Quantum randomness and value indefiniteness

Bertlmann's chocolate balls and quantum type cryptography

Some quantum cryptographic protocols can be implemented with specially prepared chocolate balls, others protected by value indefiniteness cannot. Similarities and differences of cryptography with quanta and chocolate are discussed. Motivated by these considerations it is proposed to certify quantum random number generators and quantum cryptographic protocols by value indefiniteness. This feature, which derives itself from Bell- and Kochen-Specker type arguments, is only present in systems with three or more mutually exclusive outcomes.

A Non-Probabilistic Model of Relativised Predictability in Physics

Little effort has been devoted to studying generalised notions or models of (un)predictability, yet is an important concept throughout physics and plays a central role in quantum information theory, where key results rely on the supposed inherent unpredictability of measurement outcomes. In this paper we continue the programme started in [1] developing a general, non-probabilistic model of (un)predictability in physics. We present a more refined model that is capable of studying different degrees of "relativised" unpredictability. This model is based on the ability for an agent, acting via uni…

Against "knowledge"

Quantum "states" are objective probability measures. Because their dependence on a time is not the time dependence of an evolving state, they are neither states of Nature nor "states of knowledge." There is no such thing as an evolving state. This disposes of the problem posed by the apparent existence of two modes of evolution. What essentially stands in the way of a consistent ontological interpretation of the quantum theory is our habit of projecting into the quantum world the detached, intrinsically differentiated spatiotemporal background of classical physics, for this is what entails the…

Roots and (re)sources of value (in)definiteness versus contextuality. A contribution to the Pitowsky Volume in memory of Itamar Pitowsky (1950--2010)

In Itamar Pitowsky's reading of the Gleason and the Kochen-Specker theorems, in particular, his Logical Indeterminacy Principle, the emphasis is on the value indefiniteness of observables which are not within the preparation context. This is in stark contrast to the prevalent term {\em contextuality} used by many researchers in informal, heuristic yet omni-realistic and potentially misleading ways. This paper discusses both concepts and argues in favor of value indefiniteness in all but a continuum of contexts intertwining in the vector representing a single pure (prepared) state. Even more re…

Tight analytic bound on the trade-off between device-independent randomness and nonlocality

Two parties sharing entangled quantum systems can generate correlations that cannot be produced using only shared classical resources. These nonlocal correlations are a fundamental feature of quantum theory but also have practical applications. For instance, they can be used for device-independent (DI) random number generation, whose security is certified independently of the operations performed inside the devices. The amount of certifiable randomness that can be generated from some given non-local correlations is a key quantity of interest. Here we derive tight analytic bounds on the maximum…

Classical predictions for intertwined quantum observables are contingent and thus inconclusive

Classical evaluations of configurations of intertwined quantum contexts induce relations, such as true-implies-false, true-implies-true, but also nonseparability among the input and output terminals. When combined, these exploitable configurations (aka gadgets) deliver the strongest form of classical value indefiniteness. However, the choice of the respective configuration among all such collections, and thus the relation of its terminals, remains arbitrary and cannot be motivated by some superselection principle inherent to quantum or classical physics.

Unscrambling the Quantum Omelette

Based on recent theorems about quantum value-indefiniteness it is conjectured that many issues of "Born's quantum mechanics" can be overcome by supposing that only a single pure state exists; and that the quantum evolution permutes this state.

基于链式不等式最大量子值紧上界的设备无关随机性

Device-independent randomness based on a tight upper bound of the maximal quantum value of chained inequality

推导了任意测量数量下链式Bell不等式最大量子值的紧上界，基于此给出了Werner态的设备无关随机性下界，并证明三次测量在低噪声下能提升随机性生成率。

parity-CHSH不等式最大量子值的紧上界与一夫一妻制关系及其在设备无关随机性中的应用

Tight upper bound and monogamy relation for the maximum quantum value of the parity-CHSH inequality and applied to device-independent randomness

本文推导三量子比特系统parity-CHSH不等式的最大量子值紧上界及饱和约束，给出特定态违背该不等式的充要条件，探究两体纠缠态噪声与可认证随机性的关系，并推导四量子比特GHZ类态约化矩阵对应的一夫一妻制关系。

