Entanglement cost and quantum channel simulation
Entanglement cost and quantum channel simulation
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DOI：
10.1103/physreva.98.042338
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发表时间：
2018-07
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影响因子：
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通讯作者：
M. Wilde
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文献类型：
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作者：
M. Wilde
本文提出了量子通道 $\mathcal{N}$ 纠缠成本的修订定义。特别是，这里将其定义为除了自由经典通信之外，为了模拟对 $\mathcal{N}$ 的 $n$ 调用，所需纠缠的最小速率，使得最通用的判别器无法区分模拟中对 $\mathcal{N}$ 的 $n$ 调用。最通用的鉴别器是以顺序方式一个接一个地测试通道的鉴别器，这种鉴别器被称为量子测试器 [Chiribella et al., Phys.莱特牧师。 101, 060401 (2008)] 或正在实施量子策略的人 [Gutoski 和 Watrous，第 39 届 ACM 计算理论年度研讨会论文集 STOC '07（ACM Press，纽约，2007 年），第 565--574 页]。因此，拟议的量子通道纠缠成本的修订定义导致的速率不能小于先前的通道纠缠成本概念[Berta et al., IEEE Trans.信息。 Theory 59, 6779 (2013)]，其中鉴别器仅限于区分通道的并行使用与模拟。根据这个修改后的概念，我证明了某些可模拟隐形传输通道的纠缠成本等于其底层资源状态的纠缠成本。然后，我找到了一些基本通道模型的纠缠成本的单字母公式，包括移相、擦除、三维 Werner-Holevo 通道和外极化通道（去极化通道的互补），以及单模纯损耗和纯放大器玻色高斯通道。这些例子表明，量子通道纠缠的资源理论是不可逆的。最后，我讨论如何将基本概念推广到任意资源理论。
This paper proposes a revised definition for the entanglement cost of a quantum channel $\mathcal{N}$. In particular, it is defined here to be the smallest rate at which entanglement is required, in addition to free classical communication, in order to simulate $n$ calls to $\mathcal{N}$, such that the most general discriminator cannot distinguish the $n$ calls to $\mathcal{N}$ from the simulation. The most general discriminator is one who tests the channels in a sequential manner, one after the other, and this discriminator is known as a quantum tester [Chiribella et al., Phys. Rev. Lett. 101, 060401 (2008)] or one who is implementing a quantum costrategy [Gutoski and Watrous, in Proceedings of the Thirty-Ninth Annual ACM Symposium on Theory of Computing STOC '07 (ACM Press, New York, 2007), pp. 565--574]. As such, the proposed revised definition of entanglement cost of a quantum channel leads to a rate that cannot be smaller than the previous notion of a channel's entanglement cost [Berta et al., IEEE Trans. Inf. Theory 59, 6779 (2013)], in which the discriminator is limited to distinguishing parallel uses of the channel from the simulation. Under this revised notion, I prove that the entanglement cost of certain teleportation-simulable channels is equal to the entanglement cost of their underlying resource states. Then I find single-letter formulas for the entanglement cost of some fundamental channel models, including dephasing, erasure, three-dimensional Werner-Holevo channels, and epolarizing channels (complements of depolarizing channels), as well as single-mode pure-loss and pure-amplifier bosonic Gaussian channels. These examples demonstrate that the resource theory of entanglement for quantum channels is not reversible. Finally, I discuss how to generalize the basic notions to arbitrary resource theories.