量子成像

Quantum chemistry beyond Born-Oppenheimer approximation on a quantum computer: a simulated phase estimation study

We present an efficient quantum algorithm for beyond-Born-Oppenheimer molecular energy computations. Our approach combines the quantum full configuration interaction method with the nuclear orbital plus molecular orbital (NOMO) method. We give the details of the algorithm and demonstrate its performance by classical simulations. Two isotopomers of the hydrogen molecule (H$_2$, HT) were chosen as representative examples and calculations of the lowest rotationless vibrational transition energies were simulated.

Reply to "Comment on `Gleason-type theorem including qubits and projective measurements: the Born rule beyond quantum physics' ", by Michael J. W. Hall

We present a reply to the objections raised by M. J. W. Hall against our extension of Gleason's theorem.

Reconstructing Quantum States Using Basis-Enhanced Born Machines

Rapid improvement in quantum hardware has opened the door to complex problems, but the precise characterization of quantum systems itself remains a challenge. To address this obstacle, novel tomography schemes have been developed that employ generative machine learning models, enabling quantum state reconstruction from limited classical data. In particular, quantum-inspired Born machines provide a natural way to encode measured data into a model of a quantum state. Born machines have shown great success in learning from classical data; however, the full potential of a Born machine in learning …

量子可观测量的动力学与玻姆量子力学中的玻恩规则

Dynamics of quantum observables and Born's rule in Bohmian Quantum Mechanics

本文研究了各向异性二维量子谐振子中玻姆轨迹的有序与混沌特性，通过标准量子力学和玻姆力学计算能量、动量等可观测量平均值，并分析不同节点波函数下轨迹类型对平均值的贡献。

Quantum probabilities from quantum entanglement: Experimentally unpacking the Born rule

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…

Environment-assisted invariance does not necessitate Born's rule for quantum measurement

The argument of environment-assisted invariance (known as envariance) implying Born's rule is widely used in models for quantum measurement to reason that they must yield the correct statistics, specifically for linear models. However, it has recently been shown that linear collapse models can never give rise to Born's rule. Here, we address this apparent contradiction and point out an inconsistency in the assumptions underlying the arguments based on envariance. We use a construction in which the role of the measurement machine is made explicit and show that the presence of envariance does no…

Underlying non-Hermitian character of the Born rule in open quantum systems

The absolute value squared of the probability amplitude corresponding to the overlap of an initial state with a continuum wave solution to the Schrödinger equation of the problem, has the physical interpretation provided by the Born rule. Here, it is shown that for an open quantum system, the above probability may be written in an exact analytical fashion as an expansion in terms of the non-Hermitian resonance (quasinormal) states and complex poles to the problem which provides an underlying non-Hermitian character of the Born rule.

Analysis of Wallace's Proof of the Born Rule in Everettian Quantum Mechanics II: Concepts and Axioms

Having analyzed the formal aspects of Wallace's proof of the Born rule, we now discuss the concepts and axioms upon which it is built. Justification for most axioms is shown to be problematic, and at times contradictory. Some of the problems are caused by ambiguities in the concepts used. We conclude the axioms are not reasonable enough to be taken as mandates of rationality in Everettian Quantum Mechanics. This invalidates the interpretation of Wallace's result as meaning it would be rational for Everettian agents to decide using the Born rule.

Testing Born's Rule in Quantum Mechanics for Three Mutually Exclusive Events

We present a new experimental approach using a three-path interferometer and find a tighter empirical upper bound on possible violations of Born's Rule. A deviation from Born's rule would result in multi-order interference. Among the potential systematic errors that could lead to an apparent violation we specifically study the nonlinear response of our detectors and present ways to calibrate this error in order to obtain an even better bound.

利用关于量子粒子动力学的一项物理要求改进 Born 规则的证明

Improving the proof of the Born rule using a physical requirement on the dynamics of quantum particles

本文通过引入“短时间内粒子性质保持不变”的动力学公设，改进已有结果并给出 Born 规则的完整证明，同时指出该公设被所有实验满足却无法由标准量子力学公设推出。

Justifying Born's rule $P_α=|Ψ_α|^2$ using deterministic chaos, decoherence, and the de Broglie-Bohm quantum theory

In this work we derive Born's rule from the pilot-wave theory of de Broglie and Bohm. Based on a toy model involving a particle coupled to a environement made of "qubits" (i.e., Bohmian pointers) we show that entanglement together with deterministic chaos lead to a fast relaxation from any statistitical distribution $ρ(x)$ (of finding a particle at point $x$) to the Born probability law $|Ψ(x)|^2$. Our model is discussed in the context of Boltzmann's kinetic theory and we demonstrate a kind of H theorem for the relaxation to the quantum equilibrium regime.

