Understanding Of Quantum Theory Research Articles

Quantum Perception and Quantum Computation

Quantum theory has led to the development of quantum technology and also advances in quantum technology further enhance our understanding of quantum theory. Among these technologies, quantum computing holds special importance as it is based on the quantum states concept, known as qubits or qudits. To advance quantum computation, it is crucial to deepen our understanding of quantum field theory. In this letter, we define quantum understanding as the first step towards this goal. Transitioning from classical to quantum perception is essential, as maintaining a classical viewpoint introduces numerous challenges in building a quantum computer. However, adopting quantum thinking mitigates these difficulties. This letter will first introduce quantum perception by examining the process of classical understanding and how this new approach to thinking transforms our perspective of nature. We will discuss how this shift in thinking provides a better conceptual understanding of the realization of quantum technology and quantum computing.

Do qubits dream of entangled sheep? Quantum measurement without classical output

Quantum mechanics is usually formulated with an implicit assumption that agents who can observe and interact with the world are external to it and have a classical memory. However, there is no accepted way to define the quantum–classical cut and no a priori reason to rule out fully quantum agents with coherent quantum memories. In this work, we introduce an entirely quantum notion of measurement, called a sensation, to account for quantum agents that experience the world through quantum sensors. Sensations eschew probabilities and instead describe a deterministic flow of quantum information. We quantify the information gain and disturbance of a sensation using concepts from quantum information theory and find that sensations always disturb at least as much as they inform. Viewing measurements as sensations could lead to a new understanding of quantum theory in general and to new results in the context of quantum networks.

Quantization: History and problems

In this work, I explore the concept of quantization as a mapping from classical phase space functions to quantum operators. I discuss the early history of this notion of quantization with emphasis on the works of Schrödinger and Dirac, and how quantization fit into their overall understanding of quantum theory in the 1920's. Dirac, in particular, proposed a quantization map which should satisfy certain properties, including the property that quantum commutators should be related to classical Poisson brackets in a particular way. However, in 1946, Groenewold proved that Dirac's mapping was inconsistent, making the problem of defining a rigorous quantization map more elusive than originally expected. This result, known as the Groenewold-Van Hove theorem, is not often discussed in physics texts, but here I will give an account of the theorem and what it means for potential ``corrections” to Dirac's scheme. Other proposals for quantization have arisen over the years, the first major one being that of Weyl in 1927, which was later developed by many, including Groenewold, and which has since become known as Weyl Quantization in the mathematical literature. Another, known as Geometric Quantization, formulates quantization in differential-geometric terms by appealing to the character of classical phase spaces as symplectic manifolds; this approach began with the work of Souriau, Kostant, and Kirillov in the 1960's. I will describe these proposals for quantization and comment on their relation to Dirac's original program. Along the way, the problem of operator ordering and of quantizing in curvilinear coordinates will be described, since these are natural questions that immediately present themselves when thinking about quantization.

The Quantum Revolution in Philosophy

In this thought-provoking book, Richard Healey proposes a new interpretation of quantum theory inspired by pragmatist philosophy. Healey puts forward the interpretation as an alternative to realist quantum theories on the one hand such as Bohmian mechanics, spontaneous collapse theories, and many-worlds interpretations, which are different proposals for describing what the quantum world is like and what the basic laws of physics are, and non-realist interpretations on the other hand such as quantum Bayesianism, which proposes to understand quantum theory as describing agents' subjective epistemic states. The central idea of Healey's proposal is to understand quantum theory as providing not a description of the physical world but a set of authoritative and objectively correct prescriptions about how agents should act. The book provides a detailed development and defense of that idea, and it contains interesting discussions about a wide range of philosophical issues such as representation, probability, explanation, causation, objectivity, meaning, and fundamentality. Healey's project is at the intersection of physics and philosophy. The book is divided into two parts. Part I of the book discusses the foundational questions in quantum theory from the perspective of the prescriptive interpretation. In Part II, Healey discusses the philosophical implications of the view. Both parts are written in a way that is largely accessible to non-specialists. In this brief book review, I will focus on two questions: (1) How does Healey's idea work? (2) What reasons are there to believe in it?

