完全单向自适应测量下的量子de Finetti定理
Quantum de Finetti theorem under fully-one-way adaptive measurements
摘要：
我们证明了量子de Finetti定理的一个版本：置换不变的量子态可以很好地近似为多重乘积态的概率混合。该近似是通过完全单向LOCC（本地操作和经典通信）测量下的可扩展性来测量的。我们的结果加强了Brandão和Harrow的de Finetti定理，其中一种部分单向LOCC测量用于测量近似，具有基本相同的误差界。作为主要的应用，我们显示（一）一个准多项式时间算法，检测多体纠缠量大于一个任意小的常数（测量与变量的相对熵的纠缠），及（二）证明，在量子梅林-阿瑟证明系统，多项式多证明是不是更强大的比一个单一的证明时，验证者被限制为单向LOCC操作。
英文摘要：
We prove a version of the quantum de Finetti theorem: permutation-invariant quantum states are well approximated as a probabilistic mixture of multi-fold product states. The approximation is measured by distinguishability under fully one-way LOCC (local operations and classical communication) measurements. Our result strengthens Brandão and Harrow's de Finetti theorem where a kind of partially one-way LOCC measurements was used for measuring the approximation, with essentially the same error bound. As main applications, we show (i) a quasipolynomial-time algorithm which detects multipartite entanglement with amount larger than an arbitrarily small constant (measured with a variant of the relative entropy of entanglement), and (ii) a proof that in quantum Merlin-Arthur proof systems, polynomially many provers are not more powerful than a single prover when the verifier is restricted to one-way LOCC operations.
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