Nelson随机动力学中的量子平衡弛豫与玻恩定则

Relaxation to quantum equilibrium and the Born rule in Nelson's stochastic dynamics

该研究通过数值模拟Nelson随机动力学的三种量子系统，发现引力场中自由下落粒子可在量子弛豫完成前出现干涉，为区分标准量子力学与Nelson理论提供实验方向。

那么量子理论呢？贝叶斯和玻恩解释

What About Quantum Theory? Bayes and the Born Interpretation

我证明了量子力学中的概率是对人类无知存在的信念的度量，就像所有其他概率一样。玻恩对波函数模的平方的解释来自于量子系统与观察者的相互作用，除非观察者无法获得系统波函数中所有可用的信息，否则概率不会出现。量子力学一般不允许获得所有的信息，即使在原则上，就像在相对论中不能获得来自过去光锥之外的信息一样。但概率并不意味着非决定论。相反，量子力学比经典力学更具决定性。

Modified Born-Jordan Method For Constructing The Commutation Relation Of Coordinate and Momentum

The Born-Jordan method for constructing the quantum condition of the Matrix Mechanics is pointed out to be inappropriate in the present work. We modify this method and reconstruct the quantum condition by setting up a new expression for the Bohr quantum condition with the help of the (n,n) elements of the matrix $\oint\hat{p}(t){\rm d}\hat{x}(t)$.

Emergence of the Born rule in quantum optics

The Born rule provides a fundamental connection between theory and observation in quantum mechanics, yet its origin remains a mystery. We consider this problem within the context of quantum optics using only classical physics and the assumption of a quantum electrodynamic vacuum that is real rather than virtual. The connection to observation is made via classical intensity threshold detectors that are used as a simple, deterministic model of photon detection. By following standard experimental conventions of data analysis on discrete detection events, we show that this model is capable of repr…

Born Machines for Periodic and Open XY Quantum Spin Chains

Quantum phase transitions are ubiquitous in quantum many body systems. The quantum fluctuations that occur at very low temperatures are known to be responsible for driving the system across different phases as a function of an external control parameter. The XY Hamiltonian with a transverse field is a basic model that manifests two distinct quantum phase transitions, including spontaneous $Z_2$ symmetry breaking from an ordered to a disordered state. While programmable quantum devices have shown great success in investigating the various exotic quantum phases of matter, in parallel, the quest …

时间非局域效应导致的玻恩定则偏离

Born's rule deviations from temporal non-local effects

本研究针对量子平衡假设不成立的系统，借助量子流体动力学框架揭示渡越干涉与本征记忆效应诱导的有限时间非局域关联会导致玻恩定则偏离，其表现为不稳定态生存概率的非指数衰减，挑战传统量子概率解释并为时间非局域性实验提供新动力学指导。

Quantum regression beyond the Born-Markov approximation for generalized spin-boson models

The quantum regression formula for an open quantum system consists in an infinite hierarchy of conditions for its multi-time correlation functions, thus requiring full access to the total "system+environment" evolution, and providing a stronger requirement than CP-divisibility. Here, we analyze CP-divisibility and check the validity of quantum regression beyond the Born-Markov approximation (e.g. weak coupling limit) for a class of generalized spin-boson (GSB) models giving rise to a multi-level amplitude-damping evolution; in all cases, it is possible to engineer the system-bath coupling in s…

Born Rule and Logical Inference in Quantum Mechanics

Logical inference leads to one of the major interpretations of probability theory called logical interpretation, in which the probability is seen as a measure of the plausibility of a logical statement under incomplete information. In this paper, assuming that our usual inference procedure makes sense for every set of logical propositions represented in terms of commuting projectors on a given Hilbert space, we extend the logical interpretation to quantum mechanics and derive the Born rule. Our result implies that, from the epistemological viewpoints, we can regard quantum mechanics as a natur…

