arXiv 1809.095922018-09quant-phcs.ITmath.IT

保PPT操作下量子态和信道的精确纠缠代价

Exact entanglement cost of quantum states and channels under PPT-preserving operations

Xin Wang, Mark M. Wilde

备注：: v2: 29 pages, 8 figures, accepted for publication in Physical Review A
发表信息：: Physical Review A, vol. 107, no. 1, page 012429, January 2023
DOI：: 10.1103/PhysRevA.107.012429

摘要：

本文建立了在完全保持部分转置（PPT）正性的自由量子操作下模拟量子信道的精确纠缠代价的单字母公式。首先，基于二体态$κ$-纠缠的思想，我们引入了点到点量子信道的$κ$ -纠缠度量，并建立了它的几个基本性质，包括摊销坍缩、PPT超信道下的单调性、可加性、归一化性、忠实性和非凸性。其次，我们引入并解决了在并行和顺序设置下模拟量子信道的精确纠缠代价，以及自由的PPT保持操作的帮助。特别是，我们建立了在这两种情况下的纠缠成本是由相同的单字母公式，$κ$ -纠缠测量的量子信道。我们进一步表明，这个成本等于最大的$κ$纠缠，可以共享或产生的发送器和接收器的通道。这个公式是可计算的一个半定的程序，从而允许一个有效的计算解决方案，一般的量子信道。注意到顺序机制比并行机制更强大，我们的结果的另一个值得注意的含义是，当PPT超级通道是免费的时，这两种机制对于精确的量子信道模拟具有相同的功率。对于几个基本的高斯量子信道，我们证明了精确的纠缠代价由Holevo-Werner公式给出[Holevo和Werner，Phys.Rev.A63，032312（2001）]，给出了这些信道的Holevo-Werner量的操作意义。

英文摘要：

This paper establishes single-letter formulas for the exact entanglement cost of simulating quantum channels under free quantum operations that completely preserve positivity of the partial transpose (PPT). First, we introduce the $κ$-entanglement measure for point-to-point quantum channels, based on the idea of the $κ$-entanglement of bipartite states, and we establish several fundamental properties for it, including amortization collapse, monotonicity under PPT superchannels, additivity, normalization, faithfulness, and non-convexity. Second, we introduce and solve the exact entanglement cost for simulating quantum channels in both the parallel and sequential settings, along with the assistance of free PPT-preserving operations. In particular, we establish that the entanglement cost in both cases is given by the same single-letter formula, the $κ$-entanglement measure of a quantum channel. We further show that this cost is equal to the largest $κ$-entanglement that can be shared or generated by the sender and receiver of the channel. This formula is calculable by a semidefinite program, thus allowing for an efficiently computable solution for general quantum channels. Noting that the sequential regime is more powerful than the parallel regime, another notable implication of our result is that both regimes have the same power for exact quantum channel simulation, when PPT superchannels are free. For several basic Gaussian quantum channels, we show that the exact entanglement cost is given by the Holevo--Werner formula [Holevo and Werner, Phys. Rev. A 63, 032312 (2001)], giving an operational meaning of the Holevo-Werner quantity for these channels.

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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英文摘要：

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