Quantum Measurement Process Research Articles

Hybrid quantum-classical model of quantum measurements

Two types of Hamiltonian hybrid quantum-classical theories are considered as potential models of the quantum measurement process. The two theories have the same Hamiltonian dynamics but differ in the association of states of the quantum system with states of the hybrid model. In the first type of association pure quantum states are modeled by pure states of the hybrid, while in the second type the pure quantum states are modeled by statistical mixtures of the hybrid pure states. It is shown that the second of the two theories describes correctly the quantum measurement while the first provides only an averaged description.

Three-Slit Experiments and Quantum Nonlocality

An interesting link between two very different physical aspects of quantum mechanics is revealed; these are the absence of third-order interference and Tsirelson's bound for the nonlocal correlations. Considering multiple-slit experiments - not only the traditional configuration with two slits, but also configurations with three and more slits - Sorkin detected that third-order (and higher-order) interference is not possible in quantum mechanics. The EPR experiments show that quantum mechanics involves nonlocal correlations which are demonstrated in a violation of the Bell or CHSH inequality, but are still limited by a bound discovered by Tsirelson. It now turns out that Tsirelson's bound holds in a broad class of probabilistic theories provided that they rule out third-order interference. A major characteristic of this class is the existence of a reasonable calculus of conditional probability or, phrased more physically, of a reasonable model for the quantum measurement process.

Quantum rule for detection probability from Brownian motion in the space of classical fields

We obtain Born’s rule from the classical theory of random waves in combination with the use of thresholdtype detectors. We consider a model of classical random waves interacting with classical detectors and reproducing Born’s rule. We do not discuss complicated interpretational problems of quantum foundations. The reader can select between the “weak interpretation,” the classical mathematical simulation of the quantum measurement process, and the “strong interpretation,” the classical wave model of the real quantum (in fact, subquantum) phenomena.

Emergences in Quantum Measurement Processes

Abstract Quantum mechanics is acknowledged as the fundamental theory on which the whole fabric of physics is supposed to rely. And yet, the features of quantum measurements, processes that provide information about microscopic objects, seem to contradict the principles of quantum mechanics. We make a qualitative presentation of this long standing problem and give an idea of recent progress in the elucidation of the paradox. Although governed solely by the quantum equations of motion, the dynamical process involving the tested system and the measuring apparatus veils the quantum oddities that oppose our standard logic and gives rise to the expected properties of measurements. In spite of the irreducibly probabilistic nature of the underlying quantum physics, classical concepts emerge, such as standard probabilities, ordinary correlations, disappearance of quantum fluctuations, and the possibility of making statements about individual systems.

On the nature of black holes in loop quantum gravity

A genuine notion of black holes can only be obtained in the fundamental framework of quantum gravity resolving the curvature singularities and giving an account of the statistical mechanical, microscopic degrees of freedom able to explain the black hole thermodynamical properties. As for all quantum systems, a quantum realization of black holes requires an operator algebra of the fundamental observables of the theory which is introduced in this study based on aspects of loop quantum gravity. From the eigenvalue spectra of the quantum operators for the black hole area, charge and angular momentum, it is demonstrated that a strict bound on the extensive parameters, different from the relation arising in classical general relativity, holds, implying that the extremal black hole state can neither be measured nor can its existence be proven. This is, as turns out, a result of the specific form of the chosen angular momentum operator and the corresponding eigenvalue spectrum, or rather the quantum measurement process of angular momentum. Quantum-mechanical considerations and the lowest, non-zero eigenvalue of the loop quantum gravity black hole mass spectrum indicate, on the one hand, a physical Planck scale cutoff of the Hawking temperature law and, on the other hand, give upper and lower bounds on the numerical value of the Immirzi parameter. This analysis provides an approximative description of the behavior and the nature of quantum black holes.

Emergence of the Pointer Basis through the Dynamics of Correlations

We use the classical correlation between a quantum system being measured and its measurement apparatus to analyze the amount of information being retrieved in a quantum measurement process. Accounting for decoherence of the apparatus, we show that these correlations may have a sudden transition from a decay regime to a constant level. This transition characterizes a nonasymptotic emergence of the pointer basis, while the system apparatus can still be quantum correlated. We provide a formalization of the concept of emergence of a pointer basis in an apparatus subject to decoherence. This contrast of the pointer basis emergence to the quantum to classical transition is demonstrated in an experiment with polarization entangled photon pairs.