光谱玻恩机器：用于离散数据的经典可训练量子生成模型

Spectral Born machines: classically trainable quantum generative models for discrete data

介绍光谱玻恩机器这一量子生成模型，它借量子傅里叶变换适合学习整数结构数据，难以经典采样。可通过基于图光谱分析的损失在经典硬件高效训练，实验显示其光谱偏差使参数减少，能成功学习特定RNA分布，不易过拟合。

统一量子动力学：Born规则的涌现

Unified Quantum Dynamics: The Emergence of the Born Rule

本文提出含“小信号截断”的修正Schrödinger方程，证明Born规则可自然涌现，并将多世界分支及其统计性质统一于单一运动定律。

A Continuous Variable Born Machine

Generative Modelling has become a promising use case for near term quantum computers. In particular, due to the fundamentally probabilistic nature of quantum mechanics, quantum computers naturally model and learn probability distributions, perhaps more efficiently than can be achieved classically. The Born machine is an example of such a model, easily implemented on near term quantum computers. However, in its original form, the Born machine only naturally represents discrete distributions. Since probability distributions of a continuous nature are commonplace in the world, it is essential to …

Born Rule and Finkelstein-Hartle Frequency Operator Revisited

Character of observables in classical physics and quantum theory is reflected upon. Born rule in the context of measurement being an interaction between two quantum systems is discussed. A pedagogical introduction to Finkelstein-Hartle frequency operator is presented.

The Born rule

We deduce the Born rule. No use is required of quantum postulates. One exploits only rudimentary quantum mathematics--a linear, not Hilbert', vector space--and empirical notion of the statistical length of a state. Its statistical nature comes from the experimental detector-clicks being formalized into the abstract quantum micro-events. We also comment on that it is not only that the use has not been made of some quantum axioms when deriving the rule but, in a sense, their invoking would be inconsistent.

Born-Oppenheimer approximation for open quantum systems within the quantum trajectory approach

Based on the quantum trajectory approach, we extend the Born-Oppenheimer (BO) approximation from closed quantum system to open quantum system, where the open quantum system is described by a master equation in Lindblad form. The BO approximation is defined and the validity condition is derived. We find that the dissipation in fast variables benefits the BO approximation that is different from the dissipation in slow variables. A detailed comparison between this extension and our previous approximation (that is based on the effective Hamiltonian approach, see X. L. Huang and X. X. Yi, Phys. Rev…

A simple derivation of Born's rule with and without Gleason's theorem

We present a derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. Combined to Gleason's theorem, this approach naturally leads to the usual quantum formalism, within a new conceptual framework that is discussed heuristically in details. The structure of Quantum Mechanics, from its probabilistic nature to its mathematical expression, appears as a result of the interplay between the quantized number of "modalities" accessible to a quantum system, and the continuum of "contexts" that are required to…

Verification of the Born rule via direct measurement of superposition wavefunction

The Born rule, which is one of foundational axioms of quantum theory, states that the probability of obtain outcome $a$ for the quantum state $|ψ\rangle$ is determined by $P(a)=|\langle a|ψ\rangle|^{2}$. Despite its great success in predicting the experimental outcomes, there still lacks a direct way to verify the Born rule. Here, we show that the weak value based direct measurement of superposition wavefunction is feasible, which can be used to verify the Born rule directly. The plausible experiment is suggested.

Born-Oppenheimer approximation in open systems

We generalize the standard Born-Oppenheimer approximation to the case of open quantum systems. We define the zeroth order Born-Oppenheimer approximation of an open quantum system as the regime in which its effective Hamiltonian can be diagonalized with fixed slowly changing variables. We then establish validity and invalidity conditions for this approximation for two kinds of dissipations--the spin relaxation and the dissipation of center-of-mass motion. As an example, the Born-Oppenheimer approximation of a two-level open system is analyzed.