Maximal qubit violation of n-locality inequalities in a star-shaped quantum network

Bell's theorem was a cornerstone for our understanding of quantum theory and the establishment of Bell non-locality played a crucial role in the development of quantum information. Recently, its extension to complex networks has been attracting growing attention, but a deep characterization of quantum behavior is still missing for this novel context. In this work we analyze quantum correlations arising in the bilocality scenario, that is a tripartite quantum network where the correlations between the parties are mediated by two independent sources of states. First, we prove that non-bilocal correlations witnessed through a Bell-state measurement in the central node of the network form a subset of those obtainable by means of a local projective measurement. This leads us to derive the maximal violation of the bilocality inequality that can be achieved by arbitrary two-qubit quantum states and arbitrary local projective measurements. We then analyze in details the relation between the violation of the bilocality inequality and the CHSH inequality. Finally, we show how our method can be extended to the n-locality scenario consisting of n two-qubit quantum states distributed among nodes of a star-shaped network.

Quantum Theory and the Nature of Consciousness

Our interest focusses on the idea, that consciousness is a powerful acting entity. Up to now there does not exist a scientific concept for this idea. This is not due to problems within the field of psychology or brain research, but rather in resisting theories of modern physics. That is, why we have to search for a solution in the field of physics. A solution can be found in a new understanding of the basics of physical theory. That could be given by abstract and absolute quantum bits of information (AQI bits). To avoid the popular misunderstanding of “information” as “meaningful” it was necessary to find a new word for the free-of-meaning AQI bits: the AQI bits establish a quantum pre-structure termed “Protyposis” (Greek: “pre-formation”), out of which real objects can be formed, starting from energetical and material elementary particles. The Protyposis AQI bits provide a pre-structure for all entities in natural sciences. They are the basic entities, whereof the physical nature of the brain, on the one hand, and the mental nature of consciousness, on the other hand, were formed during the cosmological and the following biological evolution. A deeper understanding of quantum structures may help to overcome the resistance against quantum theory in the field of brain research and consciousness. The key for an understanding is the concept of Protyposis, which means an abstract quantum information free of any definite meaning. With the AQI bits of the Protyposis, both, massless and massive quantum particles can be constructed. Even quantum information with special meanings, in example grammatically formulated thoughts, eventually could be explained. As long as the fundamental basis of quantum theory is misunderstood as being formed by a manifold of some small objects like atoms, quarks, or strings, the problem of understanding consciousness has no solution. If instead we understand quantum theory as based on truly simple quantum structures, there would be no longer fundamental problems for an understanding of consciousness.

Rigidity of quantum steering and one-sided device-independent verifiable quantum computation

The relationship between correlations and entanglement has played a major role in understanding quantum theory since the work of Einstein et al (1935 Phys. Rev. 47 777–80). Tsirelson proved that Bell states, shared among two parties, when measured suitably, achieve the maximum non-local correlations allowed by quantum mechanics (Cirel’son 1980 Lett. Math. Phys. 4 93–100). Conversely, Reichardt et al showed that observing the maximal correlation value over a sequence of repeated measurements, implies that the underlying quantum state is close to a tensor product of maximally entangled states and, moreover, that it is measured according to an ideal strategy (Reichardt et al 2013 Nature 496 456–60). However, this strong rigidity result comes at a high price, requiring a large number of entangled pairs to be tested. In this paper, we present a significant improvement in terms of the overhead by instead considering quantum steering where the device of the one side is trusted. We first demonstrate a robust one-sided device-independent version of self-testing, which characterises the shared state and measurement operators of two parties up to a certain bound. We show that this bound is optimal up to constant factors and we generalise the results for the most general attacks. This leads us to a rigidity theorem for maximal steering correlations. As a key application we give a one-sided device-independent protocol for verifiable delegated quantum computation, and compare it to other existing protocols, to highlight the cost of trust assumptions. Finally, we show that under reasonable assumptions, the states shared in order to run a certain type of verification protocol must be unitarily equivalent to perfect Bell states.

