Sasha Sami, Indranil Chakrabarty
In a recent work, authors prove a yet another no-go theorem that forbids the existence of a universal probabilistic quantum protocol producing a superposition of two unknown quantum states. In this short note, we show that in the presence of closed time like curves, one can indeed create superposition of unknown quantum states and evade the no-go result.
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We examine Ralph's equivalent circuit model of D-CTCs, which was proposed to derive Deutsch's maximum entropy rule of D-CTCs. By constructing counterexamples we show that the equivalent circuit model does not always reproduce the unique fixed state with the maximal von Neumann entropy. We speculate that the equivalent circuit model remains the correct description of D-CTCs and it can reproduce a revised maximum entropy rule of D-CTCs. We also suggest that the revised maximum entropy rule may eliminate the discontinuous quantum evolutions of D-CTCs.
Eigenvalue Formulation of Quantum Mechanics Near Closed Timelike Curves
爱因斯坦的引力场方程是已知的承认封闭类时曲线（CTC）的解决方案。多伊奇从量子信息的角度来处理这个问题，并提出了一个自洽条件。在这项工作中，Deutsch方程制定为一个特征值问题。证明了在CTC附近的EPR态中两个量子比特之间的纠缠消失。利用该方法分析了CTC附近两个符合时序（CR）量子比特的不连续演化。
We consider causality respecting (CR) quantum systems interacting with closed timelike curves (CTCs), within the Deutsch model. We introduce the concepts of popping up and elimination of quantum information and use them to show that no-cloning and no-deleting, which are true in CR quantum systems, are no more valid in the same that are interacting with CTCs. We also find limits on the possibility of creation of entanglement between a CR system and a CTC, and the same between two CR systems in the presence of a CTC. We prove that teleportation of quantum information, even in its approximate ver…
I argue that Deutsch's model for the behavior of systems traveling around closed timelike curves (CTCs) relies implicitly on a substantive metaphysical assumption. Deutsch is employing a version of quantum theory with a significantly supplemented ontology of parallel existent worlds, which differ in kind from the many worlds of the Everett interpretation. Standard Everett does not support the existence of multiple identical copies of the world, which the D-CTC model requires. This has been obscured because he often refers to the branching structure of Everett as a "multiverse", and describes q…
Quantum state cloning using Deutschian closed timelike curves
我们证明，在Deutschian封闭类时曲线（D-CTC）的存在下，克隆量子态到任意精度是可能的，随着CTC系统的维数变大，保真度在极限下收敛到1--从而解决了来自[Brun et al.，Physical Review Letters 102，210402（2009）]。这个结果来自于D-CTC辅助的方案，用于产生在已知本征基中制备的量子态的完美克隆，以及人们可以从信息完整测量的概率的经验估计重建量子态的近似的事实。我们的研究结果意味着更一般的是，每个连续的，但在其他任意非线性映射从状态到状态可以实现任意精度的D-CTC。此外，我们的研究结果表明，Deutsch的CTC模型实际上是一个经典的模型，在这个意义上，两个任意的，不同的密度算子是完全可区分的（在一个大的CTC系统的限制），因此，在这个模型中，量子力学成为一个经典的理论，其中每个密度算子是一个独特的点在一个经典的相空间。
Proper and improper density matrices and the consistency of the Deutsch model for Local Closed Timelike Curves
我们讨论的概念，适当的和不适当的密度矩阵，我们认为，这个问题是至关重要的理解的量子力学CTC模型提出的Deutsch。我们得出的结论是，在现实的解释下，正确的和不正确的密度算子之间的区别是不是一个相对论协变的概念，这一事实导致的结论，D-CTC模型是物理不一致的。
Brun \emph{et al.} [Phys. Rev. Lett. \textbf{102}, 210402 (2009)] showed that in the presence of a Deutschian closed timelike curve (D-CTC), one could violate the Holevo bound. It is possible to utilize the Holevo bound violation to encode $n$-bit classical information in a single qubit. Here we demonstrate a new quantum cost efficient scheme, for storing and retrieving $n$-bit classical information faithfully in the presence of a D-CTC in violation of the Holevo bound. We also propose a new protocol for cloning a qubit in the presence of a D-CTC. In both the schemes, the quantum cost is found…
