Atomic quantum zeno effect for ensembles and single systems

The so-called quantum Zeno effect is essentially a consequence of the projection postulate for ideal measurements. To test the effect, Itanoet al. have performed an experiment on an ensemble of atoms where rapidly repeated level measurements were realized by means of short laser pulses. Using dynamical considerations, we give an explanation why the projection postulate can be applied in good approximation to such measurements. Corrections to ideal measurements are determined explicitly. This is used to discuss how far the experiment of Itanoet al. can be considered as a test of the quantum Zeno effect. We also analyze a new possible experiment on a single atom where stochastic light and dark periods can be interpreted as manifestation of the quantum Zeno effect. We show that the measurement point of view gives a quick and intuitive understanding of experiments of the above type, although a finer analysis has to take the corrections into account.     

Quantum theory of state reduction and measurement

The central problem in the quantum theory of measurement, how to describe the process of state reduction in terms of the quantum mechanical formalism, is solved on the basis of the relativity of quantal states, which implies that once the apparatus is detected in a well-defined state, the object state must reduce to a corresponding one. This is a process termed by Schrödinger disentanglement. Here, it is essential to observe that Renninger's negative result does constitute an actual measurement process. From this point of view, Heisenberg's interpretation of his microscope experiment and the Einstein-Podolsky-Rosen arguments are reinvestigated. Satisfactory discussions are given to various experimental situations, such as the Stern-Gerlach-type experiment, successive measurements, macroscopic measurements, and Schrödinger's cat. Finally it is proposed to regard a state vector in quantum mechanics as an irreducible physical construct, in Margenau's sense, that is not further analyzable both mathematically and conceptually.     

Interpretation of the Experiments on Bell's Inequality

The conceptual scheme of the optical polarization experiments on Bell's inequality is discussed. By invoking the distinction between the concepts of state preparation and measumment in quantum mechanics, it is argued that Bell's theorem is not applicable to this class of experiments in the way it is generally done. Consequently, by considering the specific features of the measurements performed hitherto, it is also shown that a local approach can yield the same theoretical prediction as the nonlocal quantum interpretation, even in the absence of other experimental loopholes.     

Communication cost of simulating Bell correlations

What classical resources are required to simulate quantum correlations? For the simplest and most important case of local projective measurements on an entangled Bell pair state, we show that exact simulation is possible using local hidden variables augmented by just one bit of classical communication. Certain quantum teleportation experiments, which teleport a single qubit, therefore admit a local hidden variables model.     

The Quantum World is not Built up from Correlations

It is known that the global state of a composite quantum system can be completely determined by specifying correlations between measurements performed on subsystems only. Despite the fact that the quantum correlations thus suffice to reconstruct the quantum state, we show, using a Bell inequality argument, that they cannot be regarded as objective local properties of the composite system in question. It is well known since the work of Bell, that one cannot have locally preexistent values for all physical quantities, whether they are deterministic or stochastic. The Bell inequality argument we present here shows this is also impossible for correlations among subsystems of an individual isolated composite system. Neither of them can be used to build up a world consisting of some local realistic structure. As a corrolary to the result we argue that entanglement cannot be considered ontologically robust. The Bell inequality argument has an important advantage over others because it does not need perfect correlations but only statistical correlations. It can therefore easily be tested in currently feasible experiments using four particle entanglement.     

On the relation between quantum mechanical probabilities and event frequencies

The probability `measure' for measurements at two consecutive moments of time is non-additive. These probabilities, on the other hand, may be determined by the limit of relative frequency of measured events, which are by nature additive. We demonstrate that there are only two ways to resolve this problem. The first solution places emphasis on the precise use of the concept of conditional probability for successive measurements. The physically correct conditional probabilities define additive probabilities for two-time measurements. These probabilities depend explicitly on the resolution of the physical device and do not, therefore, correspond to a function of the associated projection operators. It follows that quantum theory distinguishes between physical events and propositions about events, the latter are not represented by projection operators and that the outcomes of two-time experiments cannot be described by quantum logic. The alternative explanation is rather radical: it is conceivable that the relative frequencies for two-time measurements do not converge, unless a particular consistency condition is satisfied. If this is true, a strong revision of the quantum mechanical formalism may prove necessary. We stress that it is possible to perform experiments that will distinguish the two alternatives.     

Illusory Decoherence

Suppose a quantum experiment includes one or more random processes. Then the results of repeated measurements may appear consistent with irreversible decoherence even if the system’s evolution prior to measurement is reversible and unitary. Two thought experiments are constructed as examples.     

Destabilization of the Zhang-Rice singlet at optimal doping

The construction of the Zhang-Rice singlet is revisited in the light of the recent understanding of high-temperature superconductors at optimal doping. A minimal local model is derived that contains the physical regime found relevant for ARPES experiments and characterized by significant direct oxygen-oxygen hopping. For the values of orbital parameters indicated by experiment, the Zhang-Rice singlet is strongly mixed with a pure oxygen singlet of the same symmetry. The Zhang-Rice ground state is destabilized because the coherence factor of the oxygen singlet with respect to oxygen-oxygen hopping is twice as large. An analogous quantum phase transition is identified in the t-t′-J model. The orbital-antisymmetric copper-oxygen singlet is confirmed to be irrelevant, as found originally. The usual symmetry analysis is extended to include dynamical symmetries.     

