论文标题
高斯行动的高斯州关键蒸馏的基本限制
Fundamental limitations to key distillation from Gaussian states with Gaussian operations
论文作者
论文摘要
我们建立了可以通过仅使用当地高斯行动，地方古典处理和公共交流来从量子高斯州提取的秘密密钥数量的基本上限。对于单向公共通信，或者允许双向公共交流，但爱丽丝和鲍勃首先执行破坏性的当地高斯测量值，我们证明，钥匙是由rényi-$ 2 $ 2 $高斯的形式纠缠$ e_ {f，2}^{\ scriptScriptScriptScriptScriptScriptScriptScriptScriptScriptStystyle g}} $。由于纯高斯州的不平等现象饱和，因此可以将纠缠的$ 2 $熵的操作解释作为纯高斯州的秘密关键率，可通过高斯操作和单向通信访问。在双向通信和任意交互式协议的一般设置中，我们认为$ 2 e_ {f，2}^{\ mathrm {\ scriptScriptScriptScriptstyle g}} $仍然是可提取键的上限。我们推测$ 2 $的因子是虚假的，这意味着$ e_ {f，2}^{\ mathrm {\ scriptscriptScriptStryle g}} $恰逢高斯州根据高斯测量值的高斯州的秘密关键利率和双向公众通信。我们使用这些结果来证明使用任意操作与高斯操作可获得的秘密密钥率之间存在差距。通过在足够低挤压或足够高的透射率的状态下，通过纯粹的损失通道发送一半的两种模式真空的状态，观察到这种差距。最后，对于包括所有两种模式状态的一系列高斯状态，我们证明了最近提出的关于$ e_ {f，2}^{\ mathrm {\ scriptscriptScriptStryStyle g}} $与高斯内在的内在纠缠之间的相等性的猜想。然后，从这种平等出现的统一纠缠量化量将以直接的操作解释为量子传送游戏的价值。
We establish fundamental upper bounds on the amount of secret key that can be extracted from quantum Gaussian states by using only local Gaussian operations, local classical processing, and public communication. For one-way public communication, or when two-way public communication is allowed but Alice and Bob first perform destructive local Gaussian measurements, we prove that the key is bounded by the Rényi-$2$ Gaussian entanglement of formation $E_{F,2}^{\mathrm{\scriptscriptstyle G}}$. Since the inequality is saturated for pure Gaussian states, this yields an operational interpretation of the Rényi-$2$ entropy of entanglement as the secret key rate of pure Gaussian states that is accessible with Gaussian operations and one-way communication. In the general setting of two-way communication and arbitrary interactive protocols, we argue that $2 E_{F,2}^{\mathrm{\scriptscriptstyle G}}$ is still an upper bound on the extractable key. We conjecture that the factor of $2$ is spurious, which would imply that $E_{F,2}^{\mathrm{\scriptscriptstyle G}}$ coincides with the secret key rate of Gaussian states under Gaussian measurements and two-way public communication. We use these results to prove a gap between the secret key rates obtainable with arbitrary versus Gaussian operations. Such a gap is observed for states produced by sending one half of a two-mode squeezed vacuum through a pure loss channel, in the regime of sufficiently low squeezing or sufficiently high transmissivity. Finally, for a wide class of Gaussian states that includes all two-mode states, we prove a recently proposed conjecture on the equality between $E_{F,2}^{\mathrm{\scriptscriptstyle G}}$ and the Gaussian intrinsic entanglement. The unified entanglement quantifier emerging from such an equality is then endowed with a direct operational interpretation as the value of a quantum teleportation game.
