Are classical probabilities instances of quantum amplitudes?

Entanglement Symmetry, Amplitudes, and Probabilities: Inverting Born's Rule

Symmetry of entangled states under a swap of outcomes ("envariance") implies their equiprobability, and leads to Born's rule. Here I show that the amplitude of a state given by a superposition of sequences of events that share same total count (e.g., n detections of 0 and m of 1 in a spin 1/2 measurement) is proportional to the square root of the fraction - square root of the relative frequency - of all the equiprobable sequences of 0's and 1's with that n and m.

"Interaction-free" discrimination between semi-transparent objects

Absorption-free (also known as ``interaction-free'') measurement aims to detect the presence of an opaque object using a test particle without that particle being absorbed by the object. Here we consider semi-transparent objects which have an amplitude $α$ of transmitting a particle while leaving the state of the object unchanged and an amplitude $β$ of absorbing the particle. The task is to devise a protocol that can decide which of two known transmission amplitudes is present while ensuring that no particle interacts with the object. We show that the probabilities of being able to achieve th…

Path probabilities for consecutive measurements, and certain "quantum paradoxes"

We consider a finite-dimensional quantum system, making a transition between known initial and final states. The outcomes of several accurate measurements, which {\it could be} made in the interim, define virtual paths, each endowed with a probability amplitude. If the measurements are {\it actually made}, the paths, which may now be called "real", acquire also the probabilities, related to the frequencies, with which a path is seen to be travelled in a series of identical trials. Different sets of measurements, made on the same system, can produce different, or incompatible, statistical ensem…

Quantum Mechanics without amplitudes

Amplitudes are the major logical object in Quantum Theory. Despite this fact they presents no physical reality and in consequence only observables can be experimetally checked. We discuss the possibility of a theory of Quantum Probabilities capable of give full account to quantum phenomena. Advanteges of this formulation are the evidence of physical processes not described by the orotodox formulation using amplitudes and the possibility of a full algoritimization of Quantum Mechanics.

Weak measurements measure probability amplitudes (and very little else)

Conventional quantum mechanics describes a pre- and post-selected system in terms of virtual (Feynman) paths via which the final state can be reached. In the absence of probabilities, a weak measurement (WM) determines the probability amplitudes for the paths involved. The weak values (VW) can be identified with these amplitudes, or their linear combinations. This allows us to explain the "unusual" properties of the VW, and avoid the "paradoxes" often associated with the WM.

Computing quopit Clifford circuit amplitudes by the sum-over-paths technique

By the Gottesman-Knill Theorem, the outcome probabilities of Clifford circuits can be computed efficiently. We present an alternative proof of this result for quopit Clifford circuits (i.e., Clifford circuits on collections of $p$-level systems, where $p$ is an odd prime) using Feynman's sum-over-paths technique, which allows the amplitudes of arbitrary quantum circuits to be expressed in terms of a weighted sum over computational paths. For a general quantum circuit, the sum over paths contains an exponential number of terms, and no efficient classical algorithm is known that can compute the …

幅度放大在组合优化中的分析与实验验证

Analysis and Experimental Demonstration of Amplitude Amplification for Combinatorial Optimization

本文通过实验验证了量子幅度放大在组合优化中的应用，展示了其在接近全局最优解时的性能表现，并在不同量子比特平台上验证了算法的准确性。

从幺正性导出的量子概率的闭环结构

Closed-loop Structure of Quantum Probabilities from Unitarity

本文证明量子概率的闭环分解是幺正性的直接结果，Bargmann不变量自然作为与这些环相关的相位不变量出现，并将干涉解释为不同类别闭环的贡献，同时指出Born规则反映了正向和反向振幅乘积的基本二次结构。

Quantum amplitude estimation with error mitigation for time-evolving probabilistic networks