Perfect state distinguishability and computational speedups with postselected closed timelike curves
Bennett和Schumacher的后选择量子隐形传态是一个封闭的类时曲线（CTC）模型，导致了与Deutsch模型物理上不同的结果。我们表明，即使是一个单一的量子比特通过一个后选择的CTC（P-CTC）是足以做任何后选择的量子测量，我们讨论了“德国”CTC（D-CTC）和P-CTC之间的一个重要区别，其中P-CTC的未来存在可能会影响目前的实验结果。然后，基于Bennett和Smith的建议，我们明确地展示了一个由P-CTC辅助的参与方如何区分一组线性无关的量子态，并证明了这样的参与方不可能区分一组线性相关的量子态.因此，P-CTC的能力弱于D-CTC，因为Holevo界限仍然适用于使用它们的电路，而不管它们是否有能力违反不确定原理。然后，我们讨论了如何在线性量子力学中不可区分的量子混合物的不同概念导致涉及P-CTC的非线性量子力学中的显著不同的结论。最后，我们给出了明确的电路结构，可以有效地因数整数，有效地解决任何决定问题的NP和coNP的交集，并概率解决任何决定问题的NP。这些电路只需要一个量子比特回到过去就可以完成这些任务，它们利用后选择的封闭类时曲线的能力为无效答案创造祖父悖论。
Experimental Implementation of the Deutsch-Jozsa Algorithm for Three-Qubit Functions using Pure Coherent Molecular Superpositions
Deutsch-Jozsa算法的实验证明了三个量子位函数使用纯相干叠加的Li $_{2}$振转本征态。该函数的字符，无论是恒定的或平衡的，是通过第一次压印的功能，使用相位成形的飞秒脉冲，在相干叠加的分子状态，然后投影叠加到离子的最终状态，使用第二飞秒脉冲在特定的时间延迟进行评估。
Closed Timelike Curve Decoding on Quantum Hardware
该研究在量子硬件上实现含Hayden--Preskill/Yoshida--Kitaev恢复映射的Deutsch类空闭合曲线解码器电路，通过Qiskit模拟和IBM硬件数据量化了解码器相关性能参数。
Closed timelike curves via post-selection: theory and experimental demonstration
封闭类时曲线（CTC）是时空中的轨迹，它有效地在时间上向后旅行：遵循CTC的测试粒子原则上可以与过去的自己相互作用。CTC出现在爱因斯坦场方程的许多解中，任何未来广义相对论的量子版本都必须使它们与量子力学和量子场论的要求相协调。Deutsch提出了一个被广泛接受的CTC的量子理论。在这里，我们探索了CTC的另一种量子公式，并表明它在物理上与Deutsch的公式不等价。因为它是基于结合量子隐形传态与后选择，我们的理论的预测/retrodictions是实验检验：我们报告的实验结果证明我们的理论的解决方案的著名的“祖父悖论。
The D-CTC condition, introduced by David Deutsch as a condition to be fulfilled by analogues for processes of quantum systems in the presence of closed timelike curves, is investigated for classical statistical (non-quantum) bi-partite systems. It is shown that the D-CTC condition can generically be fulfilled in classical statistical systems, under very general, model-independent conditions. The central property used is the convexity and completeness of the state space that allows it to generalize Deutsch's original proof for q-bit systems to more general classes of statistically described sys…
One out of many emerging implications from solutions of Einstein's general relativity equations are closed timelike curves (CTCs), which are trajectories through spacetime that allow for time travel to the past without exceeding the speed of light. Two main quantum models of computation with the use of CTCs were introduced by Deutsch (D-CTC) and by Bennett and Schumacher (P-CTC). Unlike the classical theory in which CTCs lead to logical paradoxes, the quantum D-CTC model provides a solution that is logically consistent due to the self-consistency condition imposed on the evolving system, where…
Quantum fields on closed time-like curves
近年来，量子粒子在封闭类时曲线上的演化引起了人们极大的兴趣。然而，这些模型通常假设只有两个自由度的点状粒子-考虑到问题的相对论设置，这是一个非常有问题的假设。我们表明，它是可能的推广Deutsch模型的CTC领域使用的等效电路形式主义。我们给出了相干态、压缩态和单光子态通过分束器与CTC相互作用的例子。然后，该模型进一步推广到占正常的量子力学的平滑过渡的CTC变得比它的大小的模式相互作用，在这个限制，我们发现，该系统的行为像一个标准的量子力学反馈回路。
A condition proposed by David Deutsch to describe analogues of processes in the presence of closed timelike curves (D-CTC condition) in bipartite quantum systems is investigated within the framework of local relativistic quantum field theory. The main result is that in relativistic quantum field theory on spacetimes where closed timelike curves are absent, the D-CTC condition can nevertheless be fulfilled to arbitrary precision, under very general, model-independent conditions. Therefore, the D-CTC condition should not be taken as characteristic for quantum processes in the presence of closed …
