Probability sum rules and consistent quantum histories

An example shows that weak decoherence is more restrictive than the minimal logical decoherence structure that allows probabilities to be used consistently for quantum histories. The probabilities in the sum rules that define minimal decoherence are all calculated by using a projection operator to describe each possibility for the state at each time. Weak decoherence requires more sum rules. They bring in additional variables, that require different measurements and a different way to calculate probabilities, and raise questions of operational meaning. The example shows that extending the linearly positive probability formula from weak to minimal decoherence gives probabilities that are different from those calculated in the usual way using the Born and von Neumann rules and a projection operator at each time.     

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.     

Generating functions and sum rules for quantum oscillator

Generating functions and sum rules are discussed for transition probabilities between quantum oscillator eigenstates with time-dependent parameters.     

Admissible states in quantum phase space

We address the question of which phase space functionals might represent a quantum state. We derive necessary and sufficient conditions for both pure and mixed phase space quantum states. From the pure state quantum condition we obtain a formula for the momentum correlations of arbitrary order and derive explicit expressions for the wave functions in terms of time-dependent and independent Wigner functions. We show that the pure state quantum condition is preserved by the Moyal (but not by the classical Liouville) time evolution and is consistent with a generic stargenvalue equation. As a by-product Baker's converse construction is generalized both to an arbitrary stargenvalue equation, associated to a generic phase space symbol, as well as to the time-dependent case. These results are properly extended to the mixed state quantum condition, which is proved to imply the Heisenberg uncertainty relations. Globally, this formalism yields the complete characterization of the kinematical structure of Wigner quantum mechanics. The previous results are then succinctly generalized for various quasi-distributions. Finally, the formalism is illustrated through the simple examples of the harmonic oscillator and the free Gaussian wave packet. As a by-product, we obtain in the former example an integral representation of the Hermite polynomials.     

Stationary phase method and delay times for relativistic and non-relativistic tunneling particles

The stationary phase method is frequently adopted for calculating tunneling phase times of analytically-continuous Gaussian or infinite-bandwidth step pulses which collide with a potential barrier. This report deals with the basic concepts on deducing transit times for quantum scattering: the stationary phase method and its relation with delay times for relativistic and non-relativistic tunneling particles. After reexamining the above-barrier diffusion problem, we notice that the applicability of this method is constrained by several subtleties in deriving the phase time that describes the localization of scattered wave packets. Using a recently developed procedure - multiple wave packet decomposition - for some specifical colliding configurations, we demonstrate that the analytical difficulties arising when the stationary phase method is applied for obtaining phase (traversal) times are all overcome. In this case, we also investigate the general relation between phase times and dwell times for quantum tunneling/scattering. Considering a symmetrical collision of two identical wave packets with an one-dimensional barrier, we demonstrate that these two distinct transit time definitions are explicitly connected. The traversal times are obtained for a symmetrized (two identical bosons) and an antisymmetrized (two identical fermions) quantum colliding configuration. Multiple wave packet decomposition shows us that the phase time (group delay) describes the exact position of the scattered particles and, in addition to the exact relation with the dwell time, leads to correct conceptual understanding of both transit time definitions. At last, we extend the non-relativistic formalism to the solutions for the tunneling zone of a one-dimensional electrostatic potential in the relativistic (Dirac to Klein-Gordon) wave equation where the incoming wave packet exhibits the possibility of being almost totally transmitted through the potential barrier. The conditions for the occurrence of accelerated and, eventually, superluminal tunneling transmission probabilities are all quantified and the problematic superluminal interpretation based on the non-relativistic tunneling dynamics is revisited. Lessons concerning the dynamics of relativistic tunneling and the mathematical structure of its solutions suggest revealing insights into mathematically analogous condensed-matter experiments using electrostatic barriers in single- and bi-layer graphene, for which the accelerated tunneling effect deserves a more careful investigation.     

Controlled Teleportation of Multi-Qudit Quantum Information

We present a controlled teleportation scheme for teleporting an arbitrary superposition state of an M-qudit quantum system. The scheme employs only one entangled state as quantum channel, which consists of the qudits from Alice, Bob and every agent. The quantum operations used in the teleportation process are a series of qudit Bell measurements, single-qudit projective measurements, qudit H-gates, qudit-Pauli gates and qudit phase gates. It is shown that the original state can be restored by the receiver only on the condition that all the agents collaborate. If any agent does not cooperate, the original state can not be fully recovered.     

Measurement-induced nonlocality and geometric quantum discord in two SC-charge qubits

By using geometric quantum discord and measurement-induced nonlocality, quantum correlations are investigated for two superconducting (SC) charge qubits that share a large Josephson junction where the field is assumed to be prepared initially in a coherent state. It is found that the difference between measure measurement-induced nonlocality and geometric quantum discord, of the final state of the two SC-charge qubits system which is especial case of X-states, is equal to a constant value. It is found that the quantum correlations and entanglement of the qubits are very sensitive to the mean number of the coherent photons. The entanglement exists in small intervals of death quantum discord and measurement-induced nonlocality. This is further evidence in support of the fact that quantum correlation and entanglement are not synonymous.     

Total correlations and mutual information

In quantum information theory it is generally accepted that quantum mutual information is an information-theoretic measure of total correlations of a bipartite quantum state. We argue that there exist quantum states for which quantum mutual information cannot be considered as a measure of total correlations. Moreover, for these states we propose a different way of quantifying total correlations.     