误差缓解的光子量子电路 Born 机

Error-mitigated photonic quantum circuit Born machine

针对光子系统中光子损失导致的 QCBM 训练退化问题，提出线性光学 QCBM，并通过模拟与光子集成处理器实验验证回收缓解技术可显著提升训练效果。

Updating the Born rule

Despite the tremendous empirical success of quantum theory there is still widespread disagreement about what it can tell us about the nature of the world. A central question is whether the theory is about our knowledge of reality, or a direct statement about reality itself. Regardless of their stance on this question, current interpretations of quantum theory regard the Born rule as fundamental and add an independent state-update (or "collapse") rule to describe how quantum states change upon measurement. In this paper we present an alternative perspective and derive a probability rule that su…

量子力学中玻恩规则是否意味着时间演化的幺正性？

Does Born Rule Imply Unitarity of Time Evolution in Quantum Mechanics?

探讨量子力学中玻恩规则与时间演化幺正性的关系，指出认为玻恩规则暗示幺正性的观点有缺陷，即便动力学非幺正，玻恩规则也能确保总概率守恒，适用于多种量子系统系综，还讨论了相关守恒及反对观点。

Detection of quantum non-Markovianity close to the Born-Markov approximation

We calculate in an exact way the conditional past-future correlation for the decay dynamics of a two-level system in a bosonic bath. Different measurement processes are considered. In contrast to quantum memory measures based solely on system propagator properties, here memory effects are related to a convolution structure involving two system propagators and the environment correlation. This structure allows to detect memory effects even close to the validity of the Born-Markov approximation. An alternative operational-based definition of environment-to-system backflow of information follows …

On the Hydrogen Atom Beyond the Born-Oppenheimer Approximation

Recently a new formulation of quantum mechanics has been suggested which is based on the concept of signed particles, that is, classical objects provided with a position, a momentum and a sign simultaneously. In this paper, we comment on the plausibility of simulating atomic systems beyond the Born-Oppenheimer approximation by means of the signed particle formulation of quantum mechanics. First, in order to show the new perspective offered by this new formalism, we provide an example studying quantum tunnelling through a simple Gaussian barrier in terms of the signed particle formulation. Then…

玻恩定则——百年前与今天

The Born rule -- 100 years ago and today

本文梳理玻恩定则从1926年提出至今的发展历程，涵盖早期历史、POVM推广及现代推导，同时指出其具有有限适用域，超出范围应用会产生问题。

宏观观测量和玻恩定则

Macroscopic observables and the Born rule

我们澄清玻恩定则在量子力学的哥本哈根诠释中的角色，方法是从玻尔的经典概念学说中推导出玻恩定则，并将其转化为以下数学陈述：由可观测量的非交换C *-代数描述的量子系统只能通过相关的交换C*-代数来经验地访问。玻恩概率作为量子系统长期测量结果的相对频率出现;没有必要采用单例概率的频率解释（这将是后续论文的主题）。玻恩定则的推导使用了芬克尔斯坦（1965）和哈特尔（1968）开始的一个计划中的思想，该计划旨在将玻恩定则作为量子力学的一个独立假设。从数学上讲，我们的方法改进了以前对这一方案的阐述--特别是由Farhi、Goldstone和Gutmann（1989）完成并由Van Wesep（2006）完成的方案--用C*-代数的连续域代替Hilbert空间的无限张量积。结合我们的解释背景，这种技术上的改进规避了玻恩定则早期推导所引起的有效批评，特别是这样的推导在数学上有缺陷，而且是循环的。此外，我们的推导并不依赖于量子理论中有争议的本征向量-本征值联系，而是假设经典物理学中的纯态具有通常的解释，即为可观察量赋予尖锐值的真理制造者。

Born最后通牒：基于关联子的量子生成模型经典代理化条件

The Born Ultimatum: Conditions for Classical Surrogation of Quantum Generative Models with Correlators

本文将量子电路Born机识别为量子傅里叶模型，解析量化了经典训练与量子部署间的参数差异，并推导了多种电路下Pauli传播的闭式表达式，为经典代理化提供了条件。

论新量子方法中的玻恩规则

On the Born rule in a new quantum approach

该研究在新量子基础方法中，通过跃迁概率原理这一弱条件证明了玻恩规则，并提出了比传统更简单的态概念。

Quantum Theory of the Classical: Quantum Jumps, Born's Rule, and Objective Classical Reality via Quantum Darwinism