We present a method to model a discretized time evolution of probabilistic networks on gate-based quantum computers. We consider networks of nodes, where each node can be in one of two states: good or failed. In each time step, probabilities are assigned for each node to fail (switch from good to failed) or to recover (switch from failed to good). Furthermore, probabilities are assigned for failing nodes to trigger the failure of other, good nodes. Our method can evaluate arbitrary network topologies for any number of time steps. We can therefore model events such as cascaded failure and avala…

Derivation of classical capacity of quantum channel for discrete information source

In this letter, we prove that the classical capacity of quantum channel for $M$ symmetric states is achieved by an uniform distribution on a priori probabilities. We also investigate non-symmetric cases such as a ternary amplitude shift keyed signal set and a 16-ary quadrature amplitude modulated signal set in coherent states.

Hilbert-Schmidt Geometry of n-Level Jakobczyk-Siennicki Two-Dimensional Quantum Systems

Jakobczyk and Siennicki studied two-dimensional sections of a set of (generalized) Bloch vectors corresponding to n x n density matrices of two-qubit systems (that is, the case n = 4). They found essentially five different types of (nontrivial) separability regimes. We compute the Euclidean/Hilbert-Schmidt (HS) separability probabilities assigned to these regimes, and conduct parallel two-dimensional sectional analyses for the higher-level cases n=6,8,9 and 10. Making use of the newly-introduced capability for integration over implicitly defined regions of version 5.1 of Mathematica -- also fr…

Quantum measurement theory for particle oscillations

A fundamental principle of quantum theory, clearly manifested in the two-slit experiment, is that for any alternatives that cannot be distinguished by measurement physical predictions are obtained by summation of their amplitudes. In particle oscillation experiments, a particle's time of detection is not directly measured, consequently, the detection probability should involve the summation over amplitudes corresponding to different detection times. However, in contrast to the principle above, standard treatments involve summation over probabilities rather than amplitudes; this implicitly assu…

Quantum-mechanical probability from the symmetries of two-state systems

In 1989, Deutsch gave a basic physical explanation of why quantum-mechanical probabilities are squares of amplitudes. Essentially, a general state vector is transformed into a highly symmetric equal-amplitude superposition. The argument was recently elaborated and publicised by DeWitt. It has remained incomplete, however, inasmuch as both authors anticipate the usual normalization (sum of amplitudes squared) of state vectors. In the present paper, a thought experiment is devised in which Deutsch's idea is demonstrated independently of the normalization, exploiting further symmetries instead.

Are All Probabilities Fundamentally Quantum Mechanical?

The subjective and the objective aspects of probabilities are incorporated in a simple duality axiom inspired by observer participation in quantum theory. Transcending the classical notion of probabilities, it is proposed and demonstrated that all probabilities may be fundamentally quantum mechanical in the sense that they may all be derived from the corresponding amplitudes. The classical coin-toss and the quantum double slit interference experiments are discussed as illustrative prototype examples. Absence of multi-order quantum interference effects in multiple-slit experiments and the Exper…

量子增强的条件未来概率推断：降低内存成本

Quantum-Enhanced Inference of Conditional Future Probabilities with Reduced Memory Cost

该研究针对复杂随机系统的未来概率推断问题，提出量子算法方法，在保持二次加速的同时减少系统偏差与内存成本，推进了量子技术的实际应用。

通过组合代数操作性重建量子幅的费曼规则

Operational reconstruction of Feynman rules for quantum amplitudes via composition algebras

本文通过组合代数方法改进量子幅代数的分类，提出坐标无关的框架，无需先验二维幅，揭示实 associative 组合代数作为允许的幅代数，包括复数和四元数及其分裂形式，概率与Born规则类似。

Reconstruction of quantum theory on the basis of the formula of total probability

The notion of context (complex of physical conditions) is basic in this paper. We show that the main structures of quantum theory (interference of probabilities, Born's rule, complex probabilistic amplitudes, Hilbert state space, representation of observables by operators) are present in a latent form in the classical Kolmogorov probability model. However, this model should be considered as a calculus of contextual probabilities. In our approach it is forbidden to consider abstract context independent probabilities: ``first context and then probability.'' We start with the conventional formula…