Unbounded randomness from uncharacterized sources

Randomness is a central feature of quantum mechanics and an invaluable resource for both classical and quantum technologies. Commonly, in Device-Independent and Semi-Device-Independent scenarios, randomness is certified using projective measurements and the amount of certified randomness is bounded by the dimension of the measured quantum system. In this work, we propose a new Source-Device-Independent protocol, based on Positive Operator Valued Measurement (POVM), which can arbitrarily increase the number of certified bits for any fixed dimension. A tight lower-bound on the quantum conditiona…

More randomness from a prepare-and-measure scenario with independent devices

How to generate genuine quantum randomness from untrusted devices is an important problem in quantum information processing. Inspired by previous work on a self-testing quantum random number generator [T. Lunghi et al., Phys. Rev. Lett. 114, 150501 (2015)], we present a method to generate quantum randomness from a prepare-and-measure scenario with independent devices. In existing protocols, the quantum randomness depends only on a witness value (e.g., Clauser-Horne-Shimony-Holt value), which is calculated with the observed probabilities. Differently, here all the observed probabilities are dir…

将零概率约束纳入设备无关随机性扩展

Incorporating Zero-Probability Constraints to Device-Independent Randomness Expansion

本文研究在设备无关随机性扩展中引入零概率约束对可认证随机性的影响，发现渐近情形下增加零约束可普遍提升各类随机性，但有限数据下仅对局部随机性速率有轻微改善。

Free randomness amplification using bipartite chain correlations

A direct analysis of the protocol of randomness amplification using Bell inequality violation is performed in terms of the convex combination of no-signaling boxes required to simulate quantum violation of the inequality. The probability distributions of bits generated by a Santha-Vazirani source are shown to be mixtures of permutations of Bernoulli distributions with parameter defined by the source. An intuitive proof is provided for the range of partial randomness from which perfect randomness can be extracted using quantum correlations violating the chain inequalities. Exact values are deri…

Strong Kochen-Specker theorem and incomputability of quantum randomness

The Kochen-Specker theorem shows the impossibility for a hidden variable theory to consistently assign values to certain (finite) sets of observables in a way that is non-contextual and consistent with quantum mechanics. If we require non-contextuality, the consequence is that many observables must not have pre-existing definite values. However, the Kochen-Specker theorem does not allow one to determine which observables must be value indefinite. In this paper we present an improvement on the Kochen-Specker theorem which allows one to actually locate observables which are provably value indefi…

量化序列测量中的内禀随机性

Quantifying the intrinsic randomness in sequential measurements

本文严格定义了序列测量中的量子内禀随机性，在CGLMP序列场景下量化了混合态与任意量子态在序列投影测量和序列POVM下的随机性，并利用NPA层级给出最大纠缠态与最大违背态的随机性下界。

Assessing randomness with the aid of quantum state measurement

Randomness is a valuable resource in science, cryptography, engineering, and information technology. Quantum-mechanical sources of randomness are attractive because of the indeterminism of individual quantum processes. Here we consider the production of random bits from polarization measurements on photons. We first present a pedagogical discussion of how the quantum randomness inherent in such measurements is connected to quantum coherence, and how it can be quantified in terms of the quantum state and an associated entropy value known as min-entropy. We then explore these concepts by perform…

在量子网络中认证最优的设备无关量子随机性

Certifying optimal device-independent quantum randomness in quantum networks

本文提出了一族多方贝尔不等式，用于在量子网络中认证最优的设备无关量子随机性，并自测GHZ态，提升了非最大贝尔值下的随机性认证效率。

两量子比特系统中一般Bell不等式的SOS分解及其在量子随机性中的应用

SOS decomposition for general Bell inequalities in two qubits systems and its application to quantum randomness

本文提出两量子比特系统中一般Bell不等式的SOS分解方法，可推导最大违背对应的测量算子，验证了多类Bell不等式的结果，并用于设备无关量子随机性分析，给出最大猜测概率的精确值或更优下界。

Device-independent randomness generation from several Bell estimators

Device-independent randomness generation and quantum key distribution protocols rely on a fundamental relation between the non-locality of quantum theory and its random character. This relation is usually expressed in terms of a trade-off between the probability of guessing correctly the outcomes of measurements performed on quantum systems and the amount of violation of a given Bell inequality. However, a more accurate assessment of the randomness produced in Bell experiments can be obtained if the value of several Bell expressions is simultaneously taken into account, or if the full set of p…

