J. Acacio de Barros, Federico Holik
In this paper, we examined the connection between quantum systems' indistinguishability and signed (or negative) probabilities. We do so by first introducing a measure-theoretic definition of signed probabilities inspired by research in quantum contextuality. We then argue that ontological indistinguishability leads to the no-signaling condition and negative probabilities.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Semiclassical asymptotics of multiphotonic scattering probabilities with partial indistinguishability
该研究提出计算无损多端口干涉仪多光子散射概率框架，利用环形展开定义映射，确定大光子数极限下散射概率渐近行为，建立新渐近公式，还能解释已知情形，且产生与渐近光子聚束模式相关可直接检验的结果。
It is well known that in quantum mechanics we cannot always define consistently properties that are context independent. Many approaches exist to describe contextual properties, such as Contextuality by Default (CbD), sheaf theory, topos theory, and non-standard or signed probabilities. In this paper we propose a treatment of contextual properties that is specific to quantum mechanics, as it relies on the relationship between contextuality and indistinguishability. In particular, we propose that if we assume the ontological thesis that quantum particles or properties can be indistinguishable y…
The concept of Logical Entropy, $S_L = 1- \sum_{i=1}^n p_i^2$, where the $p_i$ are normalized probabilities, was introduced by David Ellerman in a series of recent papers. Although the mathematical formula itself is not new, Ellerman provided a sound probabilistic interpretation of $S_L$ as a measure of the distinctions of a partition on a given set. The same formula comes across as a useful definition of entropy in quantum mechanics, where it is linked to the notion of purity of a quantum state. The quadratic form of the logical entropy lends itself to a generalization of the probabilities th…
We explain, on the example of Wigner's quasiprobability distribution, how negative probabilities may be used in the foundations of probability.
In this paper, we give a frequency interpretation of negative probability, as well as of extended probability, demonstrating that to a great extent, these new types of probabilities, behave as conventional probabilities. Extended probability comprises both conventional probability and negative probability. The frequency interpretation of negative probabilities gives supportive evidence to the axiomatic system built in (Burgin, 2009; arXiv:0912.4767) for extended probability as it is demonstrated in this paper that frequency probabilities satisfy all axioms of extended probability.
We demonstrate deterministic and robust generation of pulsed resonance fluorescence single photons from a single InGaAs quantum dot using the method of rapid adiabatic passage. Comparative study is performed with transform-limited, negatively chirped and positively chirped pulses, identifying the last one to be the most robust against fluctuation of driving strength. The generated single photons are background free, have a vanishing two-photon emission probability of 0.3% and a raw (corrected) two-photon Hong-Ou-Mandel interference visibility of 97.9% (99.5%), reaching a precision that places …
Typically, quantum superpositions, and thus measurement projections of quantum states involving interference, decrease (or increase) monotonically as a function of increased distinguishability. Distinguishability, in turn, can be a consequence of decoherence, for example caused by the (simultaneous) loss of excitation or due to inadequate mode matching (either deliberate or indeliberate). It is known that for some cases of multi-photon interference, non-monotonic decay of projection probabilities occurs, which has so far been attributed to interference between four or more two photons. We show…
We start from Feynman`s idea to use negative probabilities to describe the two slit experiment and other quantum interfernce experiments. Formally by using negative probability distributions we can explain the results of the two slit experiment on the basis of the pure corpuscular picture of quantum mechnanics. However, negative probabilities are absurd objects in the framework of the standard Kolmogorov theory of probability. We present a large class of non-Kolmogorovean probability models where negative probabilities are well defined on the frequency basis. These are models with probabilitie…
In this work, we elaborate on a measure-theoretic approach to negative probabilities. We study a natural notion of contextuality measure and characterize its main properties. Then, we apply this measure to relevant examples of quantum physics. In particular, we study the role played by contextuality in quantum computing circuits.
