S. M. Roy
We present a new causal quantum mechanics in one and two dimensions developed recently at TIFR by this author and V. Singh. In this theory both position and momentum for a system point have Hamiltonian evolution in such a way that the ensemble of system points leads to position and momentum probability densities agreeing exactly with ordinary quantum mechanics.
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The De Broglie-Bohm (DeBB)\cite{DeBB} Causal Quantum Mechanics played a crucial role in Bell's discovery \cite{Bell1964} that quantum mechanics violates EPR local reality \cite{EPR1935}, and also in Bell's search for an exact quantum mechanics. The experiments of Aspect et al \cite{Aspect1981} confirm quantum correlations between plane polarizations of two photons and violation of Bell's inequalities by a factor $\sqrt 2 $. I prove that similar experiments with elliptic polarizers can also show quantum violations of Bell's inequality by the same factor. I summarize our construction of a maxima…
Achieving Maximal Causal Indefiniteness in a Maximally Nonlocal Theory
本研究在广义概率框架下提出叠加概念，证明最大非局域理论中复合系统允许叠加但单系统不允许，且叠加不蕴含纠缠，并给出具体例子展示后量子违反因果不定性不等式至代数界限。
It is argued that the quantum correlations are not maximally nonlocal to make it possible to control local outcomes from outside spacetime, and quantum mechanics emerges from timeless nonlocality and biased local randomness. This rules out a world described by NL (nonlocal) boxes. A new type of experiments is suggested.
We recently constructed a causal quantum mechanics in 2 dim. phase space which is more realistic than the de Broglie-Bohm mechanics as it reproduces not just the position but also the momentum probability density of ordinary quantum theory. Here we present an even more ambitious construction in 2n dim. phase space. We conjecture that the causal Hamiltonian quantum mechanics presented here is `maximally realistic'. The positive definite phase space density reproduces as marginals the correct quantum probability densities of $n+1$ different complete commuting sets of observables (e.g. $\vec q$, …
Proofs of Bell-Kochen-Specker contextuality demonstrate that there exists sets of projectors that cannot each be assigned either 0 or 1 such that each basis formed from them contains exactly one 1-assigned projector. Instead, at least some of the projectors must have a valuation that depends on the \emph{context} in which they are measured. This motivates the question of \emph{how many} of the projectors must have contextual valuations. In this paper, we demonstrate a bound on what fraction of rank-1 projective measurements on a quantum system must be considered to have context-dependent valua…
A new possible version of multisimultaneous causality is proposed, and real experiments allowing us to decide between this view and quantum mechanical retrocausation are further discussed. The interest of testing quantum mechanics against as many nonlocal causal models as possible is stressed.
The notorious quantum measurement problem brings out the difficulty to reconcile two quantum postulates: the unitary evolution of closed quantum systems and the wave-function collapse after a measurement. This problematics is particularly highlighted in the Wigner's friend thought experiment, where the mismatch between unitary evolution and measurement collapse leads to conflicting quantum descriptions for different observers. A recent no-go theorem has established that the (quantum) statistics arising from an extended Wigner's friend scenario is incompatible when one try to hold together thre…
It is shown that probabilistic treatment of quantum mechanics can be coordinated with causality of all physical processes. The physical interpretation of quantum-mechanical phenomena such as process of measurement and collapse of quantum state is given.
Quantum mechanics permits nonlocality - both nonlocal correlations and nonlocal equations of motion - while respecting relativistic causality. Is quantum mechanics the unique theory that reconciles nonlocality and causality? We consider two models, going beyond quantum mechanics, of nonlocality: "superquantum" correlations, and nonlocal "jamming" of correlations. These models are consistent with some definitions of nonlocality and causality.
We discuss a number of comments on quant-ph/9801061, and propose to introduce the concept of 'Causal Indistinguishability'. The incompatibility between Quantum Mechanics and Nonlocal Causality appears to be unavoidable: upholding of Quantum Mechanics by experiment would mean to live with influences backward in time, just as we are now living with such faster than light.
