Environment - Assisted Invariance, Causality, and Probabilities in Quantum Physics
W. H. Zurek
我介绍了环境辅助不变性--一种与因果关系有关的对称性，由相关的量子态表现出来--并描述了它如何被用来理解无知的本质，从而理解量子物理中概率的起源。
I introduce environment - assisted invariance -- a symmetry related to causality that is exhibited by correlated quantum states -- and describe how it can be used to understand the nature of ignorance and, hence, the origin of probabilities in quantum physics.
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Quantum mechanical probabilities and general probabilistic constraints for Einstein-Podolsky-Rosen-Bohm experiments
相对论的因果关系，也就是说，不可能以超光速发出信号，限制了复合物理系统不同部分之间可能发生的相关性。在这里，我们建立了基本的限制，相对论因果性强加在联合概率涉及的实验的爱因斯坦-波多尔斯基-罗森玻姆类型。另一方面，量子力学在因果性和一致性等一般考虑所要求的限制之外设置了更多的限制。我们说明了这一事实，考虑的相关性的总和参与CHSH不等式。在CHSH不等式的一般框架下，我们还考虑了Hardy导出的非定域性定理，讨论了相对论因果性和量子力学对它的约束，最后导出了一个简单的不等式，它可以用来检验量子力学与一般概率理论的关系.
Instantaneous Spreading and Einstein Causality in Quantum Theory
在非相对论性的量子力学中，一个自由粒子的波函数，最初在一个有限的体积中，立即扩展到无穷大。在非相对论理论中，这是无关紧要的，但我们表明，在相对论量子理论中可以发生同样的瞬时扩散，并且在相距很远的系统中跃迁概率可以瞬时变为非零。我们讨论这如何影响爱因斯坦因果关系。
No-signalling-based version of Zurek's derivation of quantum probabilities: A note on "Environment-assisted invariance, entanglement, and probabilities in quantum physics"
Zurek推导出了纯联合态中二分量子系统的施密特基态的量子概率，假设如果一方的行为可以被另一方撤销，它们不应该受到另一方行为的影响（“概率不变性”）和一个辅助假设。我们认为，一个自然的推广的辅助假设实际上是强大到足以产生玻恩规则本身，但Zurek的论点和协议可以适应做没有这个假设，在成本使用概率的不变性在两个方向。我们考虑了不变性的其他动机，一个是基于无信号约束，即量子系统的一个子系统上的动作不允许向与第一个子系统完全不同的另一个子系统发送信号，另一个可能是最强的量子力学的相对态解释。部分原因是，我们认为，我们的版本和祖雷克的论点的原始版本的相对吸引力部分取决于是否解释量子形式主义的相对状态或明确的测量结果。
On Einstein Causality and Time Asymmetry in Quantum Physics
Hegerfeldt的一个定理表明，如果哈密顿量的谱是从下面有界的，那么某些概率的传播速度没有上限。我们证明了一个定理类似于Hegerfeldt的apposes到不对称的时间演化给出的一个半群的运营商。作为应用，我们考虑了因果Poincare半群的不可约表示对相对论性准稳态的刻画，并研究了新定理在这种特殊情况下的意义.
An equivalence between time-symmetry and cyclic causality in quantum theory
该研究针对量子基础中时间对称性与因果方向性的关联问题，扩展P-CTC框架定义带时间标记的P-CTC辅助梳，证明其与多时间态MTS操作等价，并探讨了MTS的资源理论偏序与未来研究方向。
It is possible to completely explain all aspects of quantum mechanics by expressing the relations between physical properties in terms of complex conditional probabilities (Phys. Rev. A 89, 042115(2014)). These fully deterministic probabilities replace the classical notions of phase space geometries and continuous trajectories with a more accurate description that takes into account the role of dynamics in the emergence of reality. We can then understand why so many previous attempts to find a detailed explanation of quantum phenomena have failed: the assumption of a static reality breaks down…
Bounds on Nonlocality and Random Access Codes from Extended Information Causality Principle
通过扩展信息因果原理，推导出更紧的量子贝尔不等式，改进Collins-Gisin族贝尔不等式的解析界，并证明扩展原理在纠缠辅助随机访问码中不优于原始原理。
Relativistic time-of-arrival measurements: predictions, post-selection and causality problem
本文在量子场论框架下研究相对论性粒子的到达时间测量，指出经后选择可得唯一预测，并揭示探测概率中的非因果项源于费曼传播，进而讨论恢复因果性的困难。
It is shown that energy transfer in a homogeneous fully connected quantum network is assisted by a decohering interaction with environmental spins. Analytic expressions for the transfer probabilities are obtained for the zero temperature case, and the effect is shown to persist at physiological temperatures. This model of decoherence-assisted energy transfer is applied to the Fenna-Matthews-Olson complex.