Everett and Structure

I address the problem of indefiniteness in quantum mechanics: the problem that the theory, without changes to its formalism, seems to predict that macroscopic quantities have no definite values. The Everett interpretation is often criticised along these lines and I shall argue that much of this criticism rests on a false dichotomy: that the macroworld must either be written directly into the formalism or be regarded as somehow illusory. By means of analogy with other areas of physics, I develop the view that the macroworld is instead to be understood in terms of certain structures and patterns…

实验量子随机性扩展的优化

Optimization of experimental quantum randomness expansion

本文提出基于贝尔不等式违反的量子随机数生成器优化方法，通过分析关键参数平衡随机性生成与消耗，提升随机性扩展率。

扩展双分量贝尔不等式以实现最大多分量随机性

Expanding bipartite Bell inequalities for maximum multi-partite randomness

本文提出了一种扩展贝尔不等式的方法，用于在多分量情况下实现最大随机性认证，揭示了偶数和奇数参与者数量下的不同权衡和结果。

On the unpredictability of individual quantum measurement outcomes

We develop a general, non-probabilistic model of prediction which is suitable for assessing the (un)predictability of individual physical events. We use this model to provide, for the first time, a rigorous proof of the unpredictability of a class of individual quantum measurement outcomes, a well-known quantum attribute postulated or claimed for a long time. We prove that quantum indeterminism - formally modelled as value indefiniteness - is incompatible with the supposition of predictability: measurements of value indefinite observables are unpredictable. The proof makes essential use of a s…

量子态的最大内禀随机性

Maximal intrinsic randomness of a quantum state

该研究针对量子态内禀随机性提取量的基础问题，分别给出条件最小熵、条件冯·诺依曼熵和条件最大熵三种度量下的最大值及对应的最优测量方式，填补了相关研究空白。

Evaluation of the phase randomness of the light source in quantum key distribution systems with an attenuated laser

The phase randomized light is one of the key assumptions in the security proof of Bennett-Brassard 1984 (BB84) quantum key distribution (QKD) protocol implemented with an attenuated laser. Though the assumption has been believed to be satisfied for conventional systems, it should be reexamined for current high speed QKD systems. The phase correlation may be induced by the overlap of the optical pulses, the interval of which decreases as the clock frequency. The phase randomness was investigated experimentally by measuring the visibility of interference. An asymmetric Mach-Zehnder interferomete…

能量受限的半设备无关场景中可实现随机性认证

Randomness can be certified in energy-constrained semi-device-independent scenarios

该研究将Navascués-Pironio-Acín层级适配能量受限场景，构造半定规划松弛，证明即使存在全量子敌手，能量受限的半设备无关框架中仍可实现认证随机性生成。

Loss-tolerant measurement-device-independent quantum random number generation

Quantum random number generators (QRNGs) output genuine random numbers based upon the uncertainty principle. A QRNG contains two parts in general --- a randomness source and a readout detector. How to remove detector imperfections has been one of the most important questions in practical randomness generation. We propose a simple solution, measurement-device-independent QRNG, which not only removes all detector side channels but is robust against losses. In contrast to previous fully device-independent QRNGs, our scheme does not require high detector efficiency or nonlocality tests. Simulation…

Practical No-Signalling proof Randomness Amplification using Hardy paradoxes and its experimental implementation

Device-Independent (DI) security is the best form of quantum cryptography, providing information-theoretic security based on the very laws of nature. In its highest form, security is guaranteed against adversaries limited only by the no-superluminal signalling rule of relativity. The task of randomness amplification, to generate secure fully uniform bits starting from weakly random seeds, is of both cryptographic and foundational interest, being important for the generation of cryptographically secure random numbers as well as bringing deep connections to the existence of free-will. DI no-sign…

The m-least significant bits operation for quantum random number generation

Quantum random number generators (QRNGs) can provide genuine randomness based on the inherent unpredictable nature of quantum physics. The extracted randomness relies not only on the physical parts of the QRNG, such as the entropy source and the measurement device, but also on appropriate postprocessing method. The m-least significant bits (m-LSBs) operation is one of the simplest randomness extraction method, which has the advantage of easy implementations. Nonetheless, a detailed analysis of the m-LSBs operation in QRNGs is still missing. In this work we give a physical explanation of the m-…

