全息码中与状态相关的原区域的认证边界魔法见证
Certified boundary-magic witness for state-dependent proto-area in a holographic code
AI总结：
研究四量子比特乘积-EPR全息码，通过七种变形比较相关算子，利用优化相干信息选择物理恢复，通过半定规划最大化纠缠保真度，建立有限码见证，揭示了与状态相关的原区域及边界见证的相关特性。
AI中文摘要：
我们研究了一种四量子比特乘积-EPR全息码，其重构区域包含物质和几何键的一条腿。通过七种变形比较局部、二分、键稳定和键移动算子。精确光谱表明，只有物质控制的键运动产生边界熵的主导二次逻辑态依赖性。我们通过优化通道Choi态的相干信息选择一种与状态无关的物理恢复。一个单独的半定规划在所有通道上最大化纠缠保真度。在固定耦合下，物理恢复在数值精度上达到最优，而恢复熵减法留下非零的变分原区域响应。对于无边界响应的变形，总稳定器Renyi魔法也非零，因此它不能表征这种效应。从成对的泡利切线投影精确的稳定器-Renyi二次形式定义了一个主导阶边界见证。其全局凸最小值对于键移动变形为正，对于六种比较为零。然而，对于参考物质-几何资源划分，成对切线在乘积-EPR基处跨越整个射影切线空间，因此见证对于每个厄米变形都消失。双边界扩展保留了这种简并性，但表现出分裂几何结构残余和逻辑态相关的切割开关。这些结果建立了一个有限码见证，而不是一个通用的魔法定律或连续体引力动力学。
英文摘要：
We study a four-qubit product-EPR holographic code whose reconstructing region contains matter and one leg of a geometry bond. Seven deformations compare local, bipartite, bond-stabilizing, and bond-moving operators. Exact spectra show that only matter-controlled bond motion produces a leading quadratic logical-state dependence of the boundary entropy. We select one state-independent physical recovery by optimizing coherent information of the channel Choi state. A separate semidefinite program maximizes entanglement fidelity over all channels. At fixed coupling the physical recovery attains that optimum to numerical precision, while recovered-entropy subtraction leaves a nonzero variational proto-area response. Total stabilizer Renyi magic is also nonzero for deformations with no boundary response, so it does not characterize the effect. Projecting the exact stabilizer-Renyi quadratic form away from pairwise Pauli tangents defines a leading-order boundary witness. Its global convex minimum is positive for the bond-moving deformation and zero for the six comparisons. For the reference-matter-geometry resource partition, however, pairwise tangents span the full projective tangent space at the product-EPR base, so the witness vanishes for every Hermitian deformation. A two-bound extension retains this degeneracy but exhibits a split-geometry structural residual and a logical-state-dependent cut switch. These results establish a finite-code witness, not a universal magic law or continuum gravitational dynamics.
