Application Of Quantum Theory Research Articles

Conditions for logical contextuality and nonlocality

Contextuality and nonlocality are nonclassical properties exhibited by quantum statistics whose implications profoundly impact both the foundations and applications of quantum theory. In this paper we provide some insights into logical contextuality and inequality-free proofs. The former can be understood as the possibility version of contextuality, while the latter refers to proofs of quantum contextuality and nonlocality that are not based on violations of some noncontextuality (or Bell) inequality. By ``possibilistic'' we mean a description in terms of possibilities for the outcomes, which are Boolean variables assuming value one when the corresponding probability is strictly larger than zero and zero otherwise. The present work aims to build a bridge between these two concepts from what we call possibilistic paradoxes, which are sets of possibilistic conditions whose occurrence implies contextuality and nonlocality. As the main result, we demonstrate the existence of possibilistic paradoxes whose occurrence is a necessary and sufficient condition for logical contextuality in a very important class of scenarios. Finally, we discuss some interesting consequences arising from the completeness of these possibilistic paradoxes.

Entropic uncertainty relations in a class of generalized probabilistic theories

Entropic uncertainty relations play an important role in both fundamentals and applications of quantum theory. Although they have been well-investigated in quantum theory, little is known about entropic uncertainty in generalized probabilistic theories (GPTs). The current study explores two types of entropic uncertainty relations, preparation and measurement uncertainty relations, in a class of GPTs which can be considered generalizations of quantum theory. Not only a method for obtaining entropic preparation uncertainty relations but also an entropic measurement uncertainty relation similar to the quantum one by Buscemi et al (2014 Phys. Rev. Lett. 112 050401) are proved in those theories. These results manifest that the entropic structure in the uncertainty relations is not restricted to quantum theory and therefore is universal one. Concrete calculations of our relations in GPTs called the regular polygon theories are also demonstrated.

Phantasy and reality-teleportation versus quantum computing

Application of quantum theory in informatics and the creation of quantum information devices have revolutionary changed our idea about the information systems. It seems to us that the only question is that quantum computers will be introduced in the next decade or in some years later. Anyhow, we should prepare to teach a radically new paradigm, the quantum algorithms, in informatics. Quantum algorithm can be demonstrated with quantum simulators. The present paper shows an educational material, which facilitates the teaching of this new field. Besides summarising the basic concepts and methods of quantum informatics, the working of a quantum algorithm on a quantum simulator will be also illustrated with the discussion of an exciting quantum physical phenomenon (the teleportation).

On properties of inner product type integral transformers

In this paper, we give characterizations of certain properties of inner product type integral transformers. We first consider unitarily invariant norms and operator valued functions. We then give results on norm inequalities for inner product type integral transformers in terms of Landau inequality, Grüss inequality. Lastly, we explore some of the applications in quantum theory.

Characterizing Correlations via Skew Information

The skew information has important applications in quantum theory. In this paper, a measure for correlations in terms of the skew information is introduced and discussed. Its fundamental properties are obtained, which include the measure is locally unitary invariant and convex on the set of states with the fixed marginal state, moreover, it decreases under local random unitary operation. Lastly, we propose an entanglement criterion in terms of the quantum skew information and illustrate the significance of this criterion by some examples.

An Optimal Measurement Strategy to Beat the Quantum Uncertainty in Correlated System

AbstractUncertainty principle is an inherent nature of quantum system that undermines the precise measurement of incompatible observables and hence the applications of quantum theory. Entanglement, another unique feature of quantum physics, may help to reduce the quantum uncertainty. In this paper, a practical method is proposed to reduce the one party measurement uncertainty by determining the measurement on the other party of an entangled bipartite system. In light of this method, a family of conditional majorization uncertainty relations in the presence of quantum memory is constructed, which is applicable to arbitrary number of observables. The new family of uncertainty relations implies sophisticated structures of quantum uncertainty and non‐locality, that are usually studied by using scalar measures. Applications to reduce the local uncertainty and to witness quantum non‐locality are also presented.

Classical instanton solutions in quantum field theory

Instantons are non-trivial solutions of classical Euclidean equations of motion with a finite action. They provide stationary phase points in the path integral for tunnel amplitude between two topologically distinct vacua. It make them useful in many applications of quantum theory, especially for describing the wave function of systems with a degenerate vacua in the framework of the path integrals formalism. Our goal is to introduce the current situation about research on instantons and prepare for experiments. In this paper we give a review of instanton effects in quantum theory. We find in stanton solutions in some quantum mechanical problems, namely, in the problems of the one-dimensional motion of a particle in two-well and periodic potentials. We describe known instantons in quantum field theory that arise, in particular, in the two-dimensional Abelian Higgs model and in SU(2) Yang – Mills gauge fields. We find instanton solutions of two-dimensional scalar field models with sine-Gordon and double-well potentials in a limited spatial volume. We show that accounting of instantons significantly changes the form of the Yukawa potential for the sine-Gordon model in two dimensions.

