Measurement Process In Quantum Mechanics Research Articles

Bohr and von Neumann on the universality of quantum mechanics: materials for the history of the quantum measurement process

The Bohr and von Neumann views on the measurement process in quantum mechanics have been interpreted for a long time in somewhat controversial terms, often leading to misconceptions. On the basis of some textual analysis, I would like to show that—contrary to a widespread opinion—their views should be taken less inconsistent, and much closer to each other, than usually thought. As a consequence, I claim that Bohr and von Neumann are conceptually on the same side on the issue of the universality of quantum mechanics: hopefully, this might contribute to a more accurate history of the measurement problem in quantum mechanics.

Nonequilibrium Full Counting Statistics and Symmetry-Resolved Entanglement from Space-Time Duality.

Owing to its probabilistic nature, a measurement process in quantum mechanics produces a distribution of possible outcomes. This distribution-or its Fourier transform known as full counting statistics (FCS)-contains much more information than say the mean value of the measured observable, and accessing it is sometimes the only way to obtain relevant information about the system. In fact, the FCS is the limit of an even more general family of observables-the charged moments-that characterize how quantum entanglement is split in different symmetry sectors in the presence of a global symmetry. Here we consider the evolution of the FCS and of the charged moments of a U(1) charge truncated to a finite region after a global quantum quench. For large scales these quantities take a simple large-deviation form, showing two different regimes as functions of time: while for times much larger than the size of the region they approach a stationary value set by the local equilibrium state, for times shorter than region size they show a nontrivial dependence on time. We show that, whenever the initial state is also U(1) symmetric, the leading order in time of FCS and charged moments in the out-of-equilibrium regime can be determined by means of a space-time duality. Namely, it coincides with the stationary value in the system where the roles of time and space are exchanged. We use this observation to find some general properties of FCS and charged moments out of equilibrium, and to derive an exact expression for these quantities in interacting integrable models. We test this expression against exact results in the Rule 54 quantum cellular automaton and exact numerics in the XXZ spin-1/2 chain.

The physicist inside the ambiguous room: an argument against the need of consciousness in the quantum mechanical measurement process

This paper aims to invalidate the hypothesis that consciousness is necessary for the quantum measurement process. To achieve this target, I propose a considerable modification of the Schroedinger cat and the Dead-Alive Physicist thought experiments, called 'PIAR', short for Physicist Inside the Ambiguous Room. A specific strategy has enabled me to plan the experiment in such a way as to logically justify the inconsistency of the above hypothesis and to oblige its supporters to rely on an alternative interpretation of quantum mechanics in which the real-world phenomena exist independently of our conscious mind and where observers play no special role. Moreover, in my description, the measurement apparatus will be complete, in the sense that the experiment, given that it includes also the experimenter, will begin and end exclusively within a sealed room. Hence, my analysis provides a logical explanation of the relationship between the observer and the objects of her/his experimental observation; this and a few other implications are discussed in the fifth section and the conclusions.

Quantum measurement process with an ideal detector array

Any observable with finite eigenvalue spectrum can be measured using a multiport apparatus realizing an appropriate unitary transformation and an array of detector instruments, where each detector operates as an indicator of one possible value of the observable. The study of this setup in the frame of von Neumann’s quantum mechanical measurement process has a remarkable result: already after the interaction of the measured system with the detector array without collapse, exactly one detector is indicating a detection. Each single detector indicates either 0 or 1 detection, and no superposition can be attributed to it.

Quantifying and Interpreting Connection Strength in Macro- and Microscopic Systems: Lessons from Bell's Approach.

