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arXiv quant-ph/0505213quant-ph
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纠缠和一个量子比特的力量

Entanglement and the Power of One Qubit

Animesh Datta, Steven T. Flammia, Carlton M. Caves

摘要:

“一个量子比特的幂”指的是一个计算模型,它只能访问量子信息的一个纯比特,以及完全混合状态的n个量子比特。这个模型虽然没有纯态量子计算机那么强大,但能够比任何已知的经典算法以指数级的速度执行某些计算任务。一个这样的任务是以固定精度估计可以在量子线路中有效实现的么正算子的归一化迹。我们表明,这种类型的电路通常会导致纠缠态,我们调查的纠缠量可能在这样的电路,作为衡量的乘负。我们表明,乘法负性是有界的常数,独立于n,所有的二分司的n+1量子比特,因此成为,当n是大的,一个消失的小部分的最大可能的乘法负性大致相等的划分。这表明纠缠的全局性质是量子计算的一个比纠缠的大小更重要的资源。

英文摘要:

The "Power of One Qubit" refers to a computational model that has access to only one pure bit of quantum information, along with n qubits in the totally mixed state. This model, though not as powerful as a pure-state quantum computer, is capable of performing some computational tasks exponentially faster than any known classical algorithm. One such task is to estimate with fixed accuracy the normalized trace of a unitary operator that can be implemented efficiently in a quantum circuit. We show that circuits of this type generally lead to entangled states, and we investigate the amount of entanglement possible in such circuits, as measured by the multiplicative negativity. We show that the multiplicative negativity is bounded by a constant, independent of n, for all bipartite divisions of the n+1 qubits, and so becomes, when n is large, a vanishingly small fraction of the maximum possible multiplicative negativity for roughly equal divisions. This suggests that the global nature of entanglement is a more important resource for quantum computation than the magnitude of the entanglement.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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