Classical sampling from noisy Boson Sampling and the negative probabilities
本文研究含噪玻色采样经典采样中由有限阶多玻色子干涉截断引起的负概率问题，指出该问题仅在接近完全可区分玻色子的消失区域内可解，并提出基于对称群特征渐近行为的新研究方向。
Negative probabilities have long been discussed in connection with the foundations of quantum mechanics. We have recently shown that, if signed measures are allowed on the hidden variables, the class of probability models which can be captured by local hidden-variable models are exactly the no-signalling models. However, the question remains of how negative probabilities are to be interpreted. In this paper, we present an operational interpretation of negative probabilities as arising from standard probabilities on signed events. This leads, by virtue of our previous result, to a systematic sc…
A signed probability distribution may extend a given traditional probability from observable events to all events. We formalize and illustrate this approach. We also illustrate its limitation. We argue that the right question is not what negative probabilities are but what they are for.
We study the outcomes in a general measurement with postselection, and derive upper bounds for the pointer readings in weak measurement. Using the idea of weak measurement, we study Hardy's gedanken experiment and show how the "negative probabilities" emerge in weak measurement. By calculating the information gain of the measuring device about which path the particles pass through, we show that the "negative probabilities" only emerge for cases when the information gain is little due to very weak coupling between the measuring device and the particles. When the coupling strength increases, we …
In this paper we discuss quantum-like decision-making experiments using negative probabilities. We do so by showing how the two-slit experiment, in the simplified version of the Mach-Zehnder interferometer, can be described by this formalism. We show that negative probabilities impose constraints to what types of counter-factual reasoning we can make with respect to (quantum) internal representations of the decision maker.
Any bipartite quantum state has quasi-probability representations in terms of separable states. For entangled states these quasi-probabilities necessarily exhibit negativities. Based on the general structure of composite quantum states, one may reconstruct such quasi-propabilities from experimental data. Because of ambiguity, the quasi-probabilities obtained by the bare reconstruction are insufficient to identify entanglement. An optimization procedure is introduced to derive quasi-probabilities with a minimal amount of negativity. Negativities of optimized quasi-probabilities unambiguously pr…
There has been a growing interest, both in physics and psychology, in understanding contextuality in experimentally observed quantities. Different approaches have been proposed to deal with contextual systems, and a promising one is contextuality-by-default, put forth by Dzhafarov and Kujala. The goal of this paper is to present a tutorial on a different approach: negative probabilities. We do so by presenting the overall theory of negative probabilities in a way that is consistent with contextuality-by-default and by examining with this theory some simple examples where contextuality appears,…
A Relationship Between Nonphysical Quasi-probabilities and Nonlocality Objectivity
本文研究非物理准概率与非定域性的关系，通过允许最小负本征值任意接近零，构造出交换组分标记后非定域性发生改变的量子态，从而揭示非定域性的观察者依赖性。
We present a path analysis of the condition under which the outcomes of previous observation affect the results of the measurements yet to be made. It is shown that this effect, also known as "signalling in time", occurs whenever the earlier measurements are set to destroy interference between two or more virtual paths. We also demonstrate that Feynman's negative "probabilities" provide for a more reliable witness of "signalling in time", than the Leggett-Garg inequalities, while both methods are frequently subject to failure
In this paper we provide a simple random-variable example of inconsistent information, and analyze it using three different approaches: Bayesian, quantum-like, and negative probabilities. We then show that, at least for this particular example, both the Bayesian and the quantum-like approaches have less normative power than the negative probabilities one.