Bell inequalities were created with the goal of improving the understanding of foundational questions in quantum mechanics. To this end, they are typically applied to measurement results generated from entangled systems of particles. They can, however, also be used as a statistical tool for macroscopic systems, where they can describe the connection strength between two components of a system under a causal model. We show that, in principle, data from macroscopic observations analyzed with Bell’ s approach can invalidate certain causal models. To illustrate this use, we describe a macroscopic game setting, without a quantum mechanical measurement process, and analyze it using the framework of Bell experiments. In the macroscopic game, violations of the inequalities can be created by cheating with classically defined strategies. In the physical context, the meaning of violations is less clear and is still vigorously debated. We discuss two measures for optimal strategies to generate a given statistic that violates the inequalities. We show their mathematical equivalence and how they can be computed from CHSH-quantities alone, if non-signaling applies. As a macroscopic example from the financial world, we show how the unfair use of insider knowledge could be picked up using Bell statistics. Finally, in the discussion of realist interpretations of quantum mechanical Bell experiments, cheating strategies are often expressed through the ideas of free choice and locality. In this regard, violations of free choice and locality can be interpreted as two sides of the same coin, which underscores the view that the meaning these terms are given in Bell’s approach should not be confused with their everyday use. In general, we conclude that Bell’s approach also carries lessons for understanding macroscopic systems of which the connectedness conforms to different causal structures.

Effects of the free evolution in the Arthurs–Kelly model of simultaneous measurement and in the retrodictive predictions of the Heisenberg uncertainty relations

The simultaneous measurement approach of Arthurs and Kelly has been a significant tool for the better understanding of the measurement process in quantum mechanics. This model considers a strong interaction Hamiltonian by discarding the free evolution part. In this work, we study the effect of the full dynamics -- taking into account the free Hamiltonian -- on the optimal limits of retrodictive and predictive accuracy of the simultaneous measurement process of position and momentum observables. To do that, we consider a minimum uncertainty Gaussian state as the system under inspection, which allows to carry out an optimal simultaneous measurement. We show that the inclusion of the free Hamiltonian induces a spreading on the probability density of the measurement setting, which increases the value of the product of the variances of the so-called retrodictive and predictive error operators, this is equivalent to a reduction in the accuracy of the measurement.

Correction to: The Dead-Alive Physicist Experiment: A Case-Study Against the Hypothesis that Consciousness Causes the Wave-Function Collapse in the Quantum Mechanical Measurement Process

Correction to: The Dead-Alive Physicist Experiment: A Case-Study Against the Hypothesis that Consciousness Causes the Wave-Function Collapse in the Quantum Mechanical Measurement Process

On the Quantum Mechanical Measurement Process

The quantum mechanical measurement process is analyzed by means of an explicit generic model describing the interaction between object and measuring device. The solution of the Schrodinger equation for the whole system reflects the ‘collapse’ of the object wave function. A necessary condition is a sufficiently sharply peaked initial measurement device wave function, which is guaranteed in its classical limit. With this assumption, it is in particular proven that the off-diagonal elements of the object density matrix vanish. This study therefore shows the reduction of the object state to be a consequence of Hamiltonian evolution of the total system.

The Dead-Alive Physicist Experiment: A Case-Study Against the Hypothesis that Consciousness Causes the Wave-Function Collapse in the Quantum Mechanical Measurement Process

This paper aims to falsify the hypothesis that the observer's consciousness is necessary for quantum measurement. To achieve our target, we propose a variation of the Schroedinger's cat thought experiment called "DAP", short for "Dead-Alive Physicist", in which a human being replaces the cat. This strategy enables us to logically disprove the consistency of the above hypothesis and to oblige its supporters either to be trapped in solipsism or to rely on an alternative interpretation of quantum mechanics in which the role of the conscious observer has to be reviewed. Our analysis hence provides support to clarify the relationship between the observer the objects of her/his experimental observation; this and a few other implications are discussed in the fourth section and in the conclusions.