Quantum mechanical phase factors can be related to dynamical effects or to the geometrical properties of a trajectory in a given space - either parameter space or Hilbert space. Here, we experimentally investigate a quantum mechanical phase factor that reflects the topology of the SO(3) group: since rotations by $π$ around antiparallel axes are identical, this space is doubly connected. Using pairs of nuclear spins in a maximally entangled state, we subject one of the spins to a cyclic evolution. If the corresponding trajectory in SO(3) can be smoothly deformed to a point, the quantum state at…
Quantum mechanics forces us to reconsider certain aspects of classical causality. The 'central mystery' of quantum mechanics manifests in different ways, depending on the interpretation. This mystery can be formulated as the possibility of selecting part of the initial conditions of the Universe 'retroactively'. This talk aims to show that there is a global, timeless, 'bird's view' of the spacetime, which makes this mystery more reasonable. We will review some well-known quantum effects from the perspective of global consistency.
The basic physical problems that necessitated the emergence of quantum physics are summarized, along with the elements of wave mechanics and its traditional statistical interpretation. Alternative interpretations to the statistical one, such as the hydrodynamical and optical interpretations, nonlinear waves and nonlinear electrodynamics, and the conception of spacetime as an ordered medium are reviewed.
We extend Pearl's definition of causal influence to the quantum domain, where two quantum systems $A$, $B$ with finite-dimensional Hilbert space are embedded in a common environment $C$ and propagated with a joint unitary $U$. For finite dimensional Hilbert space of $C$, we find the necessary and sufficient condition on $U$ for a causal influence of $A$ on $B$ and vice versa. We introduce an easily computable measure of the causal influence and use it to study the causal influence of different quantum gates, its mutuality, and quantum superpositions of different causal orders. For two two-leve…
To study which are the most general causal structures which are compatible with local quantum mechanics, Oreshkov et al. introduced the notion of a process: a resource shared between some parties that allows for quantum communication between them without a predetermined causal order. These processes can be used to perform several tasks that are impossible in standard quantum mechanics: they allow for the violation of causal inequalities, and provide an advantage for computational and communication complexity. Nonetheless, no process that can be used to violate a causal inequality is known to b…
Causal emergence is brought about when a coarse-grained description of a physical system is more effective (more deterministic and/or less degenerate) than the fine-grained corresponding model. We show, for the first time to our knowledge, a causal emergence in a quantum system: a atomic Mach-Zehnder interferometer with two which-path detectors. The atomic wave-like or particle-like descriptions are related, respectively, to \textit{coarse-grained} and \textit{fine-grained} models. The predictions of the atomic position after the passage through the interferometer when the to \textit{coarse-gr…
A new interpretation of quantum mechanics, similar to the Copenhagen interpretation, is developed from time-symmetry arguments and commonly held principles concerning time and causality. These principles, which are grounded in ideas outside of quantum mechanics, suggest that the strange features and paradoxes of quantum mechanics come from backward causation, in which future events can change the past. Using these principles this paper gives a better understanding of (and reasons for) stationary states, tunneling, wave-particle duality, the measurement problem with the collapse of the state ve…
Cramer's transactional interpretation of quantum mechanics is reviewed, and a number of issues related to advanced interactions and state vector collapse are analyzed. Where some have suggested that Cramer's predictions may not be correct or definite, I argue that they are, but I point out that the classical-quantum distinction problem in the Copenhagen interpretation has its parallel in the transactional interpretation.
