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Bounds on Instantaneous Nonlocal Quantum Computation

机译：瞬时非局部量子计算上的界限

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Instantaneous nonlocal quantum computation refers to a process in which spacelike separated parties simulate a nonlocal quantum operation on their joint systems through the consumption of pre-shared entanglement. To prevent a violation of causality, this simulation succeeds up to local errors that can only be corrected after the parties communicate classically with one another. However, this communication is non-interactive, and it involves just the broadcasting of local measurement outcomes. We refer to this operational paradigm as local operations and broadcast communication (LOBC) to distinguish it from the standard local operations and (interactive) classical communication (LOCC). In this paper, we show that an arbitrary two-qubit gate can be implemented by LOBC with epsilon -error using {O}(log (1/epsilon)) entangled bits (ebits). This offers an exponential improvement over the best known two-qubit protocols, whose ebit costs behave as {O}(1/epsilon) . We also consider the family of binary controlled gates on dimensions {d}_{A}otimes {d}_{B} . We find that any hermitian gate of this form can be implemented by LOBC using a single shared ebit. In sharp contrast, a lower bound of log {d}_{B} ebits is shown in the case of generic (i.e. non-hermitian) gates from this family, even when {d}_{A}=2 . This demonstrates an unbounded gap between the entanglement costs of LOCC and LOBC gate implementation. Whereas previous lower bounds on the entanglement cost for instantaneous nonlocal computation restrict the minimum dimension of the needed entanglement, we bound its entanglement entropy. To our knowledge this is the first such lower bound of its kind.
机译：瞬时非局部量子计算是指通过消耗预共同的纠缠在其联合系统上模拟非读数量子操作的过程。为防止违反因果关系，此模拟成功达到当地错误，只能在各方彼此经典沟通后才能纠正。然而，这种通信是非交互式的，并且它涉及局部测量结果的广播。我们将此操作范例称为本地操作和广播通信（LOBC），以将其与标准本地操作和（交互式）经典通信（LOCC）区分开。在本文中，我们表明，使用{o}（ log（1 / epsilon））纠结位（ebits），通过LOBC与 epsilon -Error实现任意的双量标门。这提供了对最佳已知的双量标协议的指数改进，其EBIT成本表现为{O}（1 / epsilon）。我们还考虑尺寸上的二元控制栅栏{d} _ {a} otimes {d} _ {b}。我们发现这种形式的任何秘密人员门可以通过LOBC使用单个共享EBIT来实现。在对比度鲜明对比中，在来自该家庭的通用（即非封闭师）门的情况下，显示了 log {d} _ {b} Ebits的下限，即使{d} _ {a} = 2。这证明了LOCC和LOBC栅极实现的纠缠成本之间的无界差距。虽然之前的下限瞬时非识别计算的纠缠成本限制了所需纠缠的最小维度，我们绑定了纠缠熵。据我们所知，这是它的第一个如此较低的界限。

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