Quasiclassicality and Quantum Measurement

We address two problems arising in the quantum measurement process: A rigorous definition of quasiclassical systems and its implications for the observed collapse of the wave function.

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.

On genetic information uncertainty and the mutator phenotype in cancer

Recent evidence supports the existence of a mutator phenotype in cancer cells, although the mechanistic basis remains unknown. In this paper, it is shown that this enhanced genetic instability is generated by an amplified measurement uncertainty on genetic information during DNA replication. At baseline, an inherent measurement uncertainty implies an imprecision of the recognition, replication and transfer genetic information, and forms the basis for an intrinsic genetic instability in all biological cells. Genetic information is contained in the sequence of DNA bases, each existing due to proton tunnelling, as a coherent superposition of quantum states composed of both the canonical and rare tautomeric forms until decoherence by interaction with DNA polymerase. The result of such a quantum measurement process may be interpreted classically as akin to a Bernoulli trial, whose outcome X is random and can be either of two possibilities, depending on whether the proton is tunnelled (X=1) or not (X=0). This inherent quantum uncertainty is represented by a binary entropy function and quantified in terms of Shannon information entropy H(X)=−P(X=1)log2P(X=1)−P(X=0)log2P(X=0). Enhanced genetic instability may either be directly derived from amplified uncertainty induced by increases in quantum and thermodynamic fluctuation, or indirectly arise from the loss of natural uncertainty reduction mechanisms.

Physical theories, eternal inflation, and the quantum universe

We present a framework in which well-defined predictions are obtained in an eternally inflating multiverse, based on the principles of quantum mechanics. We show that the entire multiverse is described purely from the viewpoint of a single "observer," who describes the world as a quantum state defined on his/her past light cones bounded by the (stretched) apparent horizons. We find that quantum mechanics plays an essential role in regulating infinities. The framework is "gauge invariant," i.e. predictions do not depend on how spacetime is parametrized, as it should be in a theory of quantum gravity. Our framework provides a fully unified treatment of quantum measurement processes and the multiverse. We conclude that the eternally inflating multiverse and many worlds in quantum mechanics are the same. Other important implications include: global spacetime can be viewed as a derived concept; the multiverse is a transient phenomenon during the world relaxing into a supersymmetric Minkowski state. We also present a theory of "initial conditions" for the multiverse. By extrapolating our framework to the extreme, we arrive at a picture that the entire multiverse is a fluctuation in the stationary, fractal "mega-multiverse," in which an infinite sequence of multiverse productions occurs. The framework discussed here does not suffer from problems/paradoxes plaguing other measures proposed earlier, such as the youngness paradox, the Boltzmann brain problem, and a peculiar "end" of time.

Computational complexity and applications of quantum algorithm

We have studied on quantum algorithm several years, and introduced a mathematical model of it in order to discuss the computational complexity. Our model of quantum algorithm, called a generalized quantum Turing machine (GQTM) contains not only unitary computation process but also quantum measurement and dissipative process. Moreover, we discovered that a chaos dynamics has very important role in quantum algorithm, that is useful to solve NP complete problem in polynomial time. In this paper, we introduce the GQTM and some applications.

Nonlinear quantum mechanics, the superposition principle, and the quantum measurement problem

There are four reasons why our present knowledge and understanding of quantum mechanics can be regarded as incomplete. (1) The principle of linear superposition has not been experimentally tested for position eigenstates of objects having more than about a thousand atoms. (2) There is no universally agreed upon explanation for the process of quantum measurement. (3) There is no universally agreed upon explanation for the observed fact that macroscopic objects are not found in superposition of position eigenstates. (4) Most importantly, the concept of time is classical and hence external to quantum mechanics: there should exist an equivalent reformulation of the theory which does not refer to an external classical time. In this paper we argue that such a reformulation is the limiting case of a nonlinear quantum theory, with the nonlinearity becoming important at the Planck mass scale. Such a nonlinearity can provide insights into the aforesaid problems. We use a physically motivated model for a nonlinear Schrodinger equation to show that nonlinearity can help in understanding quantum measurement. We also show that while the principle of linear superposition holds to a very high accuracy for atomic systems, the lifetime of a quantum superposition becomes progressively smaller, as one goes from microscopic to macroscopic objects. This can explain the observed absence of position superpositions in macroscopic objects (lifetime is too small). It also suggests that ongoing laboratory experiments may be able to detect the finite superposition lifetime for mesoscopic objects in the near future.