Causality and the Interpretation of Quantum Mechanics
针对相对论因果性、量子非定域性与量子测量的长期矛盾，研究基于量子场论提出由约化密度矩阵因果性和完备量子力学诠释构成的框架，证明约化密度矩阵不超光速演化，提出无需额外假设且兼容相对论的量子力学诠释。
The causal interpretation of quantum mechanics, as originally stated by deBroglie and Bohm, had several attractive features. Among these is the possibility that it could address some of the most fundamental questions on quantum phenomena. However, subsequent theoretical conjectures, which have now been included in the orthodox view of the deBroglie Bohm theory, are unphysical and have done much to undermine the original theory's appeal. We, therefore, return to the original theory as our starting point and address one of its perplexing areas: the quantum potential. By avoiding the unphysical c…
Test of Causal Non-Linear Quantum Mechanics by Ramsey Interferometry on the Vibrational Mode of a Trapped Ion
针对因果非线性量子力学难以通过常规光谱学检验的问题，利用谐势阱中$^{40}$Ca$^+$离子振动模式的叠加态，通过Ramsey干涉测量对因果非线性扰动的无量纲标度因子设定了严格上限。
Experimental Aspects of Indefinite Causal Order in Quantum Mechanics
本文综述了量子力学中不定因果序在量子信息处理中的优势、实验实现技术、理论支持方法及当前结果解释与未来展望。
Modern approaches to causal modeling give a central role to interventions, which require the active input of an observer and introduces an explicit `causal arrow of time'. Causal models typically adopt a mechanistic interpretation, according to which the direction of the causal arrow is intrinsic to the process being studied. Here we investigate whether the direction of the causal arrow might be a contribution from the observer, rather than an intrinsic property of the process. Working within a counterfactual and non-mechanistic interpretation of causal modeling developed in arXiv:1806.00895, …
The Explanation of Entanglement in Quantum Mechanics
该研究提出量子力学是类似热力学的唯象理论而非因果理论，重新阐释玻恩规则与薛定谔演化的性质，以此为纠缠等非定域现象提供简单的唯象解释，且不影响量子力学的计算预测与实证有效性。
In 1985, Leggett and Garg (1985 Phys. Rev. Lett. 54 857) proposed a Bell-like inequality to test (in)compatibility between two fundamental concepts of quantum mechanics. The first concept is 'macroscopic realism', which is the quality of a physical property of a quantum system being independent of observation at the macroscopic level. The second concept is 'noninvasive measurability', which is the possibility of performing a measurement without disturbing the subsequent evolution of a system. One of the key requirement for testing the violation of the Leggett-Garg inequality, or Bell's time in…
Measuring velocities requires the synchronization of spatially-separated clocks. Because this synchronization must precede the determination of velocities, no system of clock synchronization--such as that based on Einstein's presumption of light-speed isotropy--can ever be founded on an experimentally-validated velocity. I argue that this very old observation, which lingers in the philosophical literature under the heading ``Conventionality of Synchronization,'' suggests an explanation of why ``spooky'' quantum correlations can transfer no information at any speed, superluminal or otherwise. T…
Apparent violation of causality in relativistic quantum mechanics
本研究发现相对论量子力学中无质量和有质量粒子的严格局域波函数时间演化违反微观因果性，t=0局域的波函数后续在未来光锥外不消失，无质量情况有解析形式，有质量情况靠数值计算。
Several locally deterministic interpretations of quantum mechanics are presented and reviewed. The fundamental differences between these interpretations are made transparent by explicitly showing what information is carried locally by each physical system in an idealized experimental test of Bell's theorem. This also shows how each of these models can be locally causal and deterministic. First, a model is presented which avoids Bell's arguments through the assumption that space-time inflated from an initial singularity, which encapsulates the entire past light cone of every event in the univer…
We introduce a new interpretation of quantum mechanics by examining the Einstein, Podolsky and Rosen's (EPR) paradox and Bell's inequality experiments under the assumption that the vacuum has an inhomogeneous texture for energy levels below the Heisenberg time-energy uncertainty relation. In this article, selected results from the most reliable Bell's inequality experiments will be quantitatively analyzed to show that our interpretation of quantum mechanics creates a new loophole in Bell's inequality, and that the past experimental findings do not contradict our new interpretation. Under the v…
Relativistic causality, namely, the impossibility of signaling at superluminal speeds, restricts the kinds of correlations which can occur between different parts of a composite physical system. Here we establish the basic restrictions which relativistic causality imposes on the joint probabilities involved in an experiment of the Einstein-Podolsky-Rosen-Bohm type. Quantum mechanics, on the other hand, places further restrictions beyond those required by general considerations like causality and consistency. We illustrate this fact by considering the sum of correlations involved in the CHSH in…