Emergence of the classical world from the quantum substrate of our Universe is a long-standing conundrum. I describe three insights into the transition from quantum to classical that are based on the recognition of the role of the environment. I begin with derivation of preferred sets of states that help define what exists - our everyday classical reality. They emerge as a result of breaking of the unitary symmetry of the Hilbert space which happens when the unitarity of quantum evolutions encounters nonlinearities inherent in the process of amplification - of replicating information. This der…

How a wave function can collapse without violating Schroedinger's equation, and how to understand Born's rule

It is often claimed that the collapse of the wave function and Born's rule to interpret the square of the norm as a probability, have to be introduced as separate axioms in quantum mechanics besides the Schroedinger equation. Here we show that this is not true in certain models where quantum behavior can be attributed to underlying deterministic equations. It is argued that indeed the apparent spontaneous collapse of wave functions and Born's rule are features that strongly point towards determinism underlying quantum mechanics.

Entanglement and the Born-Oppenheimer approximation in an exactly solvable quantum many-body system

We investigate the correlations between different bipartitions of an exactly solvable one-dimensional many-body Moshinsky model consisting of Nn "nuclei" and Ne "electrons". We study the dependence of entanglement on the inter-particle interaction strength, on the number of particles, and on the particle masses. Consistent with kinematic intuition, the entanglement between two subsystems vanishes when the subsystems have very different masses, while it attains its maximal value for subsystems of comparable mass. We show how this entanglement feature can be inferred by means of the Born-Oppenhe…

Quantum Simulation of non-Born-Oppenheimer dynamics in molecular systems by path integrals

A numerical algorithm based on the probabilistic path integral approach for solving Schroedinger equation has been devised to treat molecular systems without Born-Oppenheimer approximation in the non relativistic limit at zero temperature as an alternative to conventional Variational and perturbation methods. Using high quality variational trial functions and path integral method based on Generalized Feynman-Kac method, we have been able to calculate the non-Born-Oppenheimer energy for hydrogen molecule for the sigma state and hydrogen molecular ion. Combining these values and the value for io…

Improved master equation approach to quantum transport: From Born to self-consistent Born approximation

Beyond the second-order Born approximation, we develop an improved master equation approach to quantum transport by virtue of a self-consistent Born approximation. The basic idea is replacing the free Green's function in the tunneling self-energy by an effective reduced propagator under the Born approximation. We found that the effect of this simple improvement is remarkable, for instance, it can not only recover the exact result of noninteracting transport under arbitrary voltages, but also predict the challenging nonequilibrium Kondo effect. In addition to having an elegant structure, the ap…

New derivation of Born's law and parameter estimation based on a relative state formulation

Excluding the concept of probability in quantum mechanics, we derive Born's law from the remaining postulates in quantum mechanics using type method. We also give a way of determining the unknown parameter in a state vector based on an indirect measurement model. While Deutsch adopt a concept of rational decision-maker who introduces probability, we adopt a concept of statistician in our measurement model and clarifies the distinguished feature of quantum measurement. Like many worlds interpretation, our scenario gives a simple solution for problem of measurement.

Born's rule as a quantum extension of Bayesian coherence

The subjective Bayesian interpretation of probability asserts that the rules of the probability calculus follow from the normative principle of Dutch-book coherence: A decision-making agent should not assign probabilities such that a series of monetary transactions based on those probabilities would lead them to expect a sure loss. Similarly, the subjective Bayesian interpretation of quantum mechanics (QBism) asserts that the Born rule is a normative rule in analogy to Dutch-book coherence, but with the addition of one or more empirically based assumptions -- i.e., the "only a little more" tha…

哪路信息的起源与玻恩定则的推广

Origin of which-way information and generalization of the Born rule

例如，在双缝实验中，恢复哪条路的信息的可能性是基于一个关于粒子位置的自然但隐含的假设，这个假设不能从量子力学的标准假设中推导出来。在本文中，这一假设是明确的，并正式假定为一个新的规则，{ \it量子典型性规则}。这条规则将粒子在两个不同时间的位置关联起来，从而定义了它们的轨迹。出乎意料的是，这个规则在解释统计实验结果方面也等同于玻恩规则。因此，它可以被认为是玻恩规则的推广。量子典型性规则的存在有力地表明了一种新的基于概率的量子力学公式的可能性。根据这个新的公式，一个封闭的量子系统被表示为一个{ \it量子过程}，它对应于一个典型的随机过程，其中的概率测度被替换为波函数和通常的频率解释的概率被替换为量子典型性规则。

