Limit Of Quantum Mechanics Research Articles

Stabilized entanglement of massive mechanical oscillators.

Quantum entanglement is a phenomenon whereby systems cannot be described independently of each other, even though they may be separated by an arbitrarily large distance 1 . Entanglement has a solid theoretical and experimental foundation and is the key resource behind many emerging quantum technologies, including quantum computation, cryptography and metrology. Entanglement has been demonstrated for microscopic-scale systems, such as those involving photons2-5, ions 6 and electron spins 7 , and more recently in microwave and electromechanical devices8-10. For macroscopic-scale objects8-14, however, it is very vulnerable to environmental disturbances, and the creation and verification of entanglement of the centre-of-mass motion of macroscopic-scale objects remains an outstanding goal. Here we report such an experimental demonstration, with the moving bodies being two massive micromechanical oscillators, each composed of about 10 12 atoms, coupled to a microwave-frequency electromagnetic cavity that is used to create and stabilize the entanglement of their centre-of-mass motion15-17. We infer the existence of entanglement in the steady state by combining measurements of correlated mechanical fluctuations with an analysis of the microwaves emitted from the cavity. Our work qualitatively extends the range of entangled physical systems and has implications for quantum information processing, precision measurements and tests of the limits of quantum mechanics.

General treatment of quantum and classical spinning particles in external fields

We develop the general theory of spinning particles with electric and magnetic dipole moments moving in arbitrary electromagnetic, inertial and gravitational fields. Both the quantum-mechanical and classical dynamics is investigated. We start from the covariant Dirac equation extended to a spin-${\frac 12}$ fermion with anomalous magnetic and electric dipole moments and then perform the relativistic Foldy-Wouthuysen transformation. This transformation allows us to obtain the quantum-mechanical equations of motion for the physical operators in the Schr\"odinger form and to establish the classical limit of relativistic quantum mechanics. The results obtained are then compared to the general classical description of the spinning particle interacting with electromagnetic, inertial and gravitational fields. The complete agreement between the quantum mechanics and the classical theory is proven in the general case. As an application of the results obtained, we consider the dynamics of a spinning particle in a gravitational wave and analyze the prospects of using the magnetic resonance setup to find possible manifestations of the gravitational wave on spin.

Classical Limit and Quantum Logic

The analysis of the classical limit of quantum mechanics usually focuses on the state of the system. The general idea is to explain the disappearance of the interference terms of quantum states appealing to the decoherence process induced by the environment. However, in these approaches it is not explained how the structure of quantum properties becomes classical. In this paper, we consider the classical limit from a different perspective. We consider the set of properties of a quantum system and we study the quantum-to-classical transition of its logical structure. The aim is to open the door to a new study based on dynamical logics, that is, logics that change over time. In particular, we appeal to the notion of hybrid logics to describe semiclassical systems. Moreover, we consider systems with many characteristic decoherence times, whose sublattices of properties become distributive at different times.

Extensions of Born’s rule to non-linear quantum mechanics, some of which do not imply superluminal communication

Nonlinear modifications of quantum mechanics have a troubled history. They were initially studied for many promising reasons: resolving the measurement problem, formulating a theory of quantum mechanics and gravity, and understanding the limits of standard quantum mechanics. However, certain non-linear theories have been experimentally tested and failed. More significantly, it has been shown that, in general, deterministic non-linear theories can be used for superluminal communication. We highlight another serious issue: the distribution of measurement results predicted by non-linear quantum mechanics depends on the formulation of quantum mechanics. In other words, Born’s rule cannot be uniquely extended to non-linear quantum mechanics. We present these generalizations of Born’s rule, and then examine whether some exclude superluminal communication. We determine that a large class do not allow for superluminal communication, but many lack a consistent definition. Nonetheless, we find a single extension of Born’s rule with a sound operational definition, and that does not exhibit superluminal communication. The non-linear time-evolution leading to a certain measurement event is driven by the state conditioned on measurements that lie within the past light cone of that event.

A New Argument for the Nomological Interpretation of the Wave Function: The Galilean Group and the Classical Limit of Nonrelativistic Quantum Mechanics

ABSTRACTIn this article I investigate, within the framework of realistic interpretations of the wave function in nonrelativistic quantum mechanics, the mathematical and physical nature of the wave function. I argue against the view that mathematically the wave function is a two-component scalar field on configuration space. First, I review how this view makes quantum mechanics non-Galilei invariant and yields the wrong classical limit. Moreover, I argue that interpreting the wave function as a ray, in agreement with many physicists, ensures that Galilei invariance is preserved. In addition, I discuss how the wave function behaves more similarly to a gauge potential than to a field. Finally, I show how this favours a nomological rather than an ontological view of the wave function.

