J. A. Miszczak, P. Gawron
We propose a quantum implementation of a capital-dependent Parrondo's paradox that uses $O(\log_2(n))$ qubits, where $n$ is the number of Parrondo games. We present its implementation in the quantum computer language (QCL) and show simulation results.
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We show that a genuine Parrondo paradox can emerge in two-state quantum walks without resorting to experimentally intricate high-dimensional coins. To achieve such goal we employ a time-dependent coin operator without breaking the translation spatial invariance of the system.
Parrondo's paradox is a well-known counterintuitive phenomenon, where the combination of unfavorable situations can establish favorable ones. In this paper, we study one-dimensional discrete-time quantum walks, manipulating two different coins (two-state) operators representing two losing games A and B, respectively, to create the Parrondo effect in the quantum domain. We exhibit that games A and B are losing games when played individually but could produce a winning expectation when played alternatively for a particular sequence of different periods for distinct choices of the relative phase.…
Parrondo's paradox in quantum walks with inhomogeneous coins
本文研究离散时间量子行走中的 Parrondo 悖论，证明仅采用时空依赖的非均匀硬币即可实现两种失败策略组合获胜，无需高维硬币或退相干，从而提升实验可行性并拓展量子输运应用。
Parrondo's paradox is ubiquitous in games, ratchets and random walks.The apparent paradox, devised by J.~M.~R.~Parrondo, that two losing games $A$ and $B$ can produce an winning outcome has been adapted in many physical and biological systems to explain their working. However, proposals on demonstrating Parrondo's paradox using quantum walks failed {for large number of steps}. In this work, we show that instead of a single coin if we consider a two coin initial state which may or may not be entangled, we can observe a genuine Parrondo's paradox with quantum walks. Further we focus on reasons f…
Parrondo's game of quantum search based on quantum walk
本文结合量子行走帕隆多博弈与量子行走搜索算法，提出基于量子行走的量子搜索帕隆多博弈，经数值模拟验证其在一、二维环面存在帕隆多悖论，且顶点为偶数、单标记顶点的d维环面上悖论范围关于原点对称。
We investigate the possibility of implementing a sequence of quantum walks whose probability distributions give an overall positive winning probability, while it is negative for the single walks (Parrondo's paradox). In particular, we have in mind an experimental realisation with a Bose-Einstein condensate in which the walker's space is momentum space. Experimental problems in the precise implementation of the coin operations for our discrete-time quantum walks are analysed in detail. We study time-dependent phase fluctuations of the coins as well as perturbations arising from the finite momen…
There exist memoryless zero-capacity quantum channels that when used jointly result in the channel with positive capacity. This phenomenon is called superactivation. Making use of Parrondo's paradox, we exhibit examples of superactivation-like effect for the capacity of classical communication channels as well as quantum and private capacity of quantum channels with memory. There are several ingredients necessary for superactivation of quantum capacity to occur in memoryless case. The first one is the requirement for the quantum channels which are amenable for superactivation to come from two …
Quantum Parrondo Paradox via a Single Phase Defect Symmetry Breaking and Directed Transport
本文通过单个量子比特硬币、固定周期的SU(2)算符序列及单个局域相位缺陷，实现量子帕尔米多效应，展示了非对称性破缺如何产生定向量子马达，且验证了位置期望值作为验证悖论的正确度量。
The Geometry of Transport in Quantum Walks and Parrondo's Paradox
本文在最小离散时间量子行走中研究帕龙多悖论，提出输运向量几何判据，当组合策略向量超出单个策略锥体时悖论出现，并计算了悖论集合的概率。
Scouring Parrondo's Paradox in Discrete-Time Quantum Walks
本文在基于硬币的离散时间量子游走中提出一种量子博弈，并给出确定性方案识别 Parrondo 悖论，证明单个均失败的量子步按序组合后可变为获胜策略，从而深化对量子游走期望值演化的理解。
A quantum walker moves on the integers with four extra degrees of freedom, performing a coin-shift operation to alter its internal state and position at discrete units of time. The time evolution is described by a unitary process. We focus on finding the limit probability law for the position of the walker and study it by means of Fourier analysis. The quantum walker exhibits both localization and a ballistic behavior. Our two results are given as limit theorems for a 2-period time-dependent walk and they describe the location of the walker after it has repeated the unitary process a large num…
We consider the discrete-time quantum walk in the plane, and present a quantum implementation of Parrondo's game for four players. Physical significance of the game strategies are also discussed.