A method for demonstrating violation of local realism with a two-photon downconverter without use of Bell inequalities

We show that the recent proposal by Hardy and Jordan for a test of local realism without the use of Bell inequalities can be implemented in two-photon coincidence measurements with linear polarizers, when the photon pairs are produced by parametric downconversion. If the probabilities measured with real detectors are proportional to the corresponding probabilities determined with ideal detectors, this method does not depend on the use of detectors with high or even known quantum efficiencies.Dedicated to H. Walther on the occasion of his 60th birthday     

Quantum particles from coarse grained classical probabilities in phase space

Quantum particles can be obtained from a classical probability distribution in phase space by a suitable coarse graining, whereby simultaneous classical information about position and momentum can be lost. For a suitable time evolution of the classical probabilities and choice of observables all features of a quantum particle in a potential follow from classical statistics. This includes interference, tunneling and the uncertainty relation.     

Quantum arrival time formula from decoherent histories

We use the decoherent histories approach to quantum mechanics to compute the probability for a wave packet to cross the origin during a given time interval. We define class operators (sums of strings of projectors) characterizing quantum-mechanical crossing and simplify them using a semiclassical approximation. Using these class operators we find that histories crossing the origin during different time intervals are approximately decoherent for a variety of initial states. Probabilities may therefore be assigned and coincide with the flux of the wave packet (the standard semiclassical formula), and are positive. The known initial states for which the flux is negative (backflow states) are shown to correspond to non-decoherent sets of histories, so probabilities may not be assigned.     

The effect and control on remaining the quantum correlation by the coupling symmetry between qubits and the bath

We study the dynamic evolution of quantum correlation of two interacting coupled qubits system in non-Markov environment, and quantify the quantum correlation using concurrence and quantum discord. We find that although both of them are physical quantities which measure the system characteristics of the quantum correlations, the quantum discord is more robust than concurrence, since it can keep a positive value even when the ESD happens. The quantum correlation of quantum system not only depends on the initial state but also strongly depends on the coupling ways between qubits and environment. For the given initial state, by keeping the coupling between qubits and environment in completely symmetric, we can completely avoid the effect the decoherence influenced on the quantum correlation and effectively prolong the survival time of quantum discord and concurrence. We also find that the stronger the interaction between qubits is, the more conducive the death of the quantum correlation is resisted.     

Undecidable Classical Properties of Observers

A property of a system is called actual, if the observation of the outcome of the test that pertains to that property yields an affirmation with certainty. We formalize the act of observation by assuming the outcome itself is an actual property of the state of the observer after the act of observation and correlates with the state of the system. For an actual property this correlation needs to be perfect. A property is called classical if either the property or its negation is actual. We show by a diagonal argument that there exist classical properties of an observer that he cannot observe perfectly. Because states are identified with the collection of properties that are actual for that state, it follows no observer can perfectly observe his own state. Implications for the quantum measurement problem are briefly discussed. PACS: 02.10-v, 03.65.Ta     

Are There Dynamical Laws?

The nature of a physical law is examined, and it is suggested that there may not be any fundamental dynamical laws. This explains the intrinsic indeterminism of quantum theory. The probabilities for transition from a given initial state to a final state then depends on the quantum geometry that is determined by symmetries, which may exist as relations between states in the absence of dynamical laws. This enables the experimentally well-confirmed quantum probabilities to be derived from the geometry of Hilbert space and gives rise to effective probabilistic laws. An arrow of time which is consistent with the one given by the second law of thermodynamics, regarded as an effective law, is obtained. Symmetries are used as the basis for a new proposed paradigm of physics. This naturally gives rise to the gravitational and gauge fields from the symmetry group of the standard model and a general procedure for obtaining interactions from any symmetry group.     

Strategies to measure a quantum state

We consider the problem of determining the mixed quantum state of a large but finite number of identically prepared quantum systems from data obtained in a sequence of ideal (von Neumann) measurements, each performed on an individual copy of the system. In contrast to previous approaches, we do not average over the possible unknown states but work out a “typical” probability distribution on the set of states, as implied by the experimental data. As a consequence, any measure of knowledge about the unknown state and thus any notion of “best strategy” (i.e., the choice of observables to be measured, and the number of times they are measured) depend on the unknown state. By learning from previously obtained data, the experimentalist re-adjusts the observable to be measured in the next step, eventually approaching an optimal strategy. We consider two measures of knowledge and exhibit all “best” strategies for the case of a two-dimensional Hilbert space. Finally, we discuss some features of the problem in higher dimensions and in the infinite dimensional case.     

Experimental motivation and empirical consistency in minimal no-collapse quantum mechanics

We analyze three important experimental domains (SQUIDs, molecular interferometry, and Bose-Einstein condensation) as well as quantum-biophysical studies of the neuronal apparatus to argue that (i) the universal validity of unitary dynamics and the superposition principle has been confirmed far into the mesoscopic and macroscopic realm in all experiments conducted thus far; (ii) all observed “restrictions” can be correctly and completely accounted for by taking into account environmental decoherence effects; (iii) no positive experimental evidence exists for physical state-vector collapse; (iv) the perception of single “outcomes” is likely to be explainable through decoherence effects in the neuronal apparatus. We also discuss recent