Effect of different filling tendencies on the spatial quantum Zeno effect

The quantum Zeno effect is deeply related to the quantum measurement process and thus studies of it may help shed light on the hitherto mysterious measurement process in quantum mechanics. Recently, the spatial quantum Zeno effect is observed in a Bose-Einstein condensate depleted by an electron beam. We theoretically investigate how different intrinsic tendencies of filling affect the quantum Zeno effect in this system by changing the impinging point of the electron beam along the inhomogeneous condensate. Surprisingly, we find no visible effect on the critical dissipation intensity at which the quantum Zeno effect appear. Our finding shows the recent capability of combining the Bose-Einstein condensate with an electron beam offers a great opportunity for studying the spatial quantum Zeno effect, and more generally the dynamics of a quantum many-body system out of equilibrium.

Neutrino oscillation measurements computed in quantum field theory

We perform such a calculation in quantum field theory, where we include simultaneously the source, detector, and neutrino fields in the Hamiltonian. Within the appropriate limits associated with current neutrino oscillation experiments, we recover the standard oscillation formula. On the other hand, we find that the dominant contributions to the amplitude are associated with different neutrino mass eigenstates being emitted at different times, such that they arrive at the detector at the same time. This is contrary to the neutrino wave packet picture, where they are emitted simultaneously and separate as they travel to the detector. This has direct consequences regarding the mechanisms that lead to a damping of neutrino oscillations for very long baselines. Our analysis also provides a pedagogical example of a measurement process in quantum mechanics.

The quantum Bayes rule and generalizations from the quantum maximum entropy method

The recent article ‘Entropic Updating of Probability and Density Matrices’ [] derives and demonstrates the inferential origins of both the standard and quantum relative entropies in unison. Operationally, the standard and quantum relative entropies are shown to be designed for the purpose of inferentially updating probability distributions and density matrices, respectively, when faced with incomplete information. We call the inferential updating procedure for density matrices the ‘quantum maximum entropy method’. Standard inference techniques in probability theory can be criticized for lacking concrete physical consequences in physics; but here, because we are updating quantum mechanical density matrices, the quantum maximum entropy method has direct physical and experimental consequences. The present article gives a new derivation of the Quantum Bayes Rule, and some generalizations, using the quantum maximum entropy method while discuss some of the limitations the quantum maximum entropy method puts on the measurement process in Quantum Mechanics.

Causality and the Modeling of the Measurement Process in Quantum Theory

AbstractIn this paper we provide a general account of the causal models which attempt to provide a solution to the famous measurement problem of Quantum Mechanics (QM). We will argue that—leaving aside instrumentalism which restricts the physical meaning of QM to the algorithmic prediction of measurement outcomes—the many interpretations which can be found in the literature can be distinguished through the way they model the measurement process, either in terms of theefficient causeor in terms of thefinal cause. We will discuss and analyze why both, ‘final cause’ and ‘efficient cause’ models, face severe difficulties to solve the measurement problem. In contradistinction to these schemes we will present a new model based on theimmanent causewhich, we will argue, provides an intuitive understanding of the measurement process in QM.

The Measurement Process in Local Quantum Physics and the EPR Paradox

We describe in a qualitative way a possible picture of the Measurement Process in Quantum Mechanics, which takes into account: 1. the finite and non zero time duration T of the interaction between the observed system and the microscopic part of the measurement apparatus; 2. the finite space size R of that apparatus; 3. the fact that the macroscopic part of the measurement apparatus, having the role of amplifying the effect of that interaction to a macroscopic scale, is composed by a very large but finite number N of particles. The conventional picture of the measurement, as an instantaneous action turning a pure state into a mixture, arises only in the limit in which N and R tend to infinity, and T tends to 0. We sketch here a proposed scheme, which still ought to be made mathematically precise in order to analyse its implications and to test it in specific models, where we argue that in Quantum Field Theory this picture should apply to the unique time evolution expressing the dynamics of a given theory, and should comply with the Principle of Locality. We comment on the Einstein Podolski Rosen thought experiment (partly modifying the discussion on this point in an earlier version of this note), reformulated here only in terms of local observables (rather than global ones, as one particle or polarisation observables). The local picture of the measurement process helps to make it clear that there is no conflict with the Principle of Locality.

