Oliveira R, Dahlsten O C O, Plenio M B
IBM Watson Research Center, Yorktown Heights, NY 10598, USA.
Phys Rev Lett. 2007 Mar 30;98(13):130502. doi: 10.1103/PhysRevLett.98.130502.
We find that generic entanglement is physical, in the sense that it can be generated in polynomial time from two-qubit gates picked at random. We prove as the main result that such a process generates the average entanglement of the uniform (unitarily invariant) measure in at most O(N3) steps for N qubits. This is despite an exponentially growing number of such gates being necessary for generating that measure fully on the state space. Numerics furthermore show a variation cutoff allowing one to associate a specific time with the achievement of the uniform measure entanglement distribution. Various extensions of this work are discussed. The results are relevant to entanglement theory and to protocols that assume generic entanglement can be achieved efficiently.
我们发现，一般纠缠是物理性的，即它可以在多项式时间内由随机选取的两比特门生成。我们证明了主要结果：对于N个量子比特，这样的过程在至多O(N³)步内生成均匀（酉不变）测度的平均纠缠。尽管在状态空间上完全生成该测度需要指数增长数量的此类门。数值计算还显示了一个变化截止，使得能够将特定时间与均匀测度纠缠分布的实现相关联。本文讨论了这项工作的各种扩展。这些结果与纠缠理论以及假设可以有效实现一般纠缠的协议相关。