Closed timelike curves in measurement-based quantum computation
关于量子计算中假设闭合类时曲线（CTC）的功率，最近已经获得了许多结果。在这里，我们表明，基于测量的量子计算的单向模型包含在一个自然的方式，由贝内特，舒马赫和Svetlichny提出的CTC模型。我们确定了一类CTC在这个模型中，可以模拟确定性和指向Deutsch的CTC模型的一个根本限制，导致预测与单向模型相冲突。
The quantum mechanics of time travel through post-selected teleportation
本文讨论了封闭类时曲线（CTC）的量子力学和其他可能的时间旅行方法。我们分析了这样的量子时间旅行的具体建议，基于后选择隐形传态（P-CTC）的CTC的量子描述。我们将P-CTC理论与之前提出的时间旅行量子理论进行了比较：该理论在物理上与Deutsch的CTC理论不等价，但它与路径积分方法（最适合分析弯曲时空中的量子场论）是一致的。我们推导出一个时序尊重系统与CTC相互作用的动力学方程。我们讨论了在广义相对论封闭类时曲线的情况下时间旅行的可能性，并研究了P-CTC对提高计算能力的影响。
We introduce a general categorical framework to reason about quantum theory and other process theories living in spacetimes where Closed Timelike Curves (CTCs) are available, allowing resources to travel back in time and provide computational speedups. Our framework is based on a weakening of the definition of traced symmetric monoidal categories, obtained by dropping the yanking axiom and the requirement that the trace be defined on all morphisms. We show that the two leading models for quantum theory with closed timelike curves---namely the P-CTC model of Lloyd et al. and the D-CTC model of …
A recent paper from Brun et al. has argued that access to a closed timelike curve (CTC) would allow for the possibility of perfectly distinguishing nonorthogonal quantum states. This result can be used to develop a protocol for instantaneous nonlocal signaling. Several commenters have argued that nonlocal signaling must fail in this and in similar cases, often citing consistency with relativity as the justification. I argue that this objection fails to rule out nonlocal signaling in the presence of a CTC. I argue that the reason these authors are motivated to exclude the prediction of nonlocal…
Revisiting consistency conditions for quantum states of systems on closed timelike curves: an epistemic perspective
近年来，人们对封闭类时曲线（CTC）在量子力学系统动力学中的作用产生了极大的兴趣。这个领域的绝大多数研究都使用了Deutsch开发的动力学方程，这些方程是从一个一致性条件发展而来的，该条件假设混合量子态唯一地描述了系统的物理状态。我们从认识论的角度批评这种一致性条件的选择，即，一种观点，其中量子态代表关于系统的知识状态。我们证明，直接应用Deutsch的条件时，混合状态被视为代表观察员的知识的系统可以隐藏时间旅行悖论的观察员，而不是解决它们。为了进一步阐明穿越CTC的量子系统的适当动力学，我们使用了一个玩具认知理论，由于Spekkens的严格经典本体论，并表明，与Deutsch的结果相反，时间旅行的许多传统的悖论效应是存在的。
General relativity predicts the existence of closed timelike curves (CTCs), along which an object could travel to its own past. A consequence of CTCs is the failure of determinism, even for classical systems: one initial condition can result in multiple evolutions. Here we introduce a new quantum formulation of a classic example, where a billiard ball can travel along two possible trajectories: one unperturbed and one, along a CTC, where it collides with its past self. Our model includes a vacuum state, allowing the ball to be present or absent on each trajectory, and a clock, which provides a…
We want in this article to show the usefulness of Quantum Turing Machine (QTM) in a high-level didactic context as well as in theoretical studies. We use QTM to show its equivalence with quantum circuit model for Deutsch and Deutsch-Jozsa algorithms. Further we introduce a strategy of translation from Quantum Circuit to Quantum Turing models by these examples. Moreover we illustrate some features of Quantum Computing such as superposition from a QTM point of view and starting with few simple examples very known in Quantum Circuit form.
