arXiv 0810.27802008-10quant-ph

隐藏基中的通用量子计算

Universal quantum computation in a hidden basis

Lawrence M. Ioannou, Michele Mosca

备注：: final version
发表信息：: Quantum Information and Computation, Vol. 10, No. 7&8, 0541-0561 (2010)

摘要：

假设$\ket{\0}$和$\ket{\1}$是两个状态，它们被保证来自正交子空间的已知子集，但在其他方面是未知的。我们的论文探讨的问题，可以实现的基础$\{\ket{\0},\ket{\1}}^{\otimes n}$的$n$逻辑量子比特，给定只有几个副本的未知状态$\ket{\0}$和$\ket{\1}$。相位不变算子是在所有$n$量子位的相对相移$\ket{\1} \mapsto e^{i θ}\ket{\1}$下对于任何$θ$不变的算子。我们表明，相位不变的酉算子可以实现完全没有副本，相位不变的状态可以准备最多的$n$副本$\ket{\0}$和$\ket{\1}$，我们给了一个明确的算法状态准备，是有效的某些类别的状态（如对称状态）。我们推测，某些非相位不变的操作是不可能准确地执行没有许多副本。受量子计算机的光学实现的启发，我们定义“隐基中的量子计算”是指对于某些潜在未知的$θ$，相对于相移隐基$\{\ket{\0}, e^{iθ}\ket{\1}\}$执行量子算法;我们给出了一个有效的近似算法，为此我们引入了光的相干态的模拟，其用作编码$θ$的有界量子相位参考系。我们的动机是量子公钥密码学，然而这些技术是通用的。我们将我们的结果应用到量子公钥认证协议，通过证明经典消息的自然类数字签名方案是不安全的。我们还给出了一个协议的识别，使用了许多讨论的想法，其安全性与我们的猜想（但我们不知道它是否是安全的）。

英文摘要：

Let $\ket{\0}$ and $\ket{\1}$ be two states that are promised to come from known subsets of orthogonal subspaces, but are otherwise unknown. Our paper probes the question of what can be achieved with respect to the basis $\{\ket{\0},\ket{\1}}^{\otimes n}$ of $n$ logical qubits, given only a few copies of the unknown states $\ket{\0}$ and $\ket{\1}$. A phase-invariant operator is one that is unchanged under the relative phase-shift $\ket{\1} \mapsto e^{i θ}\ket{\1}$, for any $θ$, of all of the $n$ qubits. We show that phase-invariant unitary operators can be implemented exactly with no copies and that phase-invariant states can be prepared exactly with at most $n$ copies each of $\ket{\0}$ and $\ket{\1}$; we give an explicit algorithm for state preparation that is efficient for some classes of states (e.g. symmetric states). We conjecture that certain non-phase-invariant operations are impossible to perform accurately without many copies. Motivated by optical implementations of quantum computers, we define ``quantum computation in a hidden basis'' to mean executing a quantum algorithm with respect to the phase-shifted hidden basis $\{\ket{\0}, e^{iθ}\ket{\1}\}$, for some potentially unknown $θ$; we give an efficient approximation algorithm for this task, for which we introduce an analogue of a coherent state of light, which serves as a bounded quantum phase reference frame encoding $θ$. Our motivation was quantum-public-key cryptography, however the techniques are general. We apply our results to quantum-public-key authentication protocols, by showing that a natural class of digital signature schemes for classical messages is insecure. We also give a protocol for identification that uses many of the ideas discussed and whose security relates to our conjecture (but we do not know if it is secure).

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。

摘要：

英文摘要：

相关论文