Definition of the Riesz derivative and its application to space fractional quantum mechanics

We investigate and compare different representations of the Riesz derivative, which plays an important role in anomalous diffusion and space fractional quantum mechanics. In particular, we show that a certain representation of the Riesz derivative, Rxα, that is generally given as also valid for α = 1, behaves no differently than the other definition given in terms of its Fourier transform. In the light of this, we discuss the α → 1 limit of the space fractional quantum mechanics and its consistency.

Carboxylate-based molecular magnet: One path toward achieving stable quantum correlations at room temperature

The control of quantum correlations in solid-state systems by means of material engineering is a broad avenue to be explored, since it makes possible steps toward the limits of quantum mechanics and the design of novel materials with applications on emerging quantum technologies. In this context, this letter explores the potential of molecular magnets to be prototypes of materials for quantum information technology. More precisely, we engineered a material and from its geometric quantum discord we found significant quantum correlations up to 9540 K (even without entanglement); and, in addition, a pure singlet state occupied up to around 80 K (above liquid nitrogen temperature). These results could only be achieved due to the carboxylate group promoting a metal-to-metal huge magnetic interaction.

On the Mean Field and Classical Limits of Quantum Mechanics

The main result in this paper is a new inequality bearing on solutions of the $N$-body linear Schr\"{o}dinger equation and of the mean field Hartree equation. This inequality implies that the mean field limit of the quantum mechanics of $N$ identical particles is uniform in the classical limit and provides a quantitative estimate of the quality of the approximation. This result applies to the case of $C^{1,1}$ interaction potentials. The quantity measuring the approximation of the $N$-body quantum dynamics by its mean field limit is analogous to the Monge-Kantorovich (or Wasserstein) distance with exponent $2$. The inequality satisfied by this quantity is reminiscent of the work of Dobrushin on the mean field limit in classical mechanics [Func. Anal. Appl. 13 (1979), 115-123]. Our approach of this problem is based on a direct analysis of the $N$-particle Liouville equation, and avoids using techniques based on the BBGKY hierarchy or on second quantization.

Preface of the Special Issue Probing the Limits of Quantum Mechanics: Theory and Experiment, Volume 2

Preface of the Special Issue Probing the Limits of Quantum Mechanics : Theory and Experiment Volume 2

Preface of the Special Issue Probing the Limits of Quantum Mechanics: Theory and Experiment, Volume 1

Preface of the Special Issue Probing the Limits of Quantum Mechanics: Theory and Experiment, Volume 1

Lévy flights in a box

It is shown that a quantum Lévy process in a box leads to a problem involving topological constraints in space, and its treatment in the framework of the path integral formalism with the Lévy measure is suggested. The eigenvalue problem for the infinite potential well is properly defined and solved. An analytical expression for the evolution operator is obtained in the path integral presentation, and the path integral takes the correct limit of the local quantum mechanics with topological constraints. An example of the Lévy process in oscillating walls is also considered in the adiabatic approximation.

Quantum : the q = 1 limit of Galois field quantum mechanics, projective geometry and the field with one element

We argue that the q = 1 limit of Galois field quantum mechanics, which was constructed on a vector space over the Galois field , corresponds to its ‘classical limit’, where superposition of states is disallowed. The limit preserves the projective geometry nature of the state space, and can be understood as being constructed on an appropriately defined analogue of a ‘vector’ space over the ‘field with one element’ .

Quantum Decoherence: A Logical Perspective

The so-called classical limit of quantum mechanics is generally studied in terms of the decoherence of the state operator that characterizes a system. This is not the only possible approach to decoherence. In previous works we have presented the possibility of studying the classical limit in terms of the decoherence of relevant observables of the system. On the basis of this approach, in this paper we introduce the classical limit from a logical perspective, by studying the way in which the logical structure of quantum properties corresponding to relevant observables acquires Boolean characteristics.

New insights on emergence from the perspective of weak values and dynamical non-locality