An elementary derivation of the Deutsch-Jozsa algorithm
相对于经典方法，量子计算充分利用叠加原理来大大（甚至指数地）提高计算速度。Deutsch-Jozsa算法是说明这种能力的最简单的量子算法。不幸的是，标准求导涉及几个巧妙的步骤，这通常会让学生觉得他们自己永远无法弄清楚算法。我们在这里提出了一个不同的制定的问题，让学生推导出的算法只使用量子力学和线性代数的基本知识。
That superpositions of states can be useful for performing tasks in quantum systems has been known since the early days of quantum information, but only recently has quantitative theory of quantum coherence been proposed. Here we apply that theory to an analysis of the Deutsch-Jozsa algorithm, which depends on quantum coherence for its operation. The Deutsch-Jozsa algorithm solves a decision problem, and we focus on a probabilistic version of that problem, comparing probability of being correct for both classical and quantum procedures. In addition, we study a related decision problem in which…
The D-CTC condition is a condition originally proposed by David Deutsch as a condition on states of a quantum communication network that contains "backward time-steps" in some of its branches. It has been argued that this is an analogue for quantum processes in the presence of closed timelike curves (CTCs). The unusual properties of states of quantum communication networks that fulfill the D-CTC condition have been discussed extensively in recent literature. In this work, the D-CTC condition is investigated in the framework of quantum field theory in the local, operator-algebraic approach due …
The present work points out that the Deutsch-Jozsa algorithm was the first formal description of a quantum decider. In particular, it is studied here the class of languages whose indicator functions allow the Deutsch-Jozsa algorithm to output a monochromatic result, beyond the trivial case z = 0 for constant indicator functions. To illustrate examples of randomly balanced languages and some monochromatic cases, it was performed classical computational simulations of the Deutsch-Jozsa quantum algorithm for the specific cases of 4 and 6 qubits, respectively. The general case of the Deutsch-Jozsa…
Using quantum state protection via dissipation in a quantum-dot molecule to solve the Deutsch problem
半导体量子点具有控制参数宽、尺寸小等优点，是实现固态量子计算的理想材料。考虑隧穿耦合的非对称双量子点，将激子态的自发发射和激光场的作用结合起来，保护了间接激子和基态的任意叠加态.作为副产品，我们展示了如何使用保护状态来解决Deutsch问题。
Quantum state tomography on closed timelike curves using weak measurements
本文提出结合量子态层析与弱测量的方法，为闭合类时曲线上的违反时序系统赋予操作性态，验证了 D-CTC 预测并恢复 P-CTC 上的唯一态。
Verifiable nonlinear quantum evolution implies failure of density matrices to represent proper mixtures
