Non-locality and Gauge Freedom in Deutsch and Hayden’s Formulation of Quantum Mechanics

Deutsch and Hayden have proposed an alternative formulation of quantum mechanics which is completely local. We argue that their proposal must be understood as having a form of ‘gauge freedom’ according to which mathematically distinct states are physically equivalent. Once this gauge freedom is taken into account, their formulation is no longer local.     

Non-locality and Gauge Freedom in Deutsch and Hayden’s Formulation of Quantum Mechanics

Deutsch and Hayden have proposed an alternative formulation of quantum mechanics which is completely local. We argue that their proposal must be understood as having a form of ‘gauge freedom’ according to which mathematically distinct states are physically equivalent. Once this gauge freedom is taken into account, their formulation is no longer local.      

Quantum Nonlocality: Not Eliminated by the Heisenberg Picture

It is argued that the Heisenberg picture of standard quantum mechanics does not save Einstein locality as claimed in Deutsch and Hayden (Proc. R. Soc. Lond. A 456, 1759–1774, 2000). In particular, the EPR-type correlations that the authors obtain by comparing two qubits in a local manner are shown to exist before that comparison. In view of this result, the local comparison argument would appear to be ineffective in supporting their locality claim.     

An Introduction to Many Worlds in Quantum Computation

The interpretation of quantum mechanics is an area of increasing interest to many working physicists. In particular, interest has come from those involved in quantum computing and information theory, as there has always been a strong foundational element in this field. This paper introduces one interpretation of quantum mechanics, a modern ‘many-worlds’ theory, from the perspective of quantum computation. Reasons for seeking to interpret quantum mechanics are discussed, then the specific ‘neo-Everettian’ theory is introduced and its claim as the best available interpretation defended. The main objections to the interpretation, including the so-called “problem of probability” are shown to fail. The local nature of the interpretation is demonstrated, and the implications of this both for the interpretation and for quantum mechanics more generally are discussed. Finally, the consequences of the theory for quantum computation are investigated, and common objections to using many worlds to describe quantum computing are answered. We find that using this particular many-worlds theory as a physical foundation for quantum computation gives several distinct advantages over other interpretations, and over not interpreting quantum theory at all.     

Information and the Brukner-Zeilinger Interpretation of Quantum Mechanics: A Critical Investigation

In Brukner and Zeilinger's interpretation of quantum mechanics, information is introduced as the most fundamental notion and the finiteness of information is considered as an essential feature of quantum systems. They also define a new measure of information which is inherently different from the Shannon information and try to show that the latter is not useful in defining the information content in a quantum object. Here, we show that there are serious problems in their approach which make their efforts unsatisfactory. The finiteness of information does not explain how objective results appear in experiments and what an instantaneous change in the so-called information vector (or catalog of knowledge) really means during the measurement. On the other hand, Brukner and Zeilinger's definition of a new measure of information may lose its significance, when the spin measurement of an elementary system is treated realistically. Hence, the sum of the individual measures of information may not be a conserved value in real experiments.     

Statistics of Local Value in Quantum Mechanics

Given a quantum mechanical observable and a state, one can construct a classical observable, that is, a real function on the configuration space, such that it is the optimal estimate of the quantum observable, in the sense of minimum variance. This optimal estimate turns out to be the quantum mechanical local value, which arises from several contexts such as de Broglie–Bohm's casual approach to quantum mechanics, instantaneous frequency in time–frequency analysis, Nelson's quantum fluctuations formalism, and phase-space approach to quantum mechanics. Accordingly, any observable can be decomposed into a local value part and a quantum fluctuation part, which are independent, both geometrically and statistically. Furthermore, the current density in quantum mechanics, the osmotic velocity in stochastic mechanics, and the Fisher information in classical statistical inference, arise naturally in connection with local value. In particular, Heisenberg uncertainty principle can be quantified more precisely by virtue of local value.     

Information and the Reconstruction of Quantum Physics

The reconstruction of quantum physics has been connected with the interpretation of the quantum formalism, and has continued to be so with the recent deeper consideration of the relation of information to quantum states and processes. This recent form of reconstruction has mainly involved conceiving quantum theory on the basis of informational principles, providing new perspectives on physical correlations and entanglement that can be used to encode information. By contrast to the traditional, interpretational approach to the foundations of quantum mechanics, which attempts directly to establish the meaning of the elements of the theory and often touches on metaphysical issues, the newer, more purely reconstructive approach sometimes defers this task, focusing instead on the mathematical derivation of the theoretical apparatus from simple principles or axioms. In its most pure form, this sort of theory reconstruction is fundamentally the mathematical derivation of the elements of theory from explicitly presented, often operational principles involving a minimum of extra‐mathematical content. Here, a representative series of specifically information‐based treatments—from partial reconstructions that make connections with information to rigorous axiomatizations, including those involving the theories of generalized probability and abstract systems—is reviewed.     

Reinterpretation of Quantum Mechanics Based on the Statistical Interpretation

I attempt to develop further the statistical interpretation of quantum mechanics proposed by Einstein and developed by Popper, Ballentine, etc. Two ideas are proposed in the present paper. One is to interpret momentum as a property of an ensemble of similarly prepared systems which is not satisfied by any one member of the ensemble of systems. Momentum is regarded as a statistical parameter like temperature in statistical mechanics. The other is the holistic assumption that a probability distribution is determined as a whole as most likely to be realized. This is the same as the chief assumption in statistical mechanics, and maximum likelihood in classical statistics. These ideas enable us to understand statistically (1) the formalism of quantum mechanics, (2) Heisenberg's uncertainty relations, and (3) the origin of quantum equations. They also explain violation of Bell's inequality and the interference of probabilities.     

