高斯费米子态中通过单占据测量实现的精确纠缠交换
Exact Entanglement Swapping through Single-Occupancy Measurements in Gaussian Fermion States
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中文总结 AI 辅助
该研究在半填充自由费米子高斯态的两个副本上，通过测量对应梯级并后选择单费米子态，得出未测量部分的纠缠熵与初始态无关，成功概率仅取决于初始关联，等权重贝尔后选择可实现最大纠缠交换。
中文摘要 AI 辅助
我们确定了如下条件态的精确纠缠结构：对任意半填充自由费米子高斯态的两个相同副本中的m个对应梯级（m≤N/2）进行测量，并在每个梯级上后选择相同的归一化单费米子态（|ψ⟩=u|10⟩+v|01⟩，其中0和1表示每个位点上的费米子占据数）。当m<N/2时，条件波函数通常依赖于初始态；但只要所选结果具有非零概率，未测量位点上的态仍保持高斯性，并精确分解为N-m个不同的正交模式，包括m个副本间纠缠模式和N-2m个局域在单个副本中的旁观模式。因此，两个副本未测量部分之间的纠缠熵为S=m h₂(|v|²)，与初始态无关，其中h₂(x)=-x ln x-(1-x) ln(1-x)。成功概率由Pₘ=det C_L det(Iₘ-C_L)=det(C_LR C_RL)给出，仅取决于初始关联，与(u,v)无关。等权重贝尔后选择是实现最大纠缠交换的特殊情况。
英文摘要
We determine the exact entanglement structure of the conditional state obtained by measuring $m$ corresponding rungs ($m\leq N/2$) in two identical copies of an arbitrary half-filled free fermion Gaussian state and post-selecting the same normalized single-fermion state ($|ψ\rangle = u|10\rangle+v|01\rangle$, where 0 and 1 denote the fermion occupancy on each sites) on each rung. For $m<N/2$, the conditional wavefunction generally depends on the initial state. Nevertheless, whenever the selected outcome has nonzero probability, the state on the unmeasured sites remains Gaussian and factorizes exactly into $N-m$ different orthogonal modes including $m$ inter-copy entangling modes and $N-2m$ spectator modes localized in one copy. Consequently, the entanglement entropy between the unmeasured parts of the two copies is $S=m h_2(|v|^2)$, independent of the initial state, where $h_2(x)=-x\ln x-(1-x)\ln(1-x)$. The success probability is given by $P_m=\det C_L\det(I_m-C_L)=\det(C_{LR}C_{RL})$, determined solely by the initial correlations and independent of ($u$,$v$). Equal-weight Bell post-selection serves as a special case that achieves the maximal entanglement swapping.
发表机构
- School of Physics, Georgia Institute of Technology（佐治亚理工学院物理学院）
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