The Quantum Measurement Problem

Analysis of this state is interesting from the point of view of the quantum measurement problem, an issue that has been debated since the inception of quantum theory by Einstein, Bohr, and others, and continues today [31]. One practical approach toward resolving this controversy is the introduction of quantum decoherence, or the environmentally induced reduction of quantum superpoations into clasacal statistical mbrtures [32], Decoherence provides a way to quantify the elusive boundary between classical and quantum worlds, and almost always precludes the existence of macroscopic Schrodinger-cat states, except for extremely short times. On the othm hand, the creation of mesoscopic Schrddinger-cat states like that of q. (10) may allow controlled studies of quantum decoherence and the quantum-classical boundary. This problem is directly relevant to quantum computation, as we discuss below. 

The concept of quantum decoherence is often at the forefront of discussions on quantum communication and quantum information since it presents a serious obstacle to the extended use of many of the suggested future techniques. At the same time, this concept is a basic ingredient in our understanding of the quantum measurement problem and for the transition from a quantum to a classical description of the physical world. 

Srikanth, R. The quantum measurement problem and physical reality a computation theoretic perspective, quant-ph/0602114... 

It is interesting to note that the Gottingen school, who later developed matrix mechanics, followed the mathematical route, while Schrodinger linked his wave mechanics to a physical picture. Despite their mathematical equivalence as Sturm-Liouville problems, the two approaches have never been reconciled. It will be argued that Schrodinger s physical model had no room for classical particles, as later assumed in the Copenhagen interpretation of quantum mechanics. Rather than contemplate the wave alternative the Copenhagen orthodoxy preferred to disperse their point particles in a probability density and to dress up their interpretation with the uncertainty principle and a quantum measurement problem to avoid any wave structure. 

In the quantum-mechanical problem, E is the difference in energies between the lowest quantum states of A and A and hence is measured from the zero vibrational levels. 

By learning the solutions of the Schrodinger equation for a few model systems, the student can better appreciate the treatment of the fundamental postulates of quantum mechanics as well as their relation to experimental measurement because the wavefunctions of the known model problems can be used to illustrate. 

In order to obtain estimates of quantum transport at the molecular scale [105], electronic structure calculations must be plugged into a formalism which would eventually lead to observables such as the linear conductance (equilibrium transport) or the current-voltage characteristics (nonequilibrium transport). The directly measurable transport quantities in mesoscopic (and a fortiori molecular) systems, such as the linear conductance, are characterized by a predominance of quantum effects—e.g., phase coherence and confinement in the measured sample. This was first realized by Landauer [81] for a so-called two-terminal configuration, where the sample is sandwiched between two metalhc electrodes energetically biased to have a measurable current. Landauer s great intuition was to relate the conductance to an elastic scattering problem and thus to quantum transmission probabilities. 

The remarkable conclusion is that the microscopic quantum state, specified by the wave function ip, can be described on a macroscopic level by the probability distribution Pj. A single pure state corresponds to a macroscopic ensemble. The interference terms that are typical for quantum mechanics no longer appear. Incidentally, this resolves the paradox of Schrodinger s cat and, in general, the quantum mechanical measurement problem. )... 

Study of the common situation in which there is no useful emission to use as a handle in kinetic analysis requires resourceful experimental programs. Measurement of the quantum yield of an A -> B reaction is of limited value, since quantum yields measure only the ratio of the nonradiative decay rates to A and B. Since both rates are expected to vary widely as a function of structure, the quantum yield alone tells next to nothing about the individual decay rates. The most popular approach to dissection of the kinetic problem involves the use of quenchers. Some third species, C, is introduced into the system in an attempt to intercept A. The most common interception process is energy transfer. 

However, it is not a good method to apply to typical Quantum-Chemistry problems. It woiks best for matrices which have small off-diagonal values and which have a small condition number. This last number is a measure of the spread of eigenvalues ... 

Having said all this, it must be admitted that there are aspects of the quantum theory which many physicists, even accepting fully its statistical features, still find worrying. The heart of the problem lies in the quantum theory of measurement which deals with the process whereby microscopic and statistical phenomena give rise to observations of a macroscopic and... 

Alternatively, we can work in momentum-space with the momentum distribution given by the square of the modulus of the momentum wavefunc-tion. However, because of Heisenberg s uncertainty relation it is impossible to specify uniquely the coordinates and the momenta simultaneously. Either the coordinates or the momenta can be defined without uncertainty. In classical mechanics, on the other hand, the coordinates as well as the momenta are simultaneously measurable at each instant. In particular, both the coordinates and the momenta must be specified at t — 0 in order to start the trajectory. Thus, we have the problem of defining a distribution function in the classical phase-space which simultaneously weights coordinates and momenta and which, at the same time, should mimic the quantum mechanical distributions as closely as possible. 

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