Aliyun and Chinese Academy of Sciences Sign MoU for Quantum Computing Laboratory

Alibaba Group's cloud computing subsidiary, Aliyun, and the Chinese Academy of Sciences (CAS) signed a memorandum of understanding on 31 July 2015 in Shanghai to co-found the Chinese Academy of Sciences – Alibaba Quantum Computing Laboratory. The aim of the new research facility is to advance the study and applications of quantum theory, thereby creating new technologies and platforms for information security, connectivity and computing.

Quantum Theory of International Relations: Approaches and Possible Gains

Abstract This paper considers the possible application of quantum theory in political studies, especially in international relations. We introduce our classification based on three logical ways of how to connect areas so remote: through the relation of identity, analogy and metaphor which reflects three basic epistemic positions. Next, we review existing work against this classification before moving on to consider some of the uses and potential gains offered by quantum mind hypothesis, quantum models of reasoning and decisionmaking, and quantum metaphor.

Noncontextuality with marginal selectivity in reconstructing mental architectures.

We present a general theory of series-parallel mental architectures with selectively influenced stochastically non-independent components. A mental architecture is a hypothetical network of processes aimed at performing a task, of which we only observe the overall time it takes under variable parameters of the task. It is usually assumed that the network contains several processes selectively influenced by different experimental factors, and then the question is asked as to how these processes are arranged within the network, e.g., whether they are concurrent or sequential. One way of doing this is to consider the distribution functions for the overall processing time and compute certain linear combinations thereof (interaction contrasts). The theory of selective influences in psychology can be viewed as a special application of the interdisciplinary theory of (non)contextuality having its origins and main applications in quantum theory. In particular, lack of contextuality is equivalent to the existence of a “hidden” random entity of which all the random variables in play are functions. Consequently, for any given value of this common random entity, the processing times and their compositions (minima, maxima, or sums) become deterministic quantities. These quantities, in turn, can be treated as random variables with (shifted) Heaviside distribution functions, for which one can easily compute various linear combinations across different treatments, including interaction contrasts. This mathematical fact leads to a simple method, more general than the previously used ones, to investigate and characterize the interaction contrast for different types of series-parallel architectures.

An analytical approach for treating unitary quantum systems with initial mixed states

Mixed states are important in quantum optics since they frequently appear in decoherence problems. When one of the components of the system is initially prepared in a mixed state and the mathematical closed form of the evolution operator of the system is not available, one cannot deduce the density matrix. We present an analytical approach to accurately solve this problem. We exploit the fact that any mixed state can be expressed in terms of the phase state. The approach can be applied on the condition that Schrödinger’s equation of the system is solvable for any arbitrary initial state. We verify the validity of the approach for two examples, namely, the Jaynes–Cummings model and the two-qubit problem. Our results are in good agreement with the available results in the literature. This approach opens new perspectives for treating complicated systems and may impact other applications in quantum theory.

On the limits of quantum theory: Contextuality and the quantum–classical cut

This paper is based on four assumptions: 1. Physical reality is made of linearly behaving components combined in non-linear ways. 2. Higher level behaviour emerges from this lower level structure. 3. The way the lower level elements behaves depends on the context in which they are embedded. 4. Quantum theory applies to the lower level entities. An implication is that higher level effective laws, based on the outcomes of non-linear combinations of lower level linear interactions, will generically not be unitary; hence the applicability of quantum theory at higher levels is strictly limited. This leads to the view that both state vector preparation and the quantum measurement process are crucially based on top-down causal effects, and helps provide criteria for the Heisenberg cut that challenge some views on Schrödinger’s cat.

A new integral transform on time scales and its applications

Abstract Integral transform methods are widely used to solve the several dynamic equations with initial values or boundary conditions which are represented by integral equations. With this purpose, the Sumudu transform is introduced in this article as a new integral transform on a time scale "Equation missing" to solve a system of dynamic equations. The Sumudu transform on time scale "Equation missing" has not been presented before. The results in this article not only can be applied on ordinary differential equations when T = ℝ , difference equations when T = ℕ 0 , but also, can be applied for q-difference equations when T = q ℕ 0 , where q ℕ 0 : = { q t : t ∈ ℕ 0 for q > 1 } or T = q ℤ ¯ : = q ℤ ∪ { 0 } for q > 1 (which has important applications in quantum theory) and on different types of time scales like T = h ℕ 0 , T = ℕ 0 2 and T = T n the space of the harmonic numbers. Finally, we give some applications to illustrate our main results. 2010 Mathematics Subject Classification. 44A85; 35G15; 44A35.