基于相空间准概率的连续变量态纠缠维度

Entanglement Dimensionality of Continuous Variable States From Phase-Space Quasi-Probabilities

本研究针对连续变量系统纠缠维度表征问题，提出基于无限维布洛赫算子协方差的CV施密特数见证算子，相比离散化方法鲁棒性与通用性更强，为纯CV纠缠维度表征方法发展及实验实现提供支撑。

Bayesian Conditioning, the Reflection Principle, and Quantum Decoherence

The probabilities a Bayesian agent assigns to a set of events typically change with time, for instance when the agent updates them in the light of new data. In this paper we address the question of how an agent's probabilities at different times are constrained by Dutch-book coherence. We review and attempt to clarify the argument that, although an agent is not forced by coherence to use the usual Bayesian conditioning rule to update his probabilities, coherence does require the agent's probabilities to satisfy van Fraassen's [1984] reflection principle (which entails a related constraint poin…

Matter-enhanced transition probabilities in quantum field theory

The relativistic quantum field theory is the unique theory that combines the relativity and quantum theory and is invariant under the Poincaré transformation. The ground state, vacuum, is singlet and one particle states are transformed as elements of irreducible representation of the group. The covariant one particles are momentum eigenstates expressed by plane waves and extended in space. Although the S-matrix defined with initial and final states of these states hold the symmetries and are applied to isolated states, out-going states for the amplitude of the event that they are detected at a…

QAOA-Predictor: 预测成功概率和最小深度以实现高效的固定参数优化

QAOA-Predictor: Forecasting Success Probabilities and Minimal Depths for Efficient Fixed-Parameter Optimization

QAOA-Predictor利用图神经网络预测QAOA的成功概率和最小层数，实现高效固定参数优化。

针对任意初始成功概率的确定性量子搜索

Deterministic Quantum Search for Arbitrary Initial Success Probabilities

本研究提出一种针对任意初始成功概率的确定性量子搜索算法，仅需至多一次额外迭代即可保证搜索成功，保留二次方加速特性，还给出多目标态精确搜索方法及电路级实现。

"Violating'' Clauser-Horne inequalities within classical mechanics

Some authors have raised the question whether the probabilities stemming from a quantum mechanical computation are entitled to enter the Bell and the Clauser-Horne inequalities. They have remarked that if the quantum probabilities are given the status of conditional ones and the statistics for the various settings of the detectors in a given experiment is properly kept into account, the inequalities happen to be no longer violated. In the present paper a classical simile modeled after the quantum mechanical instances is closely scrutinised. It is shown that the neglect of the conditional chara…

Quantum Spin probabilities at positive temperature are Hölder Gibbs probabilities

We consider the KMS state associated to the Hamiltonian $H= σ^x \otimes σ^x$ over the quantum spin lattice $\mathbb{C}^2 \otimes \mathbb{C}^2 \otimes \mathbb{C}^2 \otimes ...$. For a fixed observable of the form $L \otimes L \otimes L \otimes ...$, where $L:\mathbb{C}^2 \to \mathbb{C}^2 $ is self adjoint, and for positive temperature $T$ one can get a naturally defined stationary probability $μ_T$ on the Bernoulli space $\{1,2\}^\mathbb{N}$. The Jacobian of $μ_T$ can be expressed via a certain continued fraction expansion. We will show that this probability is a Gibbs probability for a Hölder …

Replacing the Breit-Wigner amplitude by the complex delta function to describe resonances

Whenever the Breit-Wigner amplitude appears in a calculation,there are many instances (e.g., Fermi's two-level system and the Weisskopf-Wigner approximation) where energy integrations are extended from the scattering spectrum of the Hamiltonian to the whole real line. Such extensions are performed in order to obtain a desirable, causal result. In this paper, we recall several of those instances and show that substituting the Breit-Wigner amplitude by the complex delta function allows us to recover such desirable results without having to extend energy integrations outside of the scattering spe…