在最近的一封信中，Bennett及其同事[1]认为，基于Deutsch [2]的工作，使用封闭类时曲线（CTC）或其他非线性量子动力学来证明奇异量子效应，存在一个他们称之为“线性陷阱”的谬误，即人们不能假设输入态的经典混合会导致相应输出态的相同混合。我们发现，这个处方是不一致的假设，人们可以验证假设的非线性演化。具体地说，如果某个智能体可以凭经验验证物理设备对于某组纯态输入的确定性非线性行为，则通常不能使用密度矩阵来表示不知道所准备的实际纯态的第二智能体的输入。我们的论点是认识论的，并没有呼吁CTC的详细物理。
Quantum Interactions with Closed Timelike Curves and Superluminal Signaling
在量子信息的文献中，关于封闭类时曲线（CTC）量子相互作用的Deutsch模型（D-CTC）和投影模型（P-CTC）都有大量的结果。因此，有一个初步的论点利用纠缠，CTC相互作用将使超光速，实际上，有效的瞬时信号。在信号的发送者和接收者之间的类空分离的情况下，接收者是否测量纠缠态或解纠缠态的局部部分以访问信号可以取决于参考系。我们提出了一个一致性条件，优先考虑在类空分离的情况下，纠缠的角度或解开的角度。对于D-CTC相互作用，一致性条件优先考虑状态解纠缠的参考系，而对于P-CTC相互作用，该条件选择纠缠态。使用的一致性条件，我们表明，有一个程序，允许爱丽丝信号鲍勃在过去通过类空分离的爱丽丝和克里奥，类空分离的克里奥和鲍勃之间的中继超光速通信。这为经典领域的时间旅行悖论打开了大门。Ralph（arXiv：1107.4675）首先指出了P-CTC的这一点，但我们表明，Ralph的“无线电过去”的程序是有缺陷的。由于D-CTC和P-CTC都允许经典信息围绕时空环路发送，因此从Aaronson和Watrous（Proc.Roy.Soc.A，465：631-647（2009））对于CTC增强的经典计算的结果可以得出，访问P-CTC的量子计算机将具有PSPACE的能力，相当于D-CTC增强的量子计算机。
De-Quantising the Solution of Deutsch's Problem
也许最简单和最常用的方法来说明量子计算的力量是解决所谓的{ \it Deutsch问题}。考虑一个布尔函数$f: \{0,1\} \to \{0,1\}$，假设我们有一个（经典的）黑盒来计算它，问题是$f$是常数（即$f(0) = f(1)$）还是平衡（$f(0) \not= f(1)$）。传统上，解决这个问题似乎需要计算$f(0)$和$ f(1)$，然后比较结果。能否解决在$f$上使用{ \em only one}查询的问题？在1985年发表的一篇著名论文中，Deutsch提出了这个问题，并得到了一个"量子“{ \em部分肯定的答案}。1998年，Cleve、Ekert、Macchiavello和Mosca提出了一个完整的概率1解。在这里，我们将表明，量子解决方案可以{ \it de-quantised}到一个确定性的更简单的解决方案，这是有效的量子。“叠加”的使用，量子算法的一个关键成分，在这个特定的情况下，是经典的。
Quantum-mechanical probability from the symmetries of two-state systems
1989年，多伊奇给出了量子力学概率是振幅平方的基本物理解释。从本质上讲，一般的状态矢量被转换成一个高度对称的等幅叠加。德维特最近详细阐述并公布了这一论点。它仍然是不完整的，但是，因为两个作者预期通常的归一化（振幅平方和）的状态向量。在本论文中，设计了一个思想实验，在这个实验中，Deutsch的思想独立于规范化得到了证明，而不是进一步利用对称性。
Maximum predictive power and the superposition principle
最近，有关于量子概率规则起源的讨论（Deutsch quant-ph/9906015，Polley quant-ph/9906124，Barnum et al. quant-ph/9907024，Finkelstein quant-ph/9907004）。这篇文章是发表在《国际理论物理学杂志》33，171（1994）上的一篇论文的一个稍微改写的版本，它指出了下面的问题：对一个实验者来说，世界是一个持续的离散数据流。可以肯定的是，每一次观察，他/她都比以前知道得更多，仅仅是因为他/她现在可以回答这样一个问题：“你刚刚记录了哪些可能的结果？””，而这在观察之前是不可能的。人们可能会问，这种信息的不断增加是否需要一种特定的结构。特别是，不同的观测必须如何联系起来，以确保预测变得越来越准确，过去的观测作为输入越多？这就引出了概率的复平方根相加的量子规则，而不是像经典概率那样，把概率本身相加。
Quantum computing is an emerging field of science which will eventually lead us to new and powerful logic devices with capabilities far beyond the limits of current transistor-based technology. There are certain types of problems which quantum computers can solve fundamentally faster than the tradition digital computers. There are quantum algorithms which require both superposition and entanglement (e.g. Shor algorithm). But neither the Grover algorithm nor the very first quantum algorithm due to Deutsch and Jozsa need entanglement. Is it possible to utilize classical wave superposition to spe…