Quantifying correlations via the Wigner-Yanase skew information

In order to quantify the information content of quantum states in the presence of conserved quantities, Wigner and Yanase introduced the notion of skew information [Proc. Natl. Acad. Sci. USA 49, 910, (1963)], which was later identified as a paradigmatic version of quantum Fisher information. The skew information is quite different from, yet deeply connected with, the ubiquitous quantum entropies and has important applications in quantum theory. In this paper, pursuing further the original idea of Wigner and Yanase, we propose a measure for correlations in terms of the skew information, investigate its fundamental properties, and elucidate its characteristics. An appealing feature of this measure for correlations is that its evaluation does not involve any optimization, in sharp contrast to the entanglement and discord measures, and can be straightforwardly calculated. In particular, the algorithm and explicit formulas for general bipartite states are prescribed, and simple analytical expressions for some special states, including arbitrary bipartite pure states, the Bell-diagonal states, and some highly symmetric states such as the Werner states and the isotropic states, are obtained.

Spectral parameter power series for Sturm–Liouville equations on time scales

We will derive formulas for finding two linearly independent solutions of the Sturm–Liouville dynamic equation. We will give several examples. In particular, the q-difference equation which has important applications in quantum theory will be presented.

Quantum entanglement

All our former experience with application of quantum theory seems to say that what is predicted by quantum formalism must occur in the laboratory. But the essence of quantum formalism---entanglement, recognized by Einstein, Podolsky, Rosen, and Schr\"odinger---waited over $70\phantom{\rule{0.3em}{0ex}}\text{years}$ to enter laboratories as a new resource as real as energy. This holistic property of compound quantum systems, which involves nonclassical correlations between subsystems, has potential for many quantum processes, including canonical ones: quantum cryptography, quantum teleportation, and dense coding. However, it appears that this new resource is complex and difficult to detect. Although it is usually fragile to the environment, it is robust against conceptual and mathematical tools, the task of which is to decipher its rich structure. This article reviews basic aspects of entanglement including its characterization, detection, distillation, and quantification. In particular, various manifestations of entanglement via Bell inequalities, entropic inequalities, entanglement witnesses, and quantum cryptography are discussed, and some interrelations are pointed out. The basic role of entanglement in quantum communication within a distant laboratory paradigm is stressed, and some peculiarities such as the irreversibility of entanglement manipulations are also discussed including its extremal form---the bound entanglement phenomenon. The basic role of entanglement witnesses in detection of entanglement is emphasized.

Canonical force and electromagnetic geometrical phase in particle interference

We provide arguments which demonstrate that the Berry phase effects involving particle interference in the presence of external electric and magnetic fields—namely the Aharonov–Bohm (AB), Aharonov–Casher (AC) and the Röntgen (R) effects—cannot be unambiguously explained (as has been controversially argued) through the use of any classical mechanical force. In fact, in the three scenarios which we consider, the only means to reclaim the standard quantum mechanical results is to use the expressions for the force that fail to satisfy the necessary conditions of gauge invariance. Our arguments explain the foundation of the controversy and confirm the standard idea that the Berry phase effects in question are non-local phenomena which only arise in the application of quantum theory. We lay special emphasis on the use of the concept of a canonical force, this being the quantity which ensures the agreement between the classical and quantum formulations. It is shown that if the Aharonov–Bohm effect is interpreted as being due to a force, through the use of the Bohmian formulation of quantum mechanics, then this force is equal in magnitude to the canonical force.

A Topos Perspective on State-Vector Reduction

A preliminary investigation is made of possible applications in quantum theory of the topos formed by the collection of all M-sets, where M is a monoid. Earlier results on topos aspects of quantum theory can be rederived in this way. However, the formalism also suggests a new way of constructing a ‘neo-realist’ interpretation of quantum theory in which the truth values of propositions are determined by the actions of the monoid of strings of finite projection operators. By these means, a novel topos perspective is gained on the concept of state-vector reduction.

A Topos Perspective on State-Vector Reduction

A preliminary investigation is made of possible applications in quantum theory of the topos formed by the collection of all M-sets, where M is a monoid. Earlier results on topos aspects of quantum theory can be rederived in this way. However, the formalism also suggests a new way of constructing a ‘neo-realist’ interpretation of quantum theory in which the truth values of propositions are determined by the actions of the monoid of strings of finite projection operators. By these means, a novel topos perspective is gained on the concept of state-vector reduction.

Wave equations in Riemannian spaces

With regard to applications in quantum theory, we consider the classical wave equation involving the scalar curvature with an arbitrary coefficient ξ. General properties of this equation and its solutions are studied based on modern results in group analysis with the aim to fix a physically justified value of ξ. These properties depend essentially not only on the values of ξ and the mass parameter but also on the type and dimension of the space. Form invariance and conformal invariance must be distinguished in general. A class of Lorentz spaces in which the massless equation satisfies the Huygens principle and its Green's function is free of a logarithmic singularity exists only for the conformal value of ξ. The same value of ξ follows from other arguments and the relation to the known WKB transformation method that we establish.