Weak Value Amplification in Resonance Fluorescence

The concept of weak measurement and associated weak value amplification has sharpened our understanding of the measurement process in quantum mechanics. Recent experiments show that elastic scattering events in resonance fluorescence experiments can exhibit weak value amplification effect, by post-selecting a particular measurement outcome. In this article, we theoretically analyse the physics behind this amplification process. We show that, in general, weak interaction and the associated weak value amplification in resonance fluorescence can be derived from the well-Known theory of spontaneous emission put forth by Wigner and Weiskopff. Using this theory we show that in the elastic scattering regime of resonance fluorescence, weak value amplification helps in segregating rare events. To our knowledge, weak value amplification has not been applied earlier in the time domain as a potential tool to study rare events.

The Fermionic Projector, entanglement and the collapse of the wave function

After a brief introduction to the fermionic projector approach, we review how entanglement and second quantized bosonic and fermionic fields can be described in this framework. The constructions are discussed with regard to decoherence phenomena and the measurement problem. We propose a mechanism leading to the collapse of the wave function in the quantum mechanical measurement process.

Quantum Measurement Driven by Spontaneous Symmetry Breaking

Quantum mechanics cannot be applied within a closed system. Inevitable measurement process in quantum mechanics is usually treated separately from the basic principles of the framework and requires outside observer of the system. In this paper, we propose that the quantum measurement process is actually a physical process associated with the ubiquitous mechanism of spontaneous symmetry breaking. Based on this proposal, we construct a quantum measurement model in which the mixed state evolves into a pure state as the dynamical pro-coherence process. Furthermore, the classically distinguishable pointer parameter emerges as the c-number order parameter in the formalism of closed time-path quantum field theory. We also discuss the precision of the measurement and the possible deduction of the Born probability postulate.

Noise and quantum measurements in a circular Josephson array qubit

We study the decoherence and the quantum measurement of charge in a qubit consisting of a circular array of Josephson junctions. The two-level system we consider couples the two charge states through a higher-order tunneling process thus making it possible to achieve a long relaxation time. Using the spin-boson Hamiltonian, we estimate decoherence due to ohmic as well as $1/f$ noise. We simulate the quantum-mechanical measurement process by studying the density matrix of the qubit and a capacitively coupled single-electron transistor that measures the charge.

Schrödinger's cat and the clock: lessons for quantum gravity

I review basic principles of the quantum mechanical measurement process in view of their implications for a quantum theory of general relativity. It turns out that a clock as an external classical device associated with the observer plays an essential role. This leads me to postulate a ‘principle of the integrity of the observer’. It essentially requires the observer to be part of a classical domain connected throughout the measurement process. Mathematically this naturally leads to a formulation of quantum mechanics as a kind of topological quantum field theory. Significantly, quantities with a direct interpretation in terms of a measurement process are associated only with amplitudes for connected boundaries of compact regions of spacetime. I discuss some implications of my proposal such as in–out duality for states, delocalization of the ‘collapse of the wavefunction’ and locality of the description. Differences to existing approaches to quantum gravity are also highlighted.

Structure and properties of Hughston’s stochastic extension of the Schrödinger equation

Hughston has recently proposed a stochastic extension of the Schrödinger equation, expressed as a stochastic differential equation on projective Hilbert space. We derive new projective Hilbert space identities, which we use to give a general proof that Hughston’s equation leads to state vector collapse to energy eigenstates, with collapse probabilities given by the quantum mechanical probabilities computed from the initial state. We discuss the relation of Hughston’s equation to earlier work on norm-preserving stochastic equations, and show that Hughston’s equation can be written as a manifestly unitary stochastic evolution equation for the pure state density matrix. We discuss the behavior of systems constructed as direct products of independent subsystems, and briefly address the question of whether an energy-based approach, such as Hughston’s, suffices to give an objective interpretation of the measurement process in quantum mechanics.