In this article, we will examine new fundamental aspects of "emergence" and "information" using novel approaches to quantum mechanics which originated from the group around Aharonov. The two-state vector formalism provides a complete description of pre- and post-selected quantum systems and has uncovered a host of new quantum phenomena which were previously hidden. The most important feature is that any weak coupling to a pre- and post-selected system is effectively a coupling to a "weak value" which is given by a simple expression depending on the two-state vector. In particular, weak values, are the outcomes of so called "weak measurements" which have recently become a very powerful tool for ultra-sensitive measurements. Using weak values, we will show how to separate a particle from its properties, not unlike the Cheshire cat story: "Well! I've often seen a cat without a grin," thought Alice; "but a grin without a cat! It's the most curious thing I ever saw in all my life!" Next, we address the question whether the physics on different scales "emerges" from quantum mechanics or whether the laws of physics at those scales are fundamental. We show that the classical limit of quantum mechanics is a far more complicated issue; it is in fact dramatically more involved and it requires a complete revision of all our intuitions. The revised intuitions can then serve as a guide to finding novel quantum effects. Next we show that novel experimental aspects of contextuality can be demonstrated with weak measurements and these suggest new restrictions on hidden variable approaches. Next we emphasize that the most important implication of the Aharonov-Bohm effect is the existence of non-local interactions which do not violate causality. Finally, we review some generalizations of quantum mechanics and their implications for "emergence" and "information." First, we review an alternative approach to quantum evolution in which each moment of time is viewed as a new "universe" and time evolution is given by correlations between different moments. Next, we present a new solution to the measurement problem involving future boundary conditions placed on the universe as a whole. Finally, we introduce another fundamental approach to quantum evolution which allows for tremendous richness in the types of allowable Hamiltonians.

Flow of quantum correlations from a two-qubit system to its environment

The open-system dynamics of entanglement plays an important role in the assessment of the robustness of quantum information processes and also in the investigation of the classical limit of quantum mechanics. Here we show that, subjacent to this dynamics, there is a subtle flow of quantum correlations. We use a recently proposed optical setup, which allows joint tomography of system and environment, to show that the decay of an initial bipartite entangled state leads to the buildup of multipartite entanglement and quantum discord, the latter exhibiting a nonanalytic behavior that signals the emergence of maximal genuine quantum entanglement. The origin of this analyticity is shown to be distinct from similar behavior previously found in bipartite systems. Monogamy relations within the context of open-system dynamics explain this phenomenon.

Non-perturbative quantum geometry

The beta-ensemble with cubic potential can be used to study a quantum particle in a double-well potential with symmetry breaking term. The quantum mechanical perturbative energy arises from the ensemble free energy in a novel large N limit. A relation between the generating functions of the exact non-perturbative energy, similar in spirit to the one of Dunne-Unsal, is found. The exact quantization condition of Zinn-Justin and Jentschura is equivalent to the Nekrasov-Shatashvili quantization condition on the level of the ensemble. Refined topological string theory in the Nekrasov-Shatashvili limit arises as a large N limit of quantum mechanics.

An Interview with Professor Siddiqi: Quantum Scale Measurements

An Interview with Professor Siddiqi: Quantum Scale Measurements

Classical limit of quantum mechanics induced by continuous measurements

We investigate the quantum–classical transition problem. The main issue addressed is how quantum mechanics can reproduce results provided by Newton’s laws of motion. We show that the measurement process is critical to resolve this issue. In the limit of continuous monitoring with minimal intervention the classical limit is reached. The Classical Limit of Quantum Mechanic, in Newtonian sense, is determined by two parameters: the semiclassical time (τsc) and the time interval between measurements (Δτu). If is Δτu small enough, comparing with the τsc, then the classical regime is achieved. The semiclassical time for Gaussian initial states coincides with the Ehrenfest time. We also show that the classical limit of an ensemble of Newtonian trajectories, the Liouville regime, is approximately obtained for the quartic oscillator model if the number of measurements in the time interval is large enough to destroy the revival and small enough to not reach the Newtonian regime. Namely, the Newtonian regime occurs when τsc≫Δτu and the Liouvillian regime is mimicked, for the position observable, if Δτu∈[τsc,TR], where TR is the revival time.

Distances in Probability Space and the Statistical Complexity Setup

Statistical complexity measures (SCM) are the composition of two ingredients: (i) entropies and (ii) distances in probability-space. In consequence, SCMs provide a simultaneous quantification of the randomness and the correlational structures present in the system under study. We address in this review important topics underlying the SCM structure, viz., (a) a good choice of probability metric space and (b) how to assess the best distance-choice, which in this context is called a “disequilibrium” and is denoted with the letter Q. Q, indeed the crucial SCM ingredient, is cast in terms of an associated distance D. Since out input data consists of time-series, we also discuss the best way of extracting from the time series a probability distribution P. As an illustration, we show just how these issues affect the description of the classical limit of quantum mechanics.

Bell's Inequalities, Superquantum Correlations, and String Theory

We offer an interpretation of superquantum correlations in terms of a “doubly” quantum theory. We argue that string theory, viewed as a quantum theory with two deformation parameters, the string tensionα', and the string coupling constantgs, is such a superquantum theory that transgresses the usual quantum violations of Bell's inequalities. We also discuss theℏ→∞limit of quantum mechanics in this context. As a superquantum theory, string theory should display distinct experimentally observable supercorrelations of entangled stringy states.