Ionization Probabilities through ultra-intense Fields in the extreme Limit

We continue our investigation concerning the question of whether atomic bound states begin to stabilize in the ultra-intense field limit. The pulses considered are essentially arbitrary, but we distinguish between three situations. First the total classical momentum transfer is non-vanishing, second not both the total classical momentum transfer and the total classical displacement are vanishing together with the requirement that the potential has a finite number of bound states and third both the total classical momentum transfer and the total classical displacement are vanishing. For the fir…

小尺度量子系统跃迁概率的热力学与能量约束

Thermodynamic and energetic constraints on transition probabilities of small-scale quantum systems

本研究针对初始热态量子系统的两点测量跃迁概率，提出两个分别关联耗散热与吸收能量的独立约束，适用于任意哈密顿量，在小尺度系统中限制作用显著，可通过分子结等实验系统验证。

There is no spooky action-at-a-distance in quantum correlations: Resolution of the EPR nonlocality puzzle

The long-standing puzzle of the nonlocal Einstein-Podolsky-Rosen correlations is resolved. The correct quantum mechanical correlations arise for the case of entangled particles when strict locality is assumed for the probability amplitudes instead of locality for probabilities. Locality of amplitudes implies that measurement on one particle does not collapse the companion particle to a definite state.

任意泡利基下费米子高斯纯态振幅的显式普法夫公式

Explicit Pfaffian Formula for Amplitudes of Fermionic Gaussian Pure States in Arbitrary Pauli Bases

本文提出显式普法夫公式和递归关系，用于计算任意泡利基下费米子高斯纯态的振幅，从而支持全局纠缠、Shannon-Rényi熵、形成概率研究及高效量子层析成像，并用于分析测量后纠缠熵。

Few Quantum Algorithms on Amplitude Distribution

Amplitude filtering is concerned with identifying basis-states in a superposition whose amplitudes are greater than a specified threshold; probability filtering is defined analogously for probabilities. Given the scarcity of qubits, the focus of this work is to design log-space algorithms for them. Both algorithms follow a similar pattern of estimating the amplitude (or, probability for the latter problem) of each state, in superposition, then comparing each estimate against the threshold for setting up a flag qubit upon success, finally followed by amplitude amplification of states in which t…

Quantum Probability as an Application of Data Compression Principles

Realist, no-collapse interpretations of quantum mechanics, such as Everett's, face the probability problem: how to justify the norm-squared (Born) rule from the wavefunction alone. While any basis-independent measure can only be norm-squared (due to the Gleason-Busch Theorem) this fact conflicts with various popular, non-wavefunction-based phenomenological measures - such as observer, outcome or world counting - that are frequently demanded of Everettians. These alternatives conflict, however, with the wavefunction realism upon which Everett's approach rests, which seems to call for an objecti…

调度与负载均衡中延迟尾部概率的量子估计

Quantum Estimation of Delay Tail Probabilities in Scheduling and Load Balancing

本文提出了一种基于截断再生模拟的量子框架，用于在具有可数无限状态空间的调度与负载均衡系统中高效估计延迟尾部概率。

Role of collective information in networks of quantum operating agents

A network of agents is considered whose decision processes are described by the quantum decision theory previously advanced by the authors. Decision making is done by evaluating the utility of alternatives, their attractiveness, and the available information, whose combinations form the probabilities to choose a given alternative. As a result of the interplay between these three contributions, the process of choice between several alternatives is multimodal. The agents interact by exchanging information, which can take two forms: (i) information that an agent can directly receive from another …

改进的、资源可调的近期量子算法：用于计算跃迁概率及其在物理学和变分量子线性代数中的应用

Improved resource-tunable near-term quantum algorithms for transition probabilities, with applications in physics and variational quantum linear algebra

提出三种计算跃迁概率的资源可调近期量子算法，支持非正交态并减少电路评估，在物理模拟和VQLS中验证了其优于现有NISQ算法的有效性。