Local Fields Without Restrictions on the Spectrum of 4-Momentum Operator and Relativistic Lindblad Equation

Quantum theory of Lorentz invariant local scalar fields without restrictions on 4-momentum spectrum is considered. The mass spectrum may be both discrete and continues and the square of mass as well as the energy may be positive or negative. Such fields can exist as part of a hidden matter in the Universe if they interact with ordinary fields very weakly. Generalization of Kallen-Lehmann representation for propagators of these fields is found. The considered generalized fields may violate CPT- invariance. Restrictions on mass-spectrum of CPT-violating fields are found. Local fields that annihilate vacuum state and violate CPT- invariance are constructed in this scope. Correct local relativistic generalization of Lindblad equation for density matrix is written for such fields. This generalization is particulary needed to describe the evolution of quantum system and measurement process in a unique way. Difficulties arising when the field annihilating the vacuum interacts with ordinary fields are discussed.

Knotted picture of the whole complete quantum measurement process of quantum teleportation

Based on the previous work about the knotted pictures of quantum states, quantum logic gates and unitary transformations, this paper further gives the whole complete quantum measurement process of quantum teleportation from the viewpoint of knot theory.

Reversible Measurement on Quantum States of Trapped-Ion Qubits

We consider reversible quantum measurement process with ultracold trapped ions. Two schemes will be proposed based on currently available experimental techniques. We also study the measurement process with electronic shelving amplification.

Ultracold Atoms and Quantum Measurement Processes

Ultracold Atoms and Quantum Measurement Processes

Simultaneous measurement of non-commuting observables

A dynamical model of a quantum measurement process is introduced, where the tested system S, a spin 1 2 , is simultaneously coupled with two apparatuses A and A ′ . Alone, A would measure the component s ^ z whereas A ′ alone would measure s ^ x . The apparatus A simulates an Ising magnetic dot involving N spins weakly coupled to a bath of phonons at a temperature lower than the Curie point. Initially in its metastable paramagnetic state, A tends to reach either one of its two equilibrium ferromagnetic states, with magnetization + m F or - m F along z, triggered by its interaction with the z-component s ^ z of S. Likewise, A ′ is coupled to the x-component s ^ x . The four probabilities of A + A ′ depend on the polarizations 〈 s z ( 0 ) 〉 and 〈 s x ( 0 ) 〉 of S at the initial time. The counting rates for repeated experiments then determine both 〈 s ^ z ( 0 ) 〉 and 〈 s ^ x ( 0 ) 〉 , although the process cannot be regarded as an ideal measurement. Three apparatuses simultaneously coupled to all three components of S provide full information on the initial density matrix of S through repeated runs. The lack of violation of Bell's inequalities by the indications of the apparatuses is discussed.

Two-particle coherence in an exactly solvable model of the quantum measurement process

The boson-detector model is generalized to investigate the decay of two-particle coherence. It is found from the visibility of the two-particle interferometer that the detector system not only destructs the coherence but also creates the correlation between the particles. Under certain conditions, the two-particle coherence can survive though the single particle coherence is completely destroyed.

Generalized model of the quantum measurement process in an environment

A generalized model of the quantum measurement process is considered, in which the relaxation of the detector system interacting with an environment can be treated. When the effect of the environment on the detector system is described by the quantum Markovian process, the model can be solved exactly. The time evolution of the particle and detector is investigated in detail. It is shown that the decay of quantum coherence of the particle becomes negligible when the relaxation time of the detector system is sufficiently short. Furthermore the stochastic model is found, which is equivalent to the proposed model with respect to the particle state.

A Unified Scheme of Measurement and Amplification Processes Based on Micro-Macro Duality — Stern-Gerlach Experiment as a Typical Example

A unified scheme for quantum measurement processes is formulated on the basis of micro-macro duality as a mathematical expression of the general idea of quantum-classical correspondence. In this formulation, we can naturally accommodate the amplification processes necessary for magnifying quantum state changes at the microscopic end of the probe system into the macroscopically visible motion of the measuring pointer. Its essence is exemplified and examined in the concrete model of the Stern-Gerlach experiment for spin measurement, where the Helgason duality controlling the Radon transform is seen to play essential roles.