Harmonizing de Broglie-Bohm's Causal Interpretation with the Copenhagen Interpretation of Quantum Mechanics
本文通过引入动量非线性算符，调和德布罗意-玻姆因果诠释与哥本哈根诠释，并证明该算符隐含于前者理论中。
Quantum mechanics and relativistic causality together imply nonlocality: nonlocal correlations (that violate the CHSH inequality) and nonlocal equations of motion (the Aharonov-Bohm effect). Can we invert the logical order? We consider a conjecture that nonlocality and relativistic causality together imply quantum mechanics. We show that correlations preserving relativistic causality can violate the CHSH inequality more strongly than quantum correlations. Also, we describe nonlocal equations of motion, preserving relativistic causality, that do not arise in quantum mechanics. In these nonlocal…
Recent frameworks describing quantum mechanics in the absence of a global causal order admit the existence of causally indefinite processes, where it is impossible to ascribe causal order for events A and B. These frameworks even allow for processes that violate the so-called causal inequalities, which are analogous to Bell's inequalities. However, the physicality of these exotic processes is, in the general case, still under debate, bringing into question their foundational relevance. While it is known that causally indefinite processes can be probabilistically realised by means of a quantum …
The quantum mechanical notion of unobservable causal loop and the anthropic principle
本文提出通过时间对称化补全可逆量子过程描述，揭示不可观测因果环的量子叠加结构，并以此完备人择原理，解释量子加速下的宇宙演化。
A modified lagrangian with causal and retrocausal momenta was used to derive a first causal wave equation and a second retrocausal wave equation using the principle of least action. The retrocausal wave function obtained through this method was found to be equivalent to the complex conjugate of the causal wave function, thus leading to the conclusion that a retrocausal effect is already implicit in quantum mechanics through the means of complex conjugation of the wave function when computing the probability density for a particle. Lastly, the same variational principle was employed with a frac…
It is currently unknown whether the laws of physics permit time travel into the past. While general relativity indicates the theoretical possibility of causality violation, it is now widely accepted that a theory of quantum gravity must play an essential role in such cases. As a striking example, the logical paradoxes usually associated with causality violation can be resolved by quantum effects. We ask whether the explicit construction of a theory that allows causality violation might in turn teach us something about quantum gravity. Taking the toy model of Deutsch as a starting point, in Par…
One of the basic assumptions underlying Bell's theorem is the causal arrow of time, having to do with temporal order rather than spatial separation. Nonetheless, the physical assumptions regarding causality are seldom studied in this context, and often even go unmentioned, in stark contrast with the many different possible locality conditions which have been studied and elaborated. In the present work, some retrocausal toy-models which reproduce the predictions of Quantum Mechanics for Bell-type correlations are reviewed. It is pointed out that a certain toy-model which is ostensibly superdete…
Multipartite Entanglement Measure : Genuine to Absolutely Maximally Entangled
本文提出GME-AME多体纠缠度量，非零值对应真正多体纠缠态，最大值仅由绝对最大纠缠态达到，并成功用于四体qutrit态的分类与纠缠结构研究。
We investigate quantum states that posses both maximum entanglement and maximum discord between the pertinent parties. Since entanglement (discord) is defined only for bipartite (two qubit) systems, we shall introduce an appropriate sum over of all bi-partitions as the associated measure. The ensuing definition --not new for entanglement-- is thus extended here to quantum discord. Also, additional dimensions within the parties are considered ({\it qudits}). We also discuss nonlocality (in the form of maximum violation of a Bell inequality) for all multiqubit systems. The emergence of more nonl…
Correlations that violate a Bell Inequality are said to be nonlocal, i.e. they do not admit a local and deterministic explanation. Great effort has been devoted to study how the amount of nonlocality (as measured by a Bell inequality violation) serves to quantify the amount of randomness present in observed correlations. In this work we reverse this research program and ask what do the randomness certification capabilities of a theory tell us about the nonlocality of that theory. We find that, contrary to initial intuition, maximally nonlocal theories cannot allow maximal randomness certificat…
A two boundary quantum mechanics without time ordered causal structure is advocated as consistent theory. The apparent causal structure of usual "near future" macroscopic phenomena is attributed to a cosmological asymmetry and to rules governing the transition between microscopic to macroscopic observations. Our interest is a heuristic understanding of the resulting macroscopic physics.
