength, which separates cohered and decohered phases. For open boundary conditions, the coefficient of the logarithmic term in the EE exhibits a similar transition, and this coefficient is closely related to the geometry-dependent contribution in the Cardy-Peschel free energy formula. We also study the expectation value of a certain twist operator in the doubled Hilbert space formalism, which also detects the phase transition. Possible experimental realization in ultracold gases is discussed.

The concept of symmetry-protected topological (SPT) phases has been proposed and extensively developed over the past 15 years. While bosonic SPT phases in one spatial dimension is fully classified by projective representations of the symmetry group, it is interesting to examine when nontrivial SPT phases emerge and how they compete with conventional ordered phases in concrete physical systems. Here we explore this issue in spin-1/2 XXZ ladders with four-spin interactions. We find that weak XXZ anisotropy crucially affects the phase structure, inducing SPT phases in the easy-plane regime and magnetic and chiral ordered phases in the easy-axis regime. The SPT phases identified here can be regarded as twisted variants of the well-known Haldane phase, and are distinguished by topological indices linked to the system's symmetries. Motivated by the deepening interplay between quantum magnetism and quantum information, we further explore a many-body extension of the entanglement swapping protocol, in which entangled spin pairs are replaced by quantum phases of spin-1/2 ladders. We show that Bell measurements performed between legs of topological and trivial ladder states, followed by postselection of uniform outcomes, lead to the generation of a topological state on the unmeasured legs.

近年、量子測定が量子多体系に与える影響に広く関心が集まっている。本研究ではその一例として、二つのスピン梯子系に対してエンタングルメントスワッピングを施し、測定後に実現される量子相の特定を試みる。具体的には、独立な二つのスピン梯子系の各脚にベル測定を行い、測定結果が一様となるよう事後選択を行った上で、直接測定を施していない梯子の脚に現れる状態が属する相を解析する。スピン梯子系は、トポロジカル相（Haldane 相）や自明相（rung singlet 相; RS 相）を実現するだけでなく、異方性や多体相互作用の導入によって多彩な相構造を示す。これらの相は局所的な秩序変数では検出できないが、特定の対称性を課している限り、トポロジカル指数を用いて区別することが可能である。本研究では、離散的なスピン回転対称性D2=Z2 X Z2 と並進対称性に保護された三つのトポロジカル指数に注目し、二系の合成系における指数が測定前後で不変であるという事実を基に、測定後の相の同定を行った。この議論は一般的であるが、測定後の状態の詳細が不明であるため、行列積状態（matrix product state; MPS）およびボソン化による具体的な解析も実施した。MPS を用いた解析では、Haldane 相の代表例であるvalence bond solid 状態がMPS で表現できることを利用し、測定後の状態を明示的に構成してトポロジカル指数を評価した。その結果は、トポロジカル指数のみに基づく一般的議論と整合的であり、さらに転送行列の解析を通じて、測定後の状態では相関長が増加する傾向も確認された。一方、ボソン化の枠組みでは、RS 相やHaldane 相などのギャップのある状態は、有効ハミルトニアン中のcos 項によってボソン場がロックされることに対応し、ロックされる場の種類や位置がストリング秩序変数と密接に関係することを用いた。ボソン化した有効ハミルトニアンの基底状態を求め、測定後の状態を計算し、ボソン場がロックされる位置を解析することで測定後に実現される相を特定した。ボソン化による結果も、トポロジカル指数やMPS を用いた解析と整合する。更に、測定後の状態の相関長が、測定前の各梯子の相関長の和で与えられることを解析的に導出し、MPS により観測された相関長の増加を説明した。

We study how quantum measurements can transform quantum phases in spin ladder systems through an entanglement swapping protocol. Consecutive Bell measurements are performed between the legs of two independent ladders, followed by uniform post-selection of the measurement outcomes. We analyze the resulting phase realized in the unmeasured outer legs. Our analysis is based on topological indices protected by the D_2=Z_2×Z_2 spin rotational symmetry as well as the lattice translation symmetry. We find that these indices remain unchanged through the measurement process, leading to a nontrivial inheritance rule. Namely, the output state is topological if only one of the ladders is initially topological, while it becomes trivial if both are. To illustrate this, we explicitly construct post-measurement states using matrix product states (MPS), in which the rung singlet (trivial) and Haldane (SPT) phases are represented by a product of singlets and a valence bond solid state, respectively. The MPS results are consistent with the index characterization and further reveal that the correlation length increases after measurement, indicating enhanced fluctuations. Finally, we perform a field-theoretical analysis using bosonization. By identifying the locking positions of bosonic fields associated with string order parameters, we determine the resulting phase and confirm consistency with both the index argument and MPS analysis., Interestingly, the post-measurement correlation length is approximately equal to the sum of those before measurement.

We study how quantum measurements can transform quantum phases in spin ladder systems through an entanglement swapping protocol. Consecutive Bell measurements are performed between the legs of two independent ladders, followed by uniform post-selection of the measurement outcomes. We analyze the resulting phase realized in the unmeasured outer legs. Our analysis is based on topological indices protected by the D_2=Z_2×Z_2 spin rotational symmetry as well as the lattice translation symmetry. We find that these indices remain unchanged through the measurement process, leading to a nontrivial inheritance rule. Namely, the output state is topological if only one of the ladders is initially topological, while it becomes trivial if both are. To illustrate this, we explicitly construct post-measurement states using matrix product states (MPS), in which the rung singlet (trivial) and Haldane (SPT) phases are represented by a product of singlets and a valence bond solid state, respectively. The MPS results are consistent with the index characterization and further reveal that the correlation length increases after measurement, indicating enhanced fluctuations. Finally, we perform a field-theoretical analysis using bosonization. By identifying the locking positions of bosonic fields associated with string order parameters, we determine the resulting phase and confirm consistency with both the index argument and MPS analysis., Interestingly, the post-measurement correlation length is approximately equal to the sum of those before measurement.

A quantum channel described by a CPTP map generally turns a pure quantum state into a mixed state, which can be viewed as development of system-environment entanglement. We study a phase transition in the system-environment Renyi entanglement entropy (EE) when the XXZ chain with open boundary conditions is subject to continuous density measurements. We show that the EE exhibits a volume law followed by a subleading logarithmic term; the coefficient of the latter changes from 0 to 1/4 as a function of the measurement strength. We also study the expectation value of a certain twist operator in the doubled Hilbert space formalism, that is expected to detect the phase transition. We compare our results with previous results for the periodic boundary condition as well as the boundary renormalization group analysis.