Geometry of spin: Clifford algebraic approach

Spin is a fundamental degree of freedom of matter and radiation. In quantum theory, spin is represented by Pauli matrices. Then the various algebraic properties of Pauli matrices are studied as properties of matrix algebra. What has been shown in this article is that Pauli matrices are a representation of Clifford algebra of spin and hence all the properties of Pauli matrices follow from the underlying algebra. Clifford algebraic approach provides a geometrical and hence intuitive way to understand quantum theory of spin, and is a natural formalism to study spin. Clifford algebraic formalism has lot of applications in every field where spin plays an important role.

Riding gravity away from doomsday

The discovery that most of the energy density in the universe is stored in the form of dark energy has profound consequences for our future. In particular, our current limited understanding of quantum theory of gravity indicates that some time in the future, our universe will undergo a phase transition that will destroy us and everything else around us instantaneously. However, the laws of gravity also suggest a way out — some of our descendants could survive this catastrophe by riding gravity away from the danger. This paper describes the tale of this escape from doomsday.

Simple Explanation of the Quantum Limits of Genuine n-Body Nonlocality.

Quantum n-body correlations cannot be explained with (n-1)-body nonlocality. However, this genuine n-body nonlocality cannot surpass certain bounds. Here we address the problem of identifying the principles responsible for these bounds. We show that, for any n≥2, the exclusivity principle, as derived from axioms about sharp measurements, and a technical assumption give the exact bounds predicted by quantum theory. This provides a unified explanation of the bounds of single-body contextuality and n-body nonlocality, and connects two programs towards understanding quantum theory.

The analysis of analogy use in the teaching of introductory quantum theory

This study analyzes the analogies used in the teaching of introductory quantum theory concepts. Over twelve weeks, the researcher observed each class for a semester and conducted interviews with the students and the instructor. In the interviews, students answered questions about quantum theory concepts, which the instructor had taught them using analogies, and also discussed the effectiveness of these analogies. This study identified 48 analogies used by the instructor over the course of 53 fifty minute classes. The analysis of video recordings of the classes revealed that most of the analogies were constructed at the beginning of the semester during the teaching of the particle nature of waves, which is critical for understanding quantum theory. A large proportion of the analogies were given in verbal format; however, a limited number of pictorial and body motion elements were also used together with the analogies. The analogies were mainly positioned as an embedded activator prior to drawing conclusions about the target. It was also observed that analogies were used as an advance organizer and post synthesizer. In addition, the number of simple and enriched analogies used was similar. A limited number of analog explanations were identified and none of the analogies used indicated strategy identification. The instructor never mentioned the limitation of each analogy during their use in class as well. A large proportion of the analogies used spontaneously included both anthropomorphic and environmental characteristics. Although the presentation medium of the analogies was mainly discourse, the presentation of analogies in role play, story and brainstorming was also identified. In half of the analogy use, the instructor intended their use for clarification of the concepts; however, the use of analogies for introduction of a new topic, gaining attention, increasing participation and discriminating between classical and quantum issues was also observed, indicating a diverse use of analogies. In addition, the interviews revealed that students liked the use of analogies in their classes and believed that they had a positive effect on their understanding of new concepts.

Multi-User Non-Locality Amplification

Non-local correlations are among the most fascinating features of quantum theory from the point of view of information: Such correlations, although not allowing for signaling, are unexplainable by pre-shared information. The correlations have applications in cryptography, communication complexity, and sit at the very heart of many attempts of understanding quantum theory -- and its limits -- in terms of classical information. In these contexts, the question is crucial whether such correlations can be amplified or distilled, i.e., whether and how weak correlations can be used for generating (a smaller amount of) stronger. Whereas the question has been studied quite extensively for bipartite correlations (yielding both pessimistic and optimistic results), only little is known in the multi-partite case. We introduce a general framework of reductions between multi-party input-output systems. Within this formalism, we show that a natural n-party generalization of the well-known Popescu-Rohrlich box can be distilled, by an adaptive protocol, to the algebraic maximum.We use this result further to show that a much broader class of correlations, including all purely threepartite correlations, can be distilled from arbitrarily weak to almost maximal strength with partial communication, i.e., using only a subset of the channels required for the creation of the same correlation from scratch. Alternatively, this means that arbitrarily weak non-local correlations can have a "communication value" in the context of the generation of maximal non-locality.