Classical and nonclassical randomness in quantum measurements

The space of positive operator-valued measures on the Borel sets of a compact (or even locally compact) Hausdorff space with values in the algebra of linear operators acting on a d-dimensional Hilbert space is studied from the perspectives of classical and non-classical convexity through a transform $Γ$ that associates any positive operator-valued measure with a certain completely positive linear map of the homogeneous C*-algebra $C(X)\otimes B(H)$ into $B(H)$. This association is achieved by using an operator-valued integral in which non-classical random variables (that is, operator-valued fu…

Quasi-probabilities in Conditioned Quantum Measurement and a Geometric/Statistical Interpretation of Aharonov's Weak Value

We show that the joint behaviour of an arbitrary pair of quantum observables can be described by quasi-probabilities, which are extensions of the standard probabilities used for describing the behaviour of a single observable. The physical situations that require these quasi-probabilities arise when one considers quantum measurement of an observable conditioned by some other variable, with the notable example being the weak measurement employed to obtain Aharonov's weak value. Specifically, we present a general prescription for the construction of quasi-joint-probability (QJP) distributions as…

层次化区分量子态中的Haar随机性

Hierarchically discriminating Haar-randomness in quantum states from a black-box device

本文提出一种层次化判别算法，用于测试量子设备生成的态是否与Haar随机分布相容，通过分析可观测量的统计矩来判断随机性。

Quantum Random Access Codes with Shared Randomness

We consider a communication method, where the sender encodes n classical bits into 1 qubit and sends it to the receiver who performs a certain measurement depending on which of the initial bits must be recovered. This procedure is called (n,1,p) quantum random access code (QRAC) where p > 1/2 is its success probability. It is known that (2,1,0.85) and (3,1,0.79) QRACs (with no classical counterparts) exist and that (4,1,p) QRAC with p > 1/2 is not possible. We extend this model with shared randomness (SR) that is accessible to both parties. Then (n,1,p) QRAC with SR and p > 1/2 exists for any …

Clauser-Horne Bell test with imperfect random inputs

Bell test is one of the most important tools in quantum information science. On the one hand, it enables fundamental test for the physics laws of nature, and on the other hand, it can be also applied in varieties of device independent tasks such as quantum key distribution and random number generation. In practice, loopholes existing in experimental demonstrations of Bell tests may affect the validity of the conclusions. In this work, we focus on the randomness (freewill) loophole and investigate the randomness requirement in a well-known Bell test, the Clauser-Horne test, under various condit…

量子系统中的混沌与随机性研究

A study of chaos and randomness in quantum systems

本研究针对经典混沌的量子印记问题，通过量子受击陀螺模型发现深量子区存在经典混沌痕迹，还提出利用最大混态随机性的OTOC高效测量量子算法，实现指数级加速并可用于幺正门基准测试。

Phase randomness in a gain-switched semiconductor laser: stochastic differential equation analysis

We performed theoretical analysis of the phase randomness in a gain-switched semiconductor laser in the context of its application as a quantum entropy source. Numerical simulations demonstrate that phase diffusion r.m.s. exhibits non-linear dependence on the bias current, which could be of significant practical importance, particularly, in application to high-speed optical quantum random number generators. It is shown that phase diffusion between laser pulses cannot always be assumed to exhibit required efficiency, particularly, at high pulse repetition rates. It was also revealed that the ga…

费米子随机性的魔法代价

The magic cost of fermionic randomness

该研究证明，在费米子线性光学中重现随机矩阵统计需要广泛的非高斯资源，其代价由单体缺陷ν量化，并与采样统计和制备资源定量关联。

Tests for non-randomness in quantum jumps

In a fundamental test of quantum mechanics, we have observed 228~000 quantum jumps of a single trapped and laser cooled $^{88}$Sr$^+$ ion. This represents a statistical increase of two orders of magnitude over previous similar analyses of quantum jumps. Compared to other searches for non-randomness in quantum mechanical processes, using quantum jumps simplifies the interpretation of data by eliminated multi-particle effects and providing near-unit detection efficiency of transitions. We measure the fractional reduction in the entropy of information to be $< 6.5~10^{-4}$ when the value of any i…