Entanglement-Assisted Classical Capacity of Noisy Quantum Channels
发送者和接收者之间的先前纠缠，这正好是无噪声量子信道的经典容量的两倍，可以增加一些有噪声的量子信道的经典容量，根据信道的任意大的常数因子，相对于没有纠缠的最佳已知的经典容量。增强因子是最大的非常嘈杂的信道，具有正的经典容量，但零量子容量。虽然这样的量子信道可以被经典地模拟，但并不意味着违反因果关系，因为模拟至少需要与被模拟的信道的纠缠辅助经典容量一样多的前向经典通信。我们得到确切的表达式的纠缠辅助容量的去极化和擦除通道在d维。
The quantum-mechanical rule for probabilities, in its most general form of positive-operator valued measure (POVM), is shown to be a consequence of the environment-assisted invariance (envariance) idea suggested by Zurek [Phys. Rev. Lett. 90, 120404 (2003)], being completed by Gleason's theorem. This provides also a method for derivation of the Born rule.
Quantum Theory in the Rigged Hilbert Space-Irreversibility from Causality
在回顾了时间箭头之后，我们描述了量子理论中时间不对称的可能性。而希尔伯特空间量子力学是时间对称的，从狄拉克的bra-ket形式主义产生的操纵希尔伯特空间公式，允许选择类似于麦克斯韦方程组的时间辐射箭头的延迟解的非对称边界条件。这导致了微观物理层面上的不可逆性，如衰减状态或共振所示。共振在数学上由伽莫夫矢量表示，伽莫夫矢量是一个非常好的（哈代类）矢量空间上的泛函，它是由边界条件（衰减态的输出）选择的。伽莫夫态具有准稳态所需的所有性质。对于他们来说，黄金法则可以从满足时间不对称条件的基本概率中推导出来，而这在希尔伯特空间中是无法实现的。
Quantum theory expresses the observable relations between physical properties in terms of probabilities that depend on the specific context described by the "state" of a system. However, the laws of physics that emerge at the macroscopic level are fully deterministic. Here, it is shown that the relation between quantum statistics and deterministic dynamics can be explained in terms of ergodic averages over complex valued probabilities, where the fundamental causality of motion is expressed by an action that appears as the phase of the complex probability multiplied with the fundamental constan…
This work analyses the performance of quantum circuits and general processes to transform $k$ uses of an arbitrary unitary operation $U$ into another unitary operation $f(U)$. When the desired function $f$ a homomorphism, i.e., $f(UV)=f(U)f(V)$, it is known that optimal average fidelity is attainable by parallel circuits and indefinite causality does not provide any advantage. Here we show that the situation changes dramatically when considering anti-homomorphisms, i.e., $f(UV)=f(V)f(U)$. In particular, we prove that when $f$ is an anti-homomorphism, sequential circuits could exponentially out…
We report novel interference effects in wave packet scattering of identical particles incident on the same side of a resonant barrier, different from those observed in Hong-Ou-Mandel experiments. These include significant changes in the mean number of transmissions and full counting statistics, as well as "bunching" and "anti-bunching" effects in the all-particles transmission channel. With several resonances involved, pseudo-resonant driving of the two-level system in the barrier, may result in sharp enhancement of scattering probabilities for certain values of temporal delay between the part…
The Born rule, a foundational axiom used to deduce probabilities of events from wavefunctions, is indispensable in the everyday practice of quantum physics. It is also key in the quest to reconcile the ostensibly inconsistent laws of the quantum and classical realms, as it confers physical significance to reduced density matrices, the essential tools of decoherence theory. Following Bohr's Copenhagen interpretation, textbooks postulate the Born rule outright. However, recent attempts to derive it from other quantum principles have been successful, holding promise for simplifying and clarifying…