The coevent formulation of quantum theory

Understanding quantum theory has been a subject of debate from its birth. Many different formulations and interpretations have been proposed. Here we examine a recent novel formulation, namely the coevents formulation. It is a histories formulation and has as starting point the Feynman path integral and the decoherence functional. The new ontology turns out to be that of a coarse-grained history. We start with a quantum measure defined on the space of histories, and the existence of zero covers rules out single-history as potential reality (the Kochen Specker theorem casted in histories form is a special case of a zero cover). We see that allowing coarse-grained histories as potential realities avoids the previous paradoxes, maintains deductive non-contextual logic (alas non-Boolean) and gives rise to a unique classical domain. Moreover, we can recover the probabilistic predictions of quantum theory with the use of the Cournot's principle. This formulation, being both a realist formulation and based on histories, is well suited conceptually for the purposes of quantum gravity and cosmology.

Uncertainty Relations from Simple Entropic Properties

Uncertainty relations provide constraints on how well the outcomes of incompatible measurements can be predicted, and as well as being fundamental to our understanding of quantum theory, they have practical applications such as for cryptography and witnessing entanglement. Here we shed new light on the entropic form of these relations, showing that they follow from a few simple properties, including the data-processing inequality. We prove these relations without relying on the exact expression for the entropy, and hence show that a single technique applies to several entropic quantities, including the von Neumann entropy, min- and max-entropies, and the Rényi entropies.

How to Teach Basic Quantum Mechanics to Computer Scientists and Electrical Engineers

Because of the rapid development of quantum computation and of quantum technologies in general, computer scientists and electrical engineers will have to learn quantum mechanics (QM) in the near future. Although the teaching methods of QM are well established in both undergraduate and graduate physics courses, an effective method for teaching QM to computer scientists and electrical engineers is still lacking. This paper tries to fill this gap and suggests a new teaching method based on quantum cryptography. The goal of this paper is to show that computer scientists and electrical engineers can properly understand quantum theory without studying a degree in physics.

Unexpected Hamiltonian structure in chromodynamics: a track of fundamental instant?

It is shown that a careful consideration of the Hamiltonian structure in spinorial chromodynamics leads in fact to some harmonic and totally new nonclassical picture. This picture lies beyond the understanding of quantum theory and space-time and describes the fundamental instant.

Fine, Einstein, and ensembles

Einstein insisted that the only acceptable interpretation of the quantum theory was an ensemble interpretation, that this way of understanding the quantum formalism eliminated all the problems associated with interpreting the theory as a complete description of individual systems. But he never developed his ensemble interpretation in any detail or explained how it was supposed to resolve the difficulties with the individual interpretation. We offer a reconstruction of Einstein's position that is consonant with his other beliefs and examine the “prism” reconstruction recently proposed by Arthur Fine. We show the plausibility of our reading, as an interpretation of Einstein, and criticize Fine's proposal, as an alternative interpretation and as an attempt to understand quantum theory. As we reconstruct it, Einstein's position is, nevertheless, problematic. We therefore conclude with a plausible, if unoriginal, suggestion as to the reason he failed to develop his remarks on ensembles more fully.

Reconstruction of abstract quantum theory

Understanding quantum theory as a general theory of prediction, we reconstruct “abstract” quantum theory. “Abstract” means the general frame of quantum theory, without reference to a three-dimensional position space, to concepts like particle or field, or to special laws of dynamics. “Reconstruction” is the attempt to do this by formulating simple and plausible postulates on prediction in order to derive the basic concepts of quantum theory from them. Thereby no law of “classical” physics is presupposed which would then have to be “quantized.” We briefly discuss the relationship of “theory” and “interpretation” in physics and the fundamental role of time as a basic concept for physics. Then a number ofassertions are given, formulated as succinctly as possible in order to make them easily quotable and comparable. The assertions are arranged in four groups: heuristic principles, verbal definitions of some terms, three basic postulates, and consequences. The three postulates of separable alternatives, indeterminism, and kinematics are the central points of this work. These brief assertions are commented upon, and their relationship with the interpretation of quantum theory is discussed. Also given are an outlook on the further development into “concrete quantum theory” and some philosophical reflections.