The causal quantum mechanics (i.e. Bohmian or de Broglie-Bohm or Bohm-de Broglie quantum mechanics) has made possible to calculate the trajectories of electrons in a typical double-slit experiment [C. Philippidis et al., Il Nuovo Cimento, 52 B, 15-28 (1979)]. The trajectories do not correspond to an uniform movement but to an accelerated one. The acceleration is caused by the quantum potential. From the quantum theoretical point of view, there is a probability for the electron to emit photons, with a certain emission power, during its movement from the slits to the screen. We find a quantum ge…
Tsirelson showed that $2\sqrt{2}$ is the maximum value that CHSH expression can take for quantum-correlations [B. S.Tsirelson, Lett. Math. Phys, 4 (1980) 93]. This bound simply follows from the algebra of observables. Recently by exploiting the physical structure of quantum mechanics like unitarity and linearity, Buhrman and Massar [H. Buhrman and S.Massar, Phys. Rev. A, 72 (2005) 052103] have established that violation of Tsirelson's bound in quantum mechanics will imply signalling. We prove the same with the help of realistic joint measurement in quantum mechanics and a Bell's inequality whi…
We apply the causal interpretation of quantum mechanics to homogeneous quantum cosmology and show that the quantum theory is independent of any time-gauge choice and there is no issue of time. We exemplify this result by studying a particular minisuperspace model where the quantum potential driven by a prescribed quantum state prevents the formation of the classical singularity, independently on the choice of the lapse function. This means that the fast-slow-time gauge conjecture is irrelevant within the framework of the causal interpretation of quantum cosmology.
p-Adic Quantum Mechanics, the Dirac Equation, and the violation of Einstein causality
提出以三维p进向量描述位置的新p进Dirac方程，说明Planck尺度下Lorentz对称性破缺，并证明其允许局域解但违反Einstein因果性。
It has been shown that it is theoretically possible for there to exist higher-order quantum processes in which the operations performed by separate parties cannot be ascribed a definite causal order. Some of these processes are believed to have a physical realization in standard quantum mechanics via coherent control of the times of the operations. A prominent example is the quantum SWITCH, which was recently demonstrated experimentally. However, the interpretation of such experiments as realizations of a process with indefinite causal structure as opposed to some form of simulation of such a …
A non-local hidden variables theory for non-relativisitic quantum theory is presented, which gives a realist completion of quantum mechanics, in the sense of a complete description of individual events. The proposed fundamental theory is an extension of an energetic causal set theory, which assumes that time, events, causal structure, momentum and energy are fundamental. But space and the wave function are emergent. The beables of the theory are the views of the events, which are a subset of their causal pasts. Thus, this theory asserts that the universe is a causal network of events, which co…
Practical implementation of arbitrary nonlocal controlled-unitary gate via indefinite causal order
本文提出了一种基于不定因果顺序的实用协议，实现任意受控单元arity门，通过调整单量子比特操作减少电路复杂度并提高实验灵活性。
The consequences of the theorems about ontological models are studied. "Maximally $ψ$-epistemic" is shown to be equivalent to the conjunction of two other conditions, each of which can be realized in Hilbert spaces of arbitrary dimension, but which cannot occur together for d>2. I argue that current theorems do not invalidate an epistemic interpretation of quantum states. A new condition, called "functionally $ψ$-epistemic", is introduced, which, were it to be excluded, would signal the exclusion of epistemic interpretations.
