We investigate the impact of Hilbert-space truncation upon the entanglement of an initially maximally entangled m × m bipartite quantum state, after propagation under an entanglement-preserving n × n ( n ⩾ m ) unitary. Truncation—physically enforced, e.g., by a detector’s finite cross section—projects the state onto an s × s -dimensional subspace (3 ⩽ s ⩽ n ). For a random local unitary evolution, we obtain a simple analytical formula that expresses the truncation-induced entanglement loss as a function of n , m and s .

中文翻译：

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截断量子态的纠缠

我们研究了希尔伯特空间截断对初始最大纠缠m×m二分量子态在纠缠保持n×n（n⩾m）ary传播后的影响。截断（例如通过检测器的有限横截面物理地强制执行）将状态投影到s×s维子空间（3 s s n）上。对于随机局部unit演化，我们获得一个简单的解析公式，该公式将截断引起的纠缠损失表示为n，m和s的函数。