Interference and interaction in Schrödinger's wave mechanics

Reminiscing on the fact that E. Schrodinger was rooted in the same physical tradition as M. Planck and A. Einstein, some aspects of his attitude to quantum mechanics are discussed. In particular, it is demonstrated that the quantum-mechanical paradoxes assumed by Einstein and Schrodinger should not exist, but that otherwise the epistemological problem of physical reality raised in this context by Einstein and Schrodinger is fundamental for our understanding of quantum theory. The nonexistence of such paradoxes just shows that quantum-mechanical effects are due to interference and not to interaction. This line of argument leads consequently to quantum field theories with second quantization, and accordingly quantum theory based both on Planck's constant h and on Democritus's atomism.

What is Einstein's statistical interpretation, or, is it Einstein for whom Bell's theorem tolls?

Einstein regarded the quantum theory as descriptively incomplete. What he meant was that, in typical cases, the probabilistic assertions provided by the theory for an individual quantum system do not exhaust all the relevant and true physical assertions about the system. Put briefly, according to Einstein, the typical statistical story told by quantum theory is not the whole story. Einstein arrived at this doctrine by means of a dialectical strategy that involved several beautiful and simple 'in-principle' applications of the theory, elegant thought experiments of a kind characteristic of Einstein's genius for physical insight. His strategy was to show how the alternative idea, the idea of the completeness of quantum theory, was forced into puzzling and unnatural interpretations for these special applications. By switching from completeness to incompleteness everything was supposed to 'click' into place: the fly, as it were, was to be let out of the bottle. Certainly Einstein never thought he was offering strict counterexamples to the theory itself. Nor, I believe, did he think he had strictly proved his case for incompleteness, or actually refuted the idea of completeness. Rather, he felt that the dialectical strategy showed his conception to have a powerful intuitive appeal vis-a-vis its competitor. The final stage of that strategy involved showing how the idea of incompleteness could ground a specific understanding of quantum theory, one that would make intelligible the puzzling thought experiments. That understanding comprises what is sometimes called Einstein's 'statistical interpretation' of the state functions of quantum theory; in his own words "the ~O-function is to be understood as the description not of a single system but of an ensemble of systems.' (Schilpp, 1949, p. 671). Using this idea the seeming-paradoxes generated by the alternative conception (that the ~O-function is a complete description of the single system) were supposed to disappear. From his earliest public comments on the interpretation of quantum mechanics, in the Solvay conference of 1927, down through his last papers on the subject in the 1940s and early 50s, Einstein referred to the ensemble interpretation of the state function in language virtually identical to that just cited. 1 So far as I have been able to ascertain, the same is true of his unpublished remarks. This concept of an ensemble interpretation was clearly the cornerstone of his own understanding of the quantum theory. Writing to Born in 1953, he described this concept as "the only one which does justice to the mechanism of the probabilistic quantum theory." (Born, 1971, p. 209). It is, therefore, remarkable although (curiously) scarcely ever remarked upon, that nowhere at all does Einstein say in any detail just exactly what this ensemble interpretation amounts to. In particular, he never does so for the very applications that are supposed to be treated by this interpretation 'more naturally' than by its competitor. Although it would be intriguing to speculate on the reasons behind Einstein's cryptic brevity here, and even more intriguing to think about the reluctance of his many commentators on the subject to deal with this fact, I shall defer the pleasure of those speculations, just now, in favor of another. For what, after all, was Einstein's ensemble interpretation? As just noted, there is very little textual material available on which to base an answer. One only finds a couple of vague phrases in one article, and a couple of very similar ones in the others. Despite the scant data, however, the literature seems to have settled on a standard answer. ~ This answer, the so-called 'statistical interpretation,' has been faced with difficulties at least since 1935, difficulties known to Einstein and simply ignored by him. 3 Recently these difficulties have been sharply focused, and have received a good deal of attention, through the work of John Bell. 4 Bell showed that, in principle (at least), the statistical interpretation is actually numerically inconsistent with the quantum theory when applied to coupled systems, the most favorite of Einstein's provocative examples. If the standard answer is Einstein's, then it appears that his interpretation of the quantum theory has been refuted. This conclusion is, I think, the received opinion. Given what little Einstein actually had to say on the matter and given his complete aplomb in the face of earlier