Decoherent Histories and Realism

We reconsider the decoherent histories approach to quantum mechanics and analyze some problems related to its interpretation which we believe have not been adequately clarified by its proponents. We put forward some assumptions which, in our opinion, are necessary for a realistic interpretation of the probabilities that the formalism attaches to decoherent histories. We prove that such assumptions, unless one limits the set of the decoherent families which can be taken into account, lead to a logical contradiction. The line of reasoning we follow is conceptually different from other arguments which have been presented and which have been rejected by the supporters of the decoherent histories approach. The conclusion is that the decoherent histories approach, to be considered as an interesting realistic alternative to the orthodox interpretation of quantum mechanics, requires the identification of a mathematically precise criterion to characterize an appropriate set of decoherent families which does not give rise to any problem.     

Information flow in quantum teleportation

The flow of information is discussed in the context of quantum teleportation. Situations are described which use a sequence of systems of particles in which, though there is no claim of faster-than-light signaling, it is plausible to suggest that information about measurement procedures in one wing of the apparatus does reach the other end in a non-local manner. The definition of the term ‘parameter dependence’ is discussed.     

Basic Neutron Interference Experiments and the Information Interpretation of the Wavefunction

No Heading Two fundamental neutron interference experiments are discussed, the measurement of an unknown phase-shift and the simultaneous measurement of which-way and visibility duality. The experiments have been realized solely with unitary phase transformations in the spirit of minimal interaction between the neutron and its environment. The scope of the quantum measurements is to strengthen the information interpretation of quantum mechanics. As result the interpretation of the wavefunction, describing the information about potential measurements on single quantum systems, is confirmed, and the search for realistic scenarios tor the wavefunction and the measurement process is weakened by such basic quantum experiments.     

Ensemble interpretation of the EPR-Bell correlations

The EPR-Bell correlations between the spins of a pair of particles originally in a singlet state are discussed both on the basis of the mathematical formalism of quantum mechanics and the ensemble interpretation. It is shown that the correlations predicted by the mathematical formalism are in agreement with those expected on the basis of the ensemble interpretation, if the electrons are treated as distinguishable particles after they separate and undergo observation. In this case, the correlations are only in partial agreement with agedanken experiment of Mermin on the subject. It is pointed out, however, that agreement with Mermin’s conclusions is possible if one treats the electrons as indistinguishable even when they are subjected to observation after separation, though there is no obvious theoretical justification for doing so.     

Heuristic approach to non-abelian quantum kinematics and dynamics in configuration spacetime

New plausible kinematic foundations of quantum dynamics are discussed in a heuristic manner in which the quantum rule stems directly from the non-Abelian configuration symmetries of a system. Upon quantizing the ‘complete’ configuration symmetry group itself, irreducible generalized configuration-state representations can be calculated, whose transition amplitudes yield the propagation kernel. These states results from solving a set of ‘generalized Schrödinger equations’ corresponding to the superselection rules dictated by the quantized group. The propagation kernel of the system is thus obtained as an invariant Hurwitz integral, defined over the manifold of the complete symmetry group. A heuristic argument is given in favor of this approach to non-Abelian quantum kinematics, in which sums over physical world lines are evaluated instead of sums over arbitrary paths, for obtaining the propagation kernel of quantum systems having a classical Lagrangian analog. The attained quantum kinematic formalism, however, is completely general and does not depend on this particular interpretation. Nevertheless, the heuristic argument strongly suggests that non-Abelian quantum kinematics contains the formalism of standard nonrelativistic quantum mechanics as a very special case. No examples of the issues involved are presented in this paper.     

Bohmian formalism and Fisher information from q-deformed Schrödinger equation

We discuss the Bohmian mechanics using a deformed Schrödinger equation for position-dependent mass systems, in the context of a q-algebra inspired by the nonextensive statistical mechanics. We obtain the Bohmian quantum formalism by means of a deformed version of the Fisher information functional, from which a deformed Cramér–Rao bound is derived. Lagrangian and Hamiltonian formulations, inherited by the q-algebra, are also developed. Then, we illustrate the results with a particle confined in an infinite square potential well. The preservation of the deformed Cramér–Rao bound for eigenstates shows the role played by the q-algebraic structure.     

没有薛定谔猫态

新近有个超导量子干涉器件的实验,使澄清量子力学基本解释有了可能.分析此实验和相关实验之后,作出断言,抽象量子态没有信息,且波函数是个尚待观察者要去做的实验的几率幅.故用常用术语将量子态或波函数过分具体化,恐怕要招致误解.因而从本质上讲,薛定谔猫态是不存在的.     

The modal interpretation of quantum mechanics and some of its relativistic aspects

The modal interpretation of quantum mechanics is an attempt to relate the mathematical formalism of quantum mechanics to physical properties (beables,existents) in such a way that the property attribution reflects the mathematical structure as much as possible—no additional structure is superimposed on the quantum mechanical formalism. In this article the main features of the modal interpretation are explained and the question is discussed of how this interpretation deals with some well-known problems of quantum measurement theory (relativistic covariance and the question of whether or not there is superluminal causation).     

Non-linear Liouville and Shrödinger equations in phase space

Unitary representations of the Galilei group are studied in phase space, in order to describe classical and quantum systems. Conditions to write in general form the generator of time translation and Lagrangians in phase space are then established. In the classical case, Galilean invariance provides conditions for writing the Liouville operator and Lagrangian for non-linear systems. We analyze, as an example, a generalized kinetic equation where the collision term is local and non-linear. The quantum counter-part of such unitary representations are developed by using the Moyal (or star) product. Then a non-linear Schrödinger equation in phase space is derived and analyzed. In this case, an association with the Wigner formalism is established, which provides a physical interpretation for the formalism.