Many situations in quantum theory and other areas of physics lead to quasi-probabilities which seem to be physically useful but can be negative. The interpretation of such objects is not at all clear. In this paper, we show that quasi-probabilities naturally fall into two qualitatively different types, according to whether their non-negative marginals can or cannot be matched to a non-negative probability. The former type, which we call viable, are qualitatively similar to true probabilities, but the latter type, which we call non-viable, may not have a sensible interpretation. Determining the…
The concept of negative probabilities can be used to decompose the interaction of two qubits mediated by a quantum controlled-NOT into three operations that require only classical interactions (that is, local operations and classical communication) between the qubits. For a single gate, the probabilities of the three operations are 1, 1, and -1. This decomposition can be applied in a probabilistic simulation of quantum computation by randomly choosing one of the three operations for each gate and assigning a negative statistical weight to the outcomes of sequences with an odd number of negativ…
An observation space $\mathcal S$ is a family of probability distributions $\langle P_i: i\in I \rangle$ sharing a common sample space $Ω$ in a consistent way. A \emph{grounding} for $\mathcal S$ is a signed probability distribution $\mathcal P$ on $Ω$ yielding the correct marginal distribution $P_i$ for every $i$. A wide variety of quantum scenarios can be formalized as observation spaces. We describe all groundings for a number of quantum observation spaces. Our main technical result is a rigorous proof that Wigner's distribution is the unique signed probability distribution yielding the cor…
Many-party correlations between measurement outcomes in general probabilistic theories are given by conditional probability distributions obeying the non-signalling condition. We show that any such distribution can be obtained from classical or quantum theory, by relaxing positivity constraints on either the mixed state shared by the parties, or the local functions which generate measurement outcomes. Our results apply to generic non-signalling correlations, but in particular they yield two distinct quasi-classical models for quantum correlations.
In this paper we attempt to establish a theory of negative (quasi) probability distributions from fundamental principles and apply it to the study of the double-slit experiment in quantum mechanics. We do so in a way that preserves the main conceptual issues intact but allow for a clearer analysis, by representing the double-slit experiment in terms of the Mach-Zehnder interferometer, and show that the main features of quantum systems relevant to the double-slit are present also in the Mach-Zehnder. This converts the problem from a continuous to a discrete random variable representation. We th…
For a number of non-interacting identical particles entering a multi-channel scatterer in various wave packet states, we construct a generating function for the probabilities of various scattering outcomes. This is used to evaluate the mean numbers of particles $\overline{n}_m$ scattered into a given ($m$-th) channel, single-channel statistics, and inter-channel correlations. We show that for initially uncorrelated particles, indistinguishability changes single channel statistics without altering the the value of $\overline{n}_m$. For uncorrelated bosons and fermions, bunching and anti-bunchin…
We consider properties of the measurement intensity $ρ$ of a random variable for which the probability density function represented by the corresponding Wigner function attains negative values on a part of the domain. We consider a simple economic interpretation of this problem. This model is used to present the applicability of the method to the analysis of the negative probability on markets where there are anomalies in the law of supply and demand (e.g. Giffen's goods). It turns out that the new conditions to optimize the intensity $ρ$ require a new strategy. We propose a strategy (so-calle…
Biorthogonal resource theory of genuine quantum superposition
针对现有叠加资源理论忽略基态交叠中量子叠加的问题，提出密度算符伪厄米表示构建真量子叠加统一框架，推广叠加度量并探索其在化学电子离域量化中的应用。
We introduce an experimental test for ruling out classical explanations for the statistics obtained when measuring arbitrary observables at arbitrary times using individual detectors. This test requires some trust in the measurements, represented by a few natural assumptions on the detectors. In quantum theory, the considered scenarios are well captured by von Neumann measurements. These can be described naturally in terms of the Keldysh quasi-probability distribution (KQPD), and the imprecision and backaction exerted by the measurement apparatus. We find that classical descriptions can be rul…
Bipartite quantum entangled systems can exhibit measurement correlations that violate Bell inequalities, revealing the profoundly counter-intuitive nature of the physical universe. These correlations reflect the impossibility of constructing a joint probability distribution for all values of all the different properties observed in Bell inequality tests. Physically, the impossibility of measuring such a distribution experimentally, as a set of relative frequencies, is due to the quantum back-action of projective measurements. Weakly coupling to a quantum probe, however, produces minimal back-a…
