Careful analysis of cluster separability opens a way to a completely new understanding of preparation and registration procedures for microsystems: they are changes of separation status. An important observation is that quantum mechanics does not specify what happens to systems when they change their separation status. New rules that close this gap can therefore be added without disturbing the logic of quantum mechanics. Another important observation is that registration apparatuses for microsystems must contain detectors and that their readings are signals from detectors. This leads to further restrictions on measurability of observables, especially for macroscopic quantum systems. Beltrametti-Cassinelli-Lahti model is used to show how this approach leads to solution of the measurement problem.
Careful analysis of cluster separability opens a way to a completely new understanding of preparation and registration procedures for microsystems: they are changes of separation status. An important observation is that quantum mechanics does not specify what happens to systems when they change their separation status. New rules that close this gap can therefore be added without disturbing the logic of quantum mechanics. Another important observation is that registration apparatuses for microsystems must contain detectors and that their readings are signals from detectors. This leads to further restrictions on measurability of observables, especially for macroscopic quantum systems. Beltrametti-Cassinelli-Lahti model is used to show how this approach leads to solution of the measurement problem.
The paper describes a solution to the problem of quantum measurement that has been proposed recently. The literal understanding of the basic rule of quantum mechanics on identical particles violates the cluster separation principle and so leads to difficulties. A proposal due to Peres of how such difficulties could be removed is reformulated and extended. Cluster separability leads to a locality requirement on observables and to the key notion of separation status. Separation status of a microsystem is shown to change in preparation and registration processes. The indispensability of detectors plays an important role. Changes of separation status are alterations of kinematic description rather than some parts of dynamical trajectories and so more radical than 'collapse of the wave function'. Textbook quantum mechanics does not provide any information of how separation status changes run, hence new rules must be formulated. This enables to satisfy the objectification requirement for registrations. To show how the ideas work, a simplified model of registration apparatus is constructed.
Abstract The so-called quantum measurement problems are solved from a new perspective. One of the main observations is that the basic entities of our world are particles, elementary or composite. It follows that each elementary process, hence each measurement process at its core, is a spacetime, pointlike, event. Another key idea is that, when a microsystem ψ gets into contact with the experimental device, factorization of ψ rapidly fails and entangled mixed states appear. The wave functions for the microsystem-apparatus coupled system for different measurement outcomes then lack overlapping spacetime support. It means that the aftermath of each measurement is a single term in the sum: a “wave-function collapse”. Our discussion leading to a diagonal density matrix, ρ = diag(|c 1|2,…,|cn |2,…) shows how the information encoded in the wave function <?CDATA $|\psi \rangle =\displaystyle {\sum }_{n}{c}_{n}|n\rangle $?> | ψ 〉 = ∑ n c n | n 〉 gets transcribed, via entanglement with the experimental device and environment, into the relative frequencies Pn = |cn |2 for various experimental outcomes F = fn . Our discussion represents the first, significant steps towards filling in the logical gaps in the conventional interpretation based on Born’s rule, replacing it with a clearer understanding of quantum mechanics. Accepting objective reality of quantum fluctuations, independent of any experiments, and independently of human presence, one renounces the idea that in a fundamental, complete theory of Nature the result of each single experiment must necessarily be predictable.
A complete apparatus is defined as reacting to every state of the measured system. Standard quantum mechanics of indistinguishable particles is shown to imply that apparatuses must be incomplete or else they would be drowned out by noise. Each quantum observable is then an abstract representation of many measurement apparatuses, each incomplete in a different way. Moreover, a measured system must be prepared in a state that is orthogonal to the states of all particles of the same type in the environment. This is the main purpose of preparations. A system so prepared is said to have a "separation status". A new, more satisfactory definition of separation status than the spatial one proposed in previous papers then results. Conditions are specified under which the particles in the environment may be ignored as is usually done in the theory of measurement.
The quantum measurement problems are revisited from a new perspective. One of the main ideas of this work is that the basic entities of our world are various types of particles, elementary or composite. It follows that each elementary process, hence each measurement process at its core, is a space–time, pointlike, event. Another key idea is that, when a microsystem [Formula: see text] gets into contact with the experimental device, factorization of [Formula: see text] rapidly fails and entangled mixed states appear. The wave functions for the microsystem-apparatus coupled systems for different measurement outcomes then lack overlapping space–time support. It means that the aftermath of each measurement is a single term in the sum: a “wave function collapse.” Our discussion leading to a diagonal density matrix, [Formula: see text] shows how the information encoded in the wave function [Formula: see text] gets transcribed, via entanglement with the experimental device and environment, into the relative frequencies [Formula: see text] for various experimental results [Formula: see text]. These results represent the first, significant steps towards filling in the logical gaps in the standard interpretation based on Born’s rule, and replacing it with a more natural one. Accepting objective reality of quantum fluctuations, independent of any experiments, and independently of human presence, one renounces the idea that in a fundamental, complete theory of Nature the result of each single experiment must necessarily be predictable. A few well-known puzzles such as the Schrödinger cat conundrum and the Einstein–Podolsky–Rosen (EPR) paradox are briefly reviewed: they can all be naturally explained away.
The notion of state reduction employed by the standard quantum theory of measurement is difficult to accept for two reasons: It leaves open where and when the reduction takes place and it does not give any objective conditions under which the reduction occurs. Some recently published ideas on this problem are developed an improved. The disturbance of measurement due to identical particles in the environment is shown to make any POV measure non-measurable. Truncated POV (TPOV) measures are introduced that can be measurable if object systems satisfy the additional requirement of having separation status. The separation status is generalised from domain of space to domain of phase space. Starting from the previously introduced distinction between ancillas and detectors, further study of experiments suggests that a thermodynamic mixing within a detector and the consequent loss of separation status is the objective condition for the occurrence of the state reduction. The conjecture is simple, specific and testable. The theory is illustrated by a model of a real measurement.
When developing and operating quantum computers, it is necessary to be able to check quantum registers for the presence of quantum entanglement between its subsystems, due to which quantum computers gain computational advantage in solving many problems over classical computers. The state in which a quantum system consists of two or more subsystems that are not entangled with each other is called separable.In this article, we provide an overview of various existing approaches to solving the problem of determining separability in a quantum system. To do this, we provide an overview of works on this topic, describing both established and new approaches, highlighting directions in which new possibilities for solving the problem can be explored. We provide a definition of the problem of checking a system for separability, based on which we describe several applicable separability criteria. We provide a model-theoretic approach to solving the separability problem, describing a quantum system as a blurry model.