Classical randomness in quantum measurements

Similarly to quantum states, also quantum measurements can be "mixed", corresponding to a random choice within an ensemble of measuring apparatuses. Such mixing is equivalent to a sort of hidden variable, which produces a noise of purely classical nature. It is then natural to ask which apparatuses are "indecomposable", i. e. do not correspond to any random choice of apparatuses. This problem is interesting not only for foundations, but also for applications, since most optimization strategies give optimal apparatuses that are indecomposable. Mathematically the problem is posed describing each…

基于值不定可观测量的二进制量子随机数发生器

Binary Quantum Random Number Generator Based on Value Indefinite Observables

本文利用三维值不定可观测量构造二进制量子随机数发生器，使其输出具有与三进制方案相同的最大不可预测性。

Randomness in Relational Quantum Mechanics

The relational interpretation of quantum mechanics (RQM), introduced in its present form by Carlo Rovelli in 1996, involves a number of significant departures from other QM interpretations widely discussed in the literature. We begin here by summarizing these unique RQM features, with a focus on those that suggest altered insights into the nature of the randomness exhibited in QM phenomena. One of these RQM features is the assumption that all objects in the universe are quantum objects, regardless of their material complexity. And, the interaction of any two objects can result in new relationa…

用于偏振无关可认证随机数的超表面量子图

Metasurface quantum graphs for polarization-independent certified randomness

本文提出超表面量子图框架，利用紧凑超表面实现偏振无关可认证随机数，实验制备4、6通道介质超表面完成高维POVM图，为集成量子技术提供可扩展途径。

Randomness in Classical Mechanics and Quantum Mechanics

The Copenhagen interpretation of quantum mechanics assumes the existence of the classical deterministic Newtonian world. We argue that in fact the Newton determinism in classical world does not hold and in classical mechanics there is fundamental and irreducible randomness. The classical Newtonian trajectory does not have a direct physical meaning since arbitrary real numbers are not observable. There are classical uncertainty relations, i.e. the uncertainty (errors of observation) in the determination of coordinate and momentum is always positive (non zero). A "functional" formulation of clas…

从量子速度限制中获得认证的随机性

Certified randomness from quantum speed limits

本文提出利用量子速度限制生成安全认证的随机性，通过准备和测量场景，在无额外假设条件下实现对抗者无法操控的随机性生成。

Probing the randomness of ergodic states: extreme-value statistics in the ergodic and many-body-localized phases

The extreme-value statistics of the entanglement spectrum in disordered spin chains possessing a many-body localization transition is examined. It is expected that eigenstates in the metallic or ergodic phase, behave as random states and hence the eigenvalues of the reduced density matrix, commonly referred to as the entanglement spectrum, are expected to follow the eigenvalue statistics of a trace normalized Wishart ensemble. In particular, the density of eigenvalues is supposed to follow the universal Marchenko-Pastur distribution. We find deviations in the tails both for the disordered XXZ …

无随机性非经典性检验：概念验证

Randomness-free Test of Non-classicality: a Proof of Concept

本文提出并实验验证了一种无需种子随机性的半设备无关认证技术，通过纠缠光子对产生关联硬币，证明其量子优势并认证非投影测量，为量子通信提供了经济有效的认证方案。

具有经典随机性的量子行走局域化：人工方法与监督机器学习的比较

Localization of quantum walk with classical randomness: Comparison between manual methods and supervised machine learning

本文研究经典随机性诱导的量子行走局域化转变，比较人工指标与SVM、多层感知器和卷积神经网络的识别效果，揭示机器学习处理量子—经典混合概率系统的潜力与挑战。

QPP-RNG：一个用于产生真随机性的概念性量子系统

QPP-RNG: A Conceptual Quantum System for True Randomness

本文提出并实验演示了概念性量子系统QSQS及其具体实现QPP-RNG，通过测量排列排序过程的共轭可观测量，结合CPU抖动等物理波动动态重置PRNG，生成高质量真随机数，为后量子密码系统提供了基于物理的真随机性工程视角。