The interplay between single-particle interference and quantum indistinguishability leads to signature correlations in many-body scattering. We uncover these with a semiclassical calculation of the transmission probabilities through mesoscopic cavities for systems of non-interacting particles. For chaotic cavities we provide the universal form of the first two moments of the transmission probabilities over ensembles of random unitary matrices, including weak localization and dephasing effects. If the incoming many-body state consists of two macroscopically occupied wavepackets, their time dela…
Negative Probability
本文旨在建立物理学中负概率与贝叶斯建模中负混合分布之间的联系，基于Bartlett定义给出负权重贝叶斯规则，并讨论半硬币分布、Polya-Gamma混合及对偶密度等例子。
Towards Stirling cooler operable single-photon sources based on low-noise GaAs quantum dots
该研究针对光子量子技术需求，探究低噪声GaAs量子点单光子源的温度特性，通过实验与理论分析揭示高温下光子不可区分度下降的机制，利用腔增强技术在32 K下将其提升至0.80(3)，创该温度下最高报道值。
Measures of contextuality in cyclic systems and the negative probabilities measure CNT3
本文证明了 Dzhafarov 和 Kujala 关于循环系统中 CNT2 与 CNT3 成比例的猜想，并结合 Cervantes 对 CNT2 与 CNTF 比例关系的证明，完整刻画了循环系统中各语境性度量之间的相互关系。
This paper establishes a direct, robust and intimate connection between (i) non classicality tests for various quantum features, e.g., non-Boolean logic, quantum coherence, nonlocality, quantum entanglement, quantum discord; (ii) negative probability, and (iii) anomalous weak values. It has been shown [Adhikary et al. Eur. Phys. J. D, 74(68):68, 2020] that nonexistence of a classical joint probability scheme gives rise to sufficiency conditions for nonlocality, a nonclassical feature not restricted to quantum mechanics. The conditions for nonclassical features of quantum mechanics are obtained…
Quantum coherence and negative quasi probabilities in a contextual three-path interferometer
本文提出利用五阶段干涉仪中的正交关系和负Kirkwood-Dirac分布，对三维希尔伯特空间中的纯态进行非经典关联分类。
We explore the multiparticle transition probabilities in Gaussian unitaries effected by a two-mode Bogoliubov bosonic transformation on the mode annihilation and creation operators. We show that the transition probabilities can be characterized by remarkably simple, yet unsuspected recurrence equations involving a linear combination of probabilities. The recurrence exhibits an interferometric suppression term - a negative probability - which generalizes the seminal Hong-Ou-Mandel effect to more than two indistinguishable photons impinging on a beam splitter of rational transmittance. Unexpecte…
The quantum mechanics of closed systems such as the universe is formulated using an extension of familiar probability theory that incorporates negative probabilities. Probabilities must be positive for sets of alternative histories that are the basis of fair settleable bets. However, in quantum mechanics there are sets of alternative histories that can be described but which cannot be the basis for fair settleable bets. Members of such sets can be assigned extended probabilities that are sometimes negative. A prescription for extended probabilities is introduced that assigns extended probabili…
We study the possibility to describe pure quantum states and evens with classical probability distributions and conditional probabilities and show that the distributions and/or conditional probabilities have to assume negative values, except for a simple model whose realistic space dimension is not smaller than the Hilbert space dimension of the quantum system. This gives a negative answer to a question proposed by Montina [Phys.Rev.Lett.{\bf 97}, 180401 (2006)] whether or not does there exist a classical theory whose phase-space dimension is much smaller than the Hilbert space dimension for a…
Quantum paradoxes show that quantum statistics can exceed the limits of positive joint probabilities for physical properties that cannot be measured jointly. It is therefore impossible to describe the relations between the different physical properties of a quantum system by assigning joint realities to their observable values. Instead, recent experimental results obtained by weak measurements suggest that non-classical correlations could be expressed by complex valued quasi-probabilities, where the phases of the complex probabilities express the action of transformations between the non-commu…
The extrinsic quantum mechanical arrow of time is understood to be a consequence of the interaction between quantum systems and their environment. A choice of boundary conditions for the Schrödinger equation results in a different time asymmetry intrinsic to quantum mechanical dynamics and independent of environmental interactions. Correct application of the intrinsically asymmetric dynamics, however, leads unavoidably to predictions of the experimental signatures of the extrinsic arrow of time. We are led to a new, model-independent mechanism for quantum decoherence. We need not invoke a mast…
Both the quantum mechanical and classical Bells experiment are within the focus of this paper. The fact that one measures different probabilities in both experiments is traced back to the superposition of two orthogonal but nonentangled substates in the quantum mechanical case. This superposition results in an interference term that can be splitted into two additional states representing a sink and a source of probabilities in the classical event space related to Bells experiment. As a consequence, a statistical operator can be related to the quantum mechanical Bells experiment that contains a…
We define a quantum entropy conditioned on post-selection which has the von Neumann entropy of pure states as a special case. This conditional entropy can take negative values which is consistent with part of a quantum system containing less information than the whole which can be in a pure state. The definition is based on generalised density operators for postselected ensembles. The corresponding density operators are consistent with the quantum generalisation of classical conditional probabilities following Dirac s formalism of quasiprobability distributions.