Quantum erasure and the locality problem

The problem of locality arising in connection with the quantum-erasure experiments is considered using the algebraic approach. We demonstrate that, contrary to a widespread opinion, the results of these experiments can be reconciled with the existence of a local physical reality determining the results of local measurements. A clear physical interpretation of the quantum-erasure experiments, that is consistent with the classical concepts, is given.     

The aspect experiment and the return to reality

It is argued that the results of atomic cascade photon correlation experiments of the static type may be given a natural interpretation in the framework of at least one objective local theory, namely stochastic electrodynamics. It follows that the Aspect experiment is more likely than the Clauser-Horne experiment to be crucial in deciding between objective local theories and quantum mechanics.     

On the Conclusive Tests of Local Realism and Pseudoscalar Mesons

Many beautiful experiments have been addressed to test standard quantum mechanics against local realistic models. Even if a strong evidence favouring standard quantum mechanics is emerged, a conclusive experiment is still lacking, because of low detection efficiencies. Recently, experiments based on pseudoscalar mesons have been proposed as a way for obtaining a conclusive experiment. In this paper, we investigate if this result can effectively be obtained. Our conclusions, based on a careful analysis of the proposed set ups, are that this will not be possible due to intrinsic limitations of these kind of experiments.     

Deterministic quantum evolution through modification of the hypotheses of statistical mechanics

It is claimed that for all apparatus capable of performing macroscopic measurements of microscopic systems there exist special internal states for which deterministic quantum evolution alone yields a particular macroscopic outcome rather than a superposition of macroscopically distinct outcomes. We maintain that these special states are distributed uniformly (in a certain sense) among the set of all states. It is hypothesized that for all actually performed experiments the initial conditions lie among the special states. We postulate that in the absence of precise information on apparatus initial conditions one should give equal weight to those microstates that are consistent with the macroscopic stateand are special in the sense used above. Evidence is presented for this postulate's recovering the usual quantum probabilities. This theory is fully deterministic, has no collapsing wave functions, and offers a resolution of the quantum measurement problem through a revision of the usual statistical mechanical handling of initial conditions. It requires a single wave function for the entire universe and an all encompassing conspiracy to arrange the right sort of special wave function for each experiment. In other words, an apparatus is in an appropriate microstate for the experiment that will actually happen even if an ostensibly random process is used to determine that experiment from among apparent alternatives. Although we do not provide physical or philosophical justification for our central hypothesis, some perspective is given by examining the notions implicit in the usual principles of thermodynamics.     

Optical Test of Local Hidden—Variable Model

An inequality is deduced from local realism and a supplementary assumption.This inequality defines an experiment that can be actually performed with the present technology to test local hidden-variable models,and it is violated by quantum mechanics with a factor 1.92,while it can be simplified into a form where just two measurements are required.     

Three Slit Experiments and the Structure of Quantum Theory

In spite of the interference manifested in the double-slit experiment, quantum theory predicts that a measure of interference defined by Sorkin and involving various outcome probabilities from an experiment with three slits, is identically zero. We adapt Sorkin’s measure into a general operational probabilistic framework for physical theories, and then study its relationship to the structure of quantum theory. In particular, we characterize the class of probabilistic theories for which the interference measure is zero as ones in which it is possible to fully determine the state of a system via specific sets of ‘two-slit’ experiments.     

Quantum information splitting of an arbitrary three-qubit state via the cavity input–output process

We propose a realizable quantum information splitting (QIS) scheme for an arbitrary three-qubit state via the cavity input–output process. In our scheme, a four-qubit cluster state and a three-qubit Greenberger–Horne–Zeilinge (GHZ) state are used as quantum channel. The sender and controller only need to perform Bell-state measurements and a single-qubit measurement, respectively. The receiver can reconstruct the arbitrary three-qubit state by classical communication and local operations. Compared with the scheme in Nie et al. [Optics Communications 284 (2011) 1457], the quantum resources and classical information in our scheme are decreased by 5 qubits and 1 bit, respectively. Moreover, we replace the W-state category measurement in the former with Bell-state measurements and a single-qubit measurement, which is more simple and feasible in experiment.     

Optical implementation of quantum orienteering

We present results from an optical implementation of quantum orienteering, a protocol for communicating directions in space using quantum bits. We show how different types of measurements and encodings can be used to increase the communication efficiency. In particular, if Alice and Bob use two spin- particles for communication and employ joint measurements, they do better than is possible with local operations and classical communication. Furthermore, by using oppositely oriented spins, the achievable communication efficiency is further increased. Finally, we discuss the limitations of an optical approach: our results highlight the usually overlooked nonequivalence of different physical encodings of quantum bits.     

A priori probability and localized observers

A physical and mathematical framework for the analysis of probabilities in quantum theory is proposed and developed. One purpose is to surmount the problem, crucial to any reconciliation between quantum theory and space-time physics, of requiring instantaneous wave-packet collapse across the entire universe. The physical starting point is the idea of an observer as an entity, localized in space-time, for whom any physical system can be described at any moment, by a set of (not necessarily pure) quantum states compatible with his observations of the system at that moment. The mathematical starting point is the theory of local algebras from axiomatic relativistic quantum field theory. A function defining thea priori probability of mistaking one local state for another is analysed. This function is shown to possess a broad range of appropriate properties and to be uniquely defined by a selection of them. Through a general model for observations, it is argued that the probabilities defined here are as compatible with experiment as the probabilities of conventional interpretations of quantum mechanics but are more likely to be compatible, not only with modern developments in mathematical physics, but also with a complete and consistent theory of measurement.