Quantum fractionalism: the Born rule as a consequence of the complex Pythagorean theorem

Everettian Quantum Mechanics, or the Many Worlds Interpretation, lacks an explanation for quantum probabilities. We show that the values given by the Born rule equal projection factors, describing the contraction of Lebesgue measures in orthogonal projections from the complex line of a quantum state to eigenspaces of an observable. Unit total probability corresponds to a complex Pythagorean theorem: the measure of a subset of the complex line is the sum of the measures of its projections on all eigenspaces. To show that projection factors can work as probabilities, we postulate the existence o…

Three path interference using nuclear magnetic resonance: a test of the consistency of Born's rule

The Born rule is at the foundation of quantum mechanics and transforms our classical way of understanding probabilities by predicting that interference occurs between pairs of independent paths of a single object. One consequence of the Born rule is that three way (or three paths) quantum interference does not exist. In order to test the consistency of the Born rule, we examine detection probabilities in three path intereference using an ensemble of spin-1/2 quantum registers in liquid state nuclear magnetic resonance (LSNMR). As a measure of the consistency, we evaluate the ratio of three way…

利用Born机器从时间传播推导哈密顿量

Derivation of Hamiltonians from time propagations using Born machines

本文提出哈密顿量工程Born机器（HEBM）方法，利用Born机器优化量子系统时间传播，计算并验证了向条纹分布、高斯分布及吉布斯态传播的最优哈密顿量，可实现快速准确演化。

Analysis of Wallace's Proof of the Born Rule in Everettian Quantum Mechanics: Formal Aspects

To solve the probability problem of the Many Worlds Interpretation of Quantum Mechanics, D.Wallace has presented a formal proof of the Born rule via decision theory, as proposed by D.Deutsch. The idea is to get subjective probabilities from rational decisions related to quantum measurements, showing the non-probabilistic parts of the quantum formalism, plus some rational constraints, ensure the squared modulus of quantum amplitudes play the role of such probabilities. We provide a new presentation of Wallace's proof, reorganized to simplify some arguments, and analyze it from a formal perspect…

来自量子频率主义的玻恩规则

Born's Rule from Quantum Frequentism

本文提出玻恩规则的广义形式，证明任意可分解态测量中不存在违反玻恩规则的历史，从而说明纯幺正演化可在更宽松条件下与玻恩规则共存，并将其应用于量子电路保真度，提出基于自信息率的单次基准测试替代方案。

Is the Born Rule Anthropically Determined?

I argue that various derivations of the Born probability rule within strictly unitary quantum mechanics implicitly use anthropic constraints on the properties of the probabilities, but without proposing an ensemble from which those constraints limit a selection. An argument by Mallah obtains the Born probabilities explicitly for standard unitary dynamics but via postulating a hypothetical extra noise-like component of the quantum state. I argue that the implicit anthropic constraints required for well-behaved probability rules would select for a state of the sort Mallah proposes.

Endurance of Quantum Coherence in Born-Markov Open Quantum Systems

Quantum coherence, the physical property underlying fundamental phenomena such as multi-particle interference and entanglement, has emerged as a valuable resource upon which exotic modern technologies are founded. In general, the most prominent adversary of quantum coherence is noise arising from the interaction of the associated dynamical system with its environment. Under certain conditions, however, the existence of noise may drive quantum and classical systems to endure intriguing nontrivial effects. Along these lines, here we demonstrate, both theoretically and experimentally, that when t…

On the nature of the Born rule

A physical experiment comprises along the time trajectory a start, a time evolution (duration), and an end, which is the measurement. In non relativistic quantum mechanics the start of the experiment is defined by the wave function at time 0 taking into account the starting conditions, the evolution is described by the wave function following the Schrödinger equation and the measurement by the Born rule. While the Schrödinger equation is deterministic, it is the Born rule that makes quantum mechanics statistical with all its consequences. The nature of the Born rule is thereby unknown albeit n…

时空本征规则是准概率的

The spatiotemporal Born rule is quasiprobabilistic

本文提出一种准概率描述，将量子理论中的时空本规则扩展到时间领域，并结合量子贝叶斯规则，为开放量子系统的时间反转对称性提供操作性定义。