It is widely accepted that a Born probability of 1 is sufficient for the existence of a corresponding element of reality. Recently Vaidman has extended this idea to the ABL probabilities of the time-symmetrized version of quantum mechanics originated by Aharonov, Bergmann, and Lebowitz. Several authors have objected to Vaidman's time-symmetrized elements of reality without casting doubt on the widely accepted sufficiency condition for `ordinary' elements of reality. In this paper I show that while the proper truth condition for a quantum counterfactual is an ABL probability of 1, neither a Bor…
A recent paper by Souza, Oliveira and Sarthour (SOS) reports the experimental violation of a Leggett-Garg inequality (sometimes referred to as a temporal Bell inequality). The inequality tests for quantum mechanical superposition: if the inequality is violated, the dynamics cannot be explained by a large class of classical theories under the heading of macrorealism. Experimental tests of the LG inequality are beset by the difficulty of performing the necessary so-called 'non-invasive' measurements (which for the macrorealist will extract information from a system of interest without disturbing…
The debate on the nature of quantum probabilities in relation to Quantum Non Locality has elevated Quantum Mechanics to the level of an "Operational Epistemic Theory". In such context the quantum superposition principle has an extraneous non epistemic nature. This leads us to seek purely operational foundations for Quantum Mechanics, from which to derive the current mathematical axiomatization based on Hilbert spaces. In the present work I present a set of axioms of purely operational nature, based on a general definition of "the experiment", the operational/epistemic archetype of information …
We give a simple proof of Bell's inequality in quantum mechanics which, in conjunction with experiments, demonstrates that the local hidden variables assumption is false. The proof sheds light on relationships between the notion of causal interaction and interference between particles.
Although it may seem The Delayed Choice experiments contradict causality and one could construct an experiment which could possibly affect the past, using Many World interpretation we prove it is not possible. We also find a mathematical background to Which-path information and show why its obtainability prevents system from interfering. We find a system which exhibit both interference and correlation and show why one-particle interference and correlations are complementary. Better visible interference pattern leads to worse correlations and vice versa. Then, using knowledge gained from Quantu…
Statistical mechanics from relational complex time with a pure state
本研究提出无需熵最大化或状态计数，仅通过系统与环境最大纠缠纯态的关系复时间演化，即可导出系统的正则密度矩阵，为统计力学提供新的纯态基础。
It is shown that a general radial conformal Killing vector in Minkowski space-time can be associated to a generator of time evolution in conformal quantum mechanics. Among these conformal Killing vectors one finds a class which maps causal diamonds in Minkowski space-time into themselves. The flow of such Killing vectors describes worldlines of accelerated observers with a finite lifetime within the causal diamond. Time evolution of static diamond observers is equivalent to time evolution in conformal quantum mechanics governed by a hyperbolic Hamiltonian and covering only a segment of the tim…
It is suggested that quantum mechanics is not fundamental but emerges from classical information theory applied to causal horizons. The path integral quantization and quantum randomness can be derived by considering information loss of fields or particles crossing Rindler horizons for accelerating observers. This implies that information is one of the fundamental roots of all physical phenomena. The connection between this theory and Verlinde's entropic gravity theory is also investigated.
We review the theorems of Einstein-Podolsky-Rosen (EPR), Bell, Greenberger-Horne-Zeilinger (GHZ), and Hardy, and present arguments supporting the idea that quantum mechanics is a complete, causal, non local, and non separable theory.
Quantum mechanics permits nonlocality---both nonlocal correlations and nonlocal equations of motion---while respecting relativistic causality. Is quantum mechanics the unique theory that reconciles nonlocality and causality? We consider two models, going beyond quantum mechanics, of nonlocality---``superquantum" correlations, and nonlocal ``jamming" of correlations---and derive new results for the jamming model. In one space dimension, jamming allows reversal of the sequence of cause and effect; in higher dimensions, however, effect never precedes cause.
One of Yakir Aharonov's endlessly captivating physics ideas is the conjecture that two axioms, namely relativistic causality ("no superluminal signalling") and nonlocality, so nearly contradict each other that a unique theory - quantum mechanics - reconciles them. But superquantum (or "PR-box") correlations imply that quantum mechanics is not the most nonlocal theory (in the sense of nonlocal correlations) consistent with relativistic causality. Let us consider supplementing these two axioms with a minimal third axiom: there exists a classical limit in which macroscopic observables commute. Th…
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