Even though measurement results obtained in the real world are generally both noisy and continuous, quantum measurement theory tends to emphasize the ideal limit of perfect precision and quantized measurement results. In this article, a more general concept of noisy measurements is applied to investigate the role of quantum noise in the measurement process. In particular, it is shown that the effects of quantum noise can be separated from the effects of information obtained in the measurement. However, quantum noise is required to ``cover up'' negative probabilities arising as the quantum limi…
In this work, we show that Bell's inequality violation of arise from the fact that the condition imposed upon the development of inequality is not respected when it is applied in the idealized experiment. Such a condition is that the quantities taken by probability must be non negative, and such a condition is represented by $|\cal{P(w)}|=\cal{P(w)}$. We will also show that, when trying to define the values of the joint probabilities of $ (Z_1, Z_2, Z_3) $, through the values obtained from the $ (Z_j, Z_k) $ pairs, we find that these values are negative, so not Kolmogorov's axiom is respected:…
We discuss how the language of wave functions (state vectors) and associated non-commuting Hermitian operators naturally emerges from classical mechanics by applying the inverse Wigner-Weyl transform to the phase space probability distribution and observables. In this language, the Schrödinger equation follows from the Liouville equation, with $\hbar$ now a free parameter. Classical stationary distributions can be represented as sums over stationary states with discrete (quantized) energies, where these states directly correspond to quantum eigenstates. Interestingly, it is now classical mecha…
A sequence of moments encode the corresponding probability distribution. Probing if quantum joint probability distribution can be retrieved from the associated set of moments -- realized in the sequential measurement of a dichotomic observable at different time intervals -- reveals a negative answer i.e., the joint probabilities of sequential measurements do not agree with the ones obtained by inverting the moments. This is indeed a reflection of the non-existence of a bonafide grand joint probability distribution, consistent with all the physical marginal probability distributions. Here we ex…
We consider an electron magnetically interacting with a spin-1/2 impurity, embedded in an external environment whose noisy term acts only on the impurity's spin, and we find expressions for the electron transmission and reflection probabilities in terms of the phenomenological noise parameters. Moreover, we give a simple example of the necessity of complete positivity for physical consistency, showing that a positive but not completely positive dissipative map can lead to negative transmission probabilities.
By limiting the resolution of quantum measurements, the measurement induced changes of the quantum state can be reduced, permitting subsequent measurements of variables that do not commute with the initially measured property. It is then possible to experimentally determine correlations between non-commuting variables. The application of this method to the polarization statistics of entangled photon pairs reveals that negative conditional probabilities between non-orthogonal polarization components are responsible for the violation of Bell's inequalities. Such negative probabilities can also b…
The standard approach to deriving fluctuation theorems fails to capture the effect of quantum correlation and coherence in the initial state of the system. Here we overcome this difficulty and derive heat exchange fluctuation theorem in the full quantum regime by showing that the energy exchange between two locally thermal states in the presence of initial quantum correlations is faithfully captured by a quasiprobability distribution. Its negativities, being associated with proofs of contextuality, are proxys of non-classicality. We discuss the thermodynamic interpretation of negative probabil…
Decoherent histories quantum theory is reformulated with the assumption that there is one "real" fine-grained history, specified in a preferred complete set of sum-over-histories variables. This real history is described by embedding it in an ensemble of comparable imagined fine-grained histories, not unlike the familiar ensemble of statistical mechanics. These histories are assigned extended probabilities, which can sometimes be negative or greater than one. As we will show, this construction implies that the real history is not completely accessible to experimental or other observational dis…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。