We present a quantum implementation of Parrondo's game with randomly switched strategies using 1) a quantum walk as a source of ``randomness'' and 2) a completely positive (CP) map as a randomized evolution. The game exhibits the same paradox as in the classical setting where a combination of two losing strategies might result in a winning strategy. We show that the CP-map scheme leads to significantly lower net gain than the quantum walk scheme.
Coordination and cooperation are among the most important issues of game theory. Recently, the attention turned to game theory on graphs and social networks. Encouraged by interesting results obtained in quantum evolutionary game analysis, we study cooperative Parrondo's games in a quantum setup. The game is modeled using multidimensional quantum random walks with biased coins. We use the GHZ and W entangled states as the initial state of the coins. Our analysis shows than an apparent paradox in cooperative quantum games and some interesting phenomena can be observed.
Parrondo's Paradox arises when two losing games are combined to produce a winning one. A history dependent quantum Parrondo game is studied where the rotation operators that represent the toss of a classical biased coin are replaced by general SU(2) operators to transform the game into the quantum domain. In the initial state, a superposition of qubits can be used to couple the games and produce interference leading to quite different payoffs to those in the classical case.
Parrondo's effect in continuous-time quantum walks
该研究首次在含时跃迁缺陷的连续时间量子行走中发现Parrondo效应，即单独阻碍波包扩散的缺陷交替出现可增强波包传播，为利用缺陷提升量子输运的非常规机制研究奠定基础。
Continuous-time quantum walks on a defective lattice: Boosting the spreading of delocalized states through Parrondo's strategy
该研究针对含单个缺陷的一维晶格上的连续时间量子行走，通过在两种不利缺陷构型间交替的Parrondo策略，提升了离域态的量子输运效率，揭示了其中的Parrondo悖论现象。
Parrondo-type enhancement of quantum-state transfer in spin chains
本文研究了在有限XX自旋链中，通过周期性切换两个具有不同边界耦合的哈密顿量，提升单量子比特和贝尔态传输保真度的方法，揭示了非交换驱动哈密顿量带来的纯相干干涉效应。
Controlling quantum chaos via Parrondo strategies on noisy intermediate-scale quantum hardware
针对NISQ系统的量子混沌控制问题，本研究基于Parrondo策略，利用经QFT优化的DTQW在三台NISQ设备上实现混沌到有序的转变，验证了该方案的可行性与应用价值。
Enhanced spreading in continuous-time quantum walks using aperiodic temporal modulation of defects
研究通过非周期性缺陷调制增强连续时间量子行走的扩散，发现其增强效果受序列自相关和持久性影响，展示了非周期性缺陷调制维持Parrondo效应的新方法。
Quantum cryptography compatible with noisy intermediate-scale quantum devices based on Parrondo dynamics in discrete-time quantum walks
提出一种基于离散时间量子行走的密码方案，利用Parrondo动力学实现周期演化，并在NISQ设备上通过Qiskit仿真验证其抗噪声能力，分析截获重发和中间人攻击下的量子比特错误率。
We propose an experimental setup for the implementation of weak measurements in the context of the gedankenexperiment known as Hardy's Paradox. As Aharonov et al. showed, these weak values form a language with which the paradox can be resolved. Our analysis shows that this language is indeed consistent and experimentally testable. It also reveals exactly how a combination of weak values can give rise to an apparently paradoxical result.
A recent experimental proposal by Ahnert and Payne [S.E. Ahnert and M.C. Payne, Phys. Rev. A 70, 042102 (2004)] outlines a method to measure the weak value predictions of Aharonov in Hardy's paradox. This proposal contains flaws such as the state preparation method and the procedure for carrying out the requisite weak measurements. We identify previously published solutions to some of the flaws.
We present the general Hardy-like quantum pigeonhole paradoxes for \textit{n}-particle states, and find that each of such paradoxes can be simply associated to an un-colorable solution of a specific vertex-coloring problem induced from the projected-coloring graph (a kind of unconventional graph). Besides, as a special kind of Hardy's paradox, several kinds of Hardy-like quantum pigeonhole paradoxes can even give rise to higher success probability in demonstrating the conflict between quantum mechanics and local or noncontextual realism than the previous Hardy's paradoxes. Moreover, not only m…
The comment by Lundeen et al. contains two criticisms of our proposal. While we agree that the state-preparation procedure could be replaced by a simpler setup as proposed by the authors of the comment, we do not agree with the authors on their second, and more important point regarding two-particle weak measurements. We believe this to be the result of a misunderstanding of our original paper.
I reply to Ravon and Vaidman's criticism (quant-ph/0606067) of my classical implementation (quant-ph/0207124) of a three-box system as a card game.
Device-Independent (DI) security is the best form of quantum cryptography, providing information-theoretic security based on the very laws of nature. In its highest form, security is guaranteed against adversaries limited only by the no-superluminal signalling rule of relativity. The task of randomness amplification, to generate secure fully uniform bits starting from weakly random seeds, is of both cryptographic and foundational interest, being important for the generation of cryptographically secure random numbers as well as bringing deep connections to the existence of free-will. DI no-sign…
The Hilbert hotel is an old mathematical paradox about sets of infinite numbers. This paradox deals with the accommodation of a new guest in a hotel with an infinite number of occupied rooms. Over the past decade, there have been many attempts to implement these ideas in photonic systems. In addition to the fundamental interest that this paradox has attracted, this research is motivated by the implications that the Hilbert hotel has for quantum communication and sensing. In this work, we experimentally demonstrate the fractional vortex Hilbert's hotel scheme proposed by G. Gbur [Optica 3, 222-…
The Einstein-Podolsky-Rosen (EPR) paradox is one of the milestones in quantum foundations, arising from the lack of local realistic description of quantum mechanics. The EPR paradox has stimulated an important concept of "quantum nonlocality", which manifests itself by three different types: quantum entanglement, quantum steering, and Bell nonlocality. Although Bell nonlocality is more often used to show the "quantum nonlocality", the original EPR paradox is essentially a steering paradox. In this work, we formulate the original EPR steering paradox into a contradiction equality,thus making it…
We propose an implementation of a twin paradox scenario in superconducting circuits, with velocities as large as a few percent of the speed of light. Ultrafast modulation of the boundary conditions for the electromagnetic field in a microwave cavity simulates a clock moving at relativistic speeds. Since our cavity has a finite length, the setup allows us to investigate the role of clock size as well as interesting quantum effects on time dilation. In particular, our theoretical results show that the time dilation increases for larger cavity lengths and is shifted due to quantum particle creati…
There has been much interest in developing phase estimation schemes which beat the so-called Heisenberg limit, i.e., for which the phase resolution scales better than 1/n, where n is a measure of resources such as the average photon number or the number of atomic qubits. In particular, a number of nonlinear schemes have been proposed for which the resolution appears to scale as 1/n^k or even exp(-n), based on optimising the quantum Cramer-Rao bound. Such schemes include the use of entangled coherent states. However, it may be shown that the average root mean square errors of the proposed schem…
The Quantum Eraser Paradox
该研究通过扩展延迟选择量子擦除实验提出一个悖论，论证量子力学中选择不能影响过去，需违反统计独立性而非反向因果，并提出可区分隐变量理论的新实验。
Resolution of the century-long paradox on Maxwell's demon reveals a deep connection between information theory and thermodynamics. Although initially introduced as a thought experiment, Maxwell's demon can now be implemented in several physical systems, leading to intriguing test of information-thermodynamic relations. Here, we report experimental realization of a quantum version of Maxwell's demon using solid state spins where the information acquiring and feedback operations by the demon are achieved through conditional quantum gates. A unique feature of this implementation is that the demon…
Beyond the Expressivity-Trainability Paradox: A Dynamical Lie Algebra Perspective on Navigating Barren Plateaus in Quantum Machine Learning
本文通过动力学李代数框架揭示参数化量子电路的贫瘠高原源于其希尔伯特空间容量，并提出基于群论几何先验的结构正则化方法，在保持多项式级DLA增长的同时确保梯度丰富，实现可设计可训练性。
The validation and parallel implementation of a numerical method for the solution of the time-dependent Dirac equation is presented. This numerical method is based on a split operator scheme where the space-time dependence is computed in coordinate space using the method of characteristics. Thus, most of the steps in the splitting are calculated exactly, making for a very efficient and unconditionally stable method. We show that it is free from spurious solutions related to the fermion-doubling problem and that it can be parallelized very efficiently. We consider a few simple physical systems …
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