Marcelo A. Pires, Sílvio M. Duarte Queirós
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.
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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。
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.
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 …
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。
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。
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…
Playing a Parrondo's game with a qutrit is the subject of this paper. We show that a true quantum Parrondo's game can be played with a 3 state coin(qutrit) in a 1D quantum walk in contrast to the fact that playing a true Parrondo's game with a 2 state coin(qubit) in 1D quantum walk fails in the asymptotic limits.
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 games are coin flipping games with the surprising property that alternating plays of two losing games can produce a winning game. We show that this phenomenon can be modelled by probabilistic lattice gas automata. Furthermore, motivated by the recent introduction of quantum coin flipping games, we show that quantum lattice gas automata provide an interesting definition for quantum Parrondo games.
We study a quantum walk in one-dimension using two different "coin" operators. By mixing two operators, both of which give a biased walk with negative expectation value for the walker position, it is possible to reverse the bias through interference effects. This effect is analogous to that in Parrondo's games, where alternating two losing (gambling) games can produce a winning game. The walker bias is produced by introducing a phase factor into the coin operator, with two different phase factors giving games $A$ and $B$. We give the range of phases for which the Parrondo effect can be obtaine…
We present a new form of a Parrondo game using discrete-time quantum walk on a line. The two players A and B with different quantum coins operators, individually losing the game can develop a strategy to emerge as joint winners by using their coins alternatively, or in combination for each step of the quantum walk evolution. We also present a strategy for a player A (B) to have a winning probability more than player B (A). Significance of the game strategy in information theory and physical applications are also discussed.
Quantum Parrondo Games in Low-Dimensional Hilbert Spaces
本文研究低维Hilbert空间上的量子Parrondo博弈，将组成博弈实现为环上量子行走，并利用量子硬币引入随机序列，发现长时间下因纠缠与自干涉产生复杂的系统性输赢结构。
We construct a Parrondo's game using discrete time quantum walks. Two lossing games are represented by two different coin operators. By mixing the two coin operators $U_{A}(α_{A},β_{A},γ_{A})$ and $U_{B}(α_{B},β_{B},γ_{B})$, we may win the game. Here we mix the two games in position instead of time. With a number of selections of the parameters, we can win the game with sequences ABB, ABBB, \emph{et al}. If we set $β_{A}=45^{\circ},γ_{A}=0,α_{B}=0,β_{B}=88^{\circ}$, we find the game 1\emph{}with {\normalsize $U_{A}^{S}=U^{S}(-51^{\circ},45^{\circ},0)$, $U_{B}^{S}=U^{S}(0,88^{\circ},-16^{\circ}…
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。
Quantum entanglement has multiple applications in quantum information processing. Developing methods to generate highly entangled states independent of initial conditions is an essential task. Herein we aim to generate highly entangled states via discrete-time quantum walks. We propose deterministic Parrondo sequences that generate states that are generally much more entangled than states produced by sequences using only one of the two coins. We show that some Parrondo sequences generate highly entangled states, which are independent of the phase of the initial state used and further lead to m…
Temporal-order-controlled Parrondo reversal in a periodically switched quantum walk acting on NEQR image states
本文提出基于离散时间量子行走的量子图像加密方案，利用帕尔伦多悖论提升加密性能，实现高熵和低相关性。
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。
We introduce a multi-coin discrete quantum random walk where the amplitude for a coin flip depends upon previous tosses. Although the corresponding classical random walk is unbiased, a bias can be introduced into the quantum walk by varying the history dependence. By mixing the biased random walk with an unbiased one, the direction of the bias can be reversed leading to a new quantum version of Parrondo's paradox.
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。
Local realistic models cannot completely describe all predictions of quantum mechanics. This is known as Bell's theorem that can be revealed either by violations of Bell inequality, or all-versus-nothing proof of nonlocality. Hardy's paradox is an important all-versus-nothing proof and is considered as "the simplest form of Bell's theorem". In this work, we theoretically build the general framework of Hardy-type paradox based on Bell inequality. Previous Hardy's paradoxes have been found to be special cases within the framework. Stronger Hardy-type paradox has been found even for the two-qubit…
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…
Can the Infamous Boundary Be Found in Macromolecules? Also, von Neumann vs. Schroedinger ensembles, and `Hund's Paradox' in quantum chemistry
本文探讨经典-量子分界（臭名昭著的边界）是否可能位于 macromolecules 层级，并将其与热力学系综选择和量子化学中的 Hund 佯谬联系起来，进而提出一个可在不对称 macromolecules 中揭示该边界的实验方案。
I show that Quantum Electrodynamics (QED) predicts a sort of uncertainty principle on the number of the "soft photons" that can be produced in coincidence with the particles that are observed in any EPR experiment. This result is argued to be sufficient to remove the original EPR paradox. A signature of this soft-photons solution of the EPR paradox would be the observation of apparent symmetry violation in single events. On the other hand, in the case of the EPR experiments that have actually been realized, the QED correlations are argued to be very close to those calculated by the previous, i…
The main distinction between classical mechanics and quantum mechanics is the lack in the latter of a full mechanical determinism: different final states can arise from the same physical state, after the measurement. No hidden variable is supposed to exist, nothing can discriminate two apparently identical states even if they give a different result. In this paper we try to put the basis for a more fundamental theory that (approximately) coincides with quantum mechanics when comparing statistics, but it is more fundamental, since it mathematically describes measurement processes giving an expl…
When elementary quantum systems, such as polarized photons, are used to transmit digital information, the uncertainty principle gives rise to novel cryptographic phenomena unachievable with traditional transmission media, e.g. a communications channel on which it is impossible in principle to eavesdrop without a high probability of disturbing the transmission in such a way as to be detected. Such a quantum channel can be used in conjunction with ordinary insecure classical channels to distribute random key information between two users with the assurance that it remains unknown to anyone else,…
Hardy-type self-testing and exposedness of tripartite GHZ correlations
研究三体两输入两输出场景中Hardy型悖论的自检验，证明最大Hardy成功概率关联自检验GHZ态和测量，且该关联是量子关联集的极点和暴露点，与Mermin不等式最大违反点重合。
The quantum pigeonhole effect as a new form of Bell's theorem without inequality
该研究通过量子情境性解释了量子鸽笼效应，证明其为一种无需不等式的贝尔定理形式，揭示了非情境本征值分配的不可能性。
A theory is developed which attempts to reconcile the measurements of nonlocal quantum observables with special relativity and quantum mechanics. The collapse of a wave function, which coincides with a nonlocal measurement by some macroscopic measuring device, is associated with the triggering of an absorber mechanism due to the interaction of the apparatus with the charges in the rest of the universe. The standard retarded electromagnetic field plus radiation damping is converted, for a short time during the collapse of the wave function, to an advanced field plus radiation. The reversal of t…
Two seemingly distinct notions regarding black holes have captured the imagination of theoretical physicists over the past decade: First, black holes are conjectured to be fast scramblers of information, a notion that is further supported through connections to quantum chaos and decay of mutual information via AdS/CFT holography. Second, black hole information paradox has motivated exotic quantum structure near horizons of black holes (e.g., gravastars, fuzzballs, or firewalls) that may manifest themselves through delayed gravitational wave echoes in the aftermath of black hole formation or me…
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