Order-preserving condition for coherence measures of projective measurements with One Example
本文针对投影测量和正交子空间的相干性度量提出了保序条件，通过推广相干性的1/2-affinity验证其满足该条件及其他合理条件，并探讨了POVM情形下的保序条件。
Quantum Computing by Two-Dimensional NMR using Spin- and Transition-Selective Pulses
使用二维NMR的量子计算最近已被描述为使用标量耦合演化技术[J. Chem. Phys.，109，10603（1998）]。本文描述了利用选择性脉冲实现二维核磁共振量子计算。使用两个和三个量子位实现了许多逻辑门，其中一个额外的观察者自旋。实现了一些多合一门（或Portmanteau门）。Toffoli门（或AND/NAND门）和OR/NOR门在三个量子位上实现。Deutsch-Jozsa量子算法的一个和两个量子位，使用一个额外的工作量子位，也已经实现了使用选择性脉冲后，创建一个相干叠加态，在二维的方法。
Leveraging Quantum Superposition to Infer the Dynamic Behavior of a Spatial-Temporal Neural Network Signaling Model
本文提出并解决了一类与大规模网络动态持续性相关的新问题，通过扩展Grover和Deutsch-Jozsa算法并以耦合工作流利用量子叠加，高效判断网络活动是持续、静息还是癫痫样饱和。
Quantum computers, which take advantage of the superposition and entanglement of physical states, could outperform their classical counterparts in solving problems with technological impact, such as factoring large numbers and searching databases. A quantum processor executes algorithms by applying a programmable sequence of gates to an initialized state of qubits, which coherently evolves into a final state containing the result of the computation. Although quantum processors with a few qubits have been demonstrated on multiple quantum computing platforms, realization of solid-state programma…
Superposition states of circular currents of exciton-polaritons mimic the superconducting flux qubits. The phase of a polariton fluid must change by an integer number of $2π$, when going around the ring. If one introduces a $π$-phase delay line in the ring, the fluid is obliged to propagate a clockwise or anticlockwise circular current to reduce the total phase gained over one round-trip to zero or to build it up to $2π$. We show that such a $π$-delay line can be provided by a dark soliton pinned to a potential well created by a C-shape non-resonant pump-spot. The resulting split-ring polarito…
Demonstration of Two-Qubit Algorithms with a Superconducting Quantum Processor
通过利用物理状态的叠加和纠缠，量子计算机可以在解决技术影响问题方面优于经典计算机，例如分解大量数据和搜索数据库。量子处理器通过将可编程的门序列应用于量子位的初始化寄存器来执行算法，该寄存器相干地演变成包含计算结果的最终状态。同时满足长相干性、状态准备、通用门操作和量子比特读出的相互冲突的要求，使得构建量子处理器具有挑战性。在核磁共振、冷离子阱和光学系统中已经显示了少量子位处理器，但是固态实现仍然是一个突出的挑战。在这里，我们展示了一个双量子比特超导处理器和Grover搜索和Deutsch-Jozsa量子算法的实现。我们采用了一种新的双量子位相互作用，强度可调的两个数量级的纳秒时间尺度上，这是介导的腔总线在电路量子电动力学（cQED）架构。这种相互作用允许产生高度纠缠态，同时高达94%。尽管该处理器构成了使用集成电路进行量子计算的重要一步，但仍需要继续努力提高量子位相干时间、门性能和寄存器大小，以实现可扩展技术的承诺。
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