Certified quantum supremacy in entanglement-assisted prepare-measure random-access-code
研究在 n→l 随机访问码框架下的纠缠辅助制备-测量通信游戏，通过分析技术得出 4→l、5→l 等情况下的最优量子成功概率，展示量子优越性，验证爱丽丝酉操作，还扩展了 n→n - 2 情况的量子优势证明。
Inaccurate (weak) measurements classical and quantum
研究不准确测量对经典和量子系统的影响，发现个体试验信息丢失，但可提取统计参数。量子准概率可为负，导致指针读数异常，但源于分布重塑而非量子变量异常大值。
Universal quantum gates lie at the heart of designing quantum computer. We construct two compact quantum circuits to implement post-selected controlled-phase-flip (CPF) gate and Toffoli gate with linear optics assisted by one and two single photons, respectively. The current existing maximum success probability of 1/4 for linear optical CPF gate is achieved by resorting to an ancillary single photon rather than an entangled photon pair or two single photons. Remarkably, our Toffoli gate is accomplished with current maximum success probability of 1/30 without using additional entangled photon p…
A physical distinction between a covariant and non covariant reduction process in relativistic quantum theories
因果性对在相对论性量子理论中可能是可观测的算符的类型施加了严格的限制。事实上，当使用标准的非协变过程计算某些部分因果连接测量的条件概率时，会出现因果违规。在这里，我们介绍另一种计算条件概率的方法，基于事件的内在协变关系顺序，当包括这些类型的测量时，它不同于标准的方法。这个替代过程与更广泛和非常自然的一类算子兼容，而不会破坏因果关系。如果这些测量中的一些可以在实践中实现我们的形式主义所预测的，非协变的，传统的方法应该放弃。此外，我们在这里推广的描述将意味着一个新的物理效应，其中干扰项被抑制作为测量过程中的协变阶数的结果。
The Hilbert space formalism describes causality as a statistical relation between initial experimental conditions and final measurement outcomes, expressed by the inner products of state vectors representing these conditions. This representation of causality is in fundamental conflict with the classical notion that causality should be expressed in terms of the continuity of intermediate realities. Quantum mechanics essentially replaces this continuity of reality with phase sensitive superpositions, all of which need to interfere in order to produce the correct conditional probabilities for the…
We consider a topological Hamiltonian and establish a correspondence between its eigenstates and the resource for a causal order game introduced in Ref. [1] known as process matrix. We show that quantum correlations generated in the quantum many-body energy eigenstates of the model can mimic the statistics that can be obtained by exploiting different quantum measurements on the process matrix of the game. This provides an interpretation of the expectation values of the observables computed for the quantum many-body states in terms of the success probabilities of the game. As a result, we show …
Causality in Time-Neutral Cosmologies
盖尔曼和哈特尔（GMH）最近考虑了时间中性的宇宙学模型，其中初始和最终条件是独立指定的，几位作者研究了这种模型的实验测试。我们在这里指出，GMH时间中性模型可以允许超光速信号，在这个意义上说，它可以为观察者在这些宇宙学，通过检测和利用在最终状态的超光速，以构建设备，发送和接收信号之间的空间分离点。在合适的宇宙学中，任何一个超光速信息都可以通过使用冗余信号以任意接近1的概率传输。然而，量子测量的结果概率通常精确地取决于过去的{ \it和未来的}测量发生。由于任何信号的传输都依赖于量子测量，因此其传输概率类似地依赖于上下文。因此，标准的超光速信号悖论并不适用。尽管这些模型具有不寻常的特征，但它们在内部是一致的。这些结果说明了一个有趣的概念点。闵可夫斯基因果关系的标准观点并不是相对论性量子理论的数学形式中绝对不可缺少的一部分。这取决于经验观察，即自然发生的集合可以自然地预先选择，但不能事后选择。
A fundamental problem in quantum information is to explore the roles of different quantum correlations in a quantum information procedure. Recent work [Phys. Rev. Lett., 107 (2011) 080401] shows that the protocol for assisted optimal state discrimination (AOSD) may be implemented successfully without entanglement, but with another correlation, quantum dissonance. However, both the original work and the extension to discrimination of $d$ states [Phys. Rev. A, 85 (2012) 022328] have only proved that entanglement can be absent in the case with equal a \emph{priori} probabilities. By improving the…
Collaborative communication tasks such as random access codes (RACs) employing quantum resources have manifested great potential in enhancing information processing capabilities beyond the classical limitations. The two quantum variants of RACs, namely, quantum random access code (QRAC) and the entanglement-assisted random access code (EARAC), have demonstrated equal prowess for a number of tasks. However, there do exist specific cases where one outperforms the other. In this article, we study a family of $3 \rightarrow 1$ distributed RACs \cite{network} and present its general construction of…
Entanglement-assisted phase estimation algorithm for calculating dynamical response functions
本文提出一种采用最优纠缠输入态的纠缠辅助量子相位估计算法，有效缓解了固有频谱泄漏问题，实现了更精确的跃迁能与跃迁概率估计，并在凝聚态物理、量子化学和核物理的数值模拟中验证了其有效性。
LEAD: A Local Ensemble-Assisted Parallel Decoding Framework for Quantum Tanner Codes
本文提出LEAD框架，通过利用Cayley复形的可分解结构，将全局码投影到由顶点邻域定义的重叠局部子码上，并通过并行估计误差概率，从而实现低复杂度且兼容多种局部搜索启发式的高效解码。
Quantum channel coding: Approximation algorithms and strong converse exponents
该研究通过证明非信号辅助与元逆松弛的等价性，并给出舍入近似算法，为纠缠辅助量子信道编码提供了强逆指数的紧刻画。
Assisted quantum teleportation
本文研究了通过非最大纠缠对进行量子 teleportation 时诱导的噪声通道问题，提出了一种辅助量子 teleportation 框架，通过第三方提供辅助多粒子纠缠来恢复完美贝尔对，并分析了第三方在不同操作模型中的作用，展示了 W 资源的操作不等价性以及有限次数概率恢复的最优成功概率。
Chaos assisted tunnelling with cold atoms
在量子混沌的背景下，理论和数值分析预测大波动的隧道跃迁概率时，不规则的动力学是目前在经典水平。本文研究了两束激光产生的含时调制周期势场中冷原子的非耗散量子演化。我们给出了一些精确的指导方针，观察混沌辅助隧穿之间的不变的相空间结构配对的时间反演对称性。
Probabilities from Entanglement, Born's Rule from Envariance
我展示了概率如何出现在量子物理中，通过探索{ \it环境辅助不变性}或{ \it不变性}的影响，最近发现的纠缠量子系统所表现出的对称性。完美纠缠的“钟形”态的不变性可以用来严格证明观察者完全不知道纠缠对中任何一个成员的任何测量结果。对于更一般的状态，不变性导致玻恩规则，$p_k \propto |ψ_k|^2$用于与施密特状态相关的结果。以这种方式导出的概率是系统基本状态的客观反映--它们代表了实验上可验证的对称性，而不仅仅是观察者的主观“知识状态”。基于方差的方法进行了比较，并发现优于前量子定义的概率，包括{ \it标准定义}的基础上的“无差异原则”由于拉普拉斯，和{ \it相对频率的方法}主张冯米塞斯。不变性对量子理论解释的意义超出了玻恩定则的推导：不变性足以建立复合系统演化态矢量的优先分支的动力学独立性，从而得出{ \it环境诱导的指针态超选择（einselection）}，这通常是通过呼吁退相干而得出的。玻恩概率法则的不变起源为无知（以及信息）与量子态的本质之间的关系提供了新的线索。
Photon-assisted entanglement creation by minimum-error generalized quantum measurements in the strong coupling regime
本文研究强耦合区利用光子辅助最小误差广义测量纠缠远距离量子比特，通过后选择制备高保真贝尔态，规避弱耦合限制，为量子中继器提供新方案。
Reliable entangling gates for qubits encoded in single-photon states represent a major challenge on the road to scalable quantum computing architectures based on linear optics. In this work, we present two approaches to develop high-fidelity, near-deterministic controlled-sign-shift gates based on the techniques of quantum gate teleportation. On the one hand, teleportation in a discrete-variable setting, i.e., for qubits, offers unit-fidelity operations but suffers from low success probabilities. Here, we apply recent results on advanced linear optical Bell measurements to reach a near-determi…
Scattering theory of plasmon-assisted entanglement transfer and distillation
分析了E. Altewischer，M.P. van Exter和J.P. Woerdman [Nature，418，304（2002）]。在两个线性介质（如实验中的穿孔金属膜）后面的光电探测器处贝尔不等式的最大违反S可以用两个与偏振相关的透射概率的比值tau_1、tau_2来描述。当tau_1=tau_2时，完全纠缠的入射态在传输过程中没有退化，但在S减小的情况下，tau_1和tau_2的相对较大的失配是可以容忍的。我们预言，如果τ_1和τ_2满足一对不等式，完全纠缠的Bell对可以从部分纠缠辐射中分离出来。
Control landscape of measurement-assisted transition probability for a three-level quantum system with dynamical symmetry
本文针对具有动力学对称性的三能级量子系统，完整刻画测量辅助跃迁概率随欧拉角变化的控制景观及其临界点类型，并比较不同能级跃迁与测量方案。
The Born rule for probabilities of measurement results is deduced from the set of five assumptions. The assumptions state that: (a) the state vector fully determines the probabilities of all measurement results; (b) between measurements, any quantum system is governed by that part of standard quantum mechanics, which does not refer to measurements; (c) probabilities of measurement results obey the rules of the classical theory of probability; (d) no information transfer is possible without interaction; (e) if two spin-1/2 particles are in the entangled state (sqrt(1-λ)|up>|up> + sqrt(λ)|down>|…
Bell's go theorem: regaining local causality with a new notion of realism
该研究提出新本体论框架，将贝尔“不行”定理转为“可行”定理，使局域因果模型能达到贝尔-CHSH 代数最大值内所有值，为量子预测提供非阴谋性实在性解释。
We address the standard quantum error correction using the three-qubit bit-flip code, yet in continuous-time. This entails rendering a target manifold of quantum states globally attractive. Previous feedback designs could feature spurious equilibria, or resort to discrete kicks pushing the system away from these equilibria to ensure global asymptotic stability. We present a new approach that consists of introducing controls driven by Brownian motions. Unlike the previous methods, the resulting closed-loop dynamics can be shown to stabilize the target manifold exponentially. We further present …
Bridging General Relativity and Quantum Dynamics Through Finite-Resource Logical Models
本文提出 Energy Constrained Linear Causality (ECLC) 框架，利用 Kripke 语义和线性逻辑将因果性、能量和信息视为有限资源，从而桥接广义相对论与量子动力学，为有限物理宇宙中的因果、计算与涌现提供统一的资源感知逻辑。
The resource theory of coherence studies the operational value of superpositions in quantum technologies. A key question in this theory concerns the efficiency of manipulation and inter-conversion of the resource. Here we solve this question completely for qubit states by determining the optimal probabilities for mixed state conversions via stochastic incoherent operations. Extending the discussion to distributed scenarios, we introduce and address the task of assisted incoherent state conversion where the process is enhanced by making use of correlations with a second party. Building on these…
Operationalism, Causality, and Quantum Theory: a mostly time symmetric perspective
本文从时间对称视角探讨操作概率理论，提出简单与复杂操作的因果结构，并证明时间对称与时间正向视角等价，发展了Hilbert对象的图示符号。
Extending quantum theory with AI-assisted deterministic game theory
本文提出用AI辅助的确定性博弈理论扩展量子理论，通过学习博弈奖励函数和非纳什解算法，探索本地隐变量理论的可能性。
An unexpected breakdown in the existing theory of quantum serial turbo coding is that a quantum convolutional encoder cannot simultaneously be recursive and non-catastrophic. These properties are essential for quantum turbo code families to have a minimum distance growing with blocklength and for their iterative decoding algorithm to converge, respectively. Here, we show that the entanglement-assisted paradigm simplifies the theory of quantum turbo codes, in the sense that an entanglement-assisted quantum (EAQ) convolutional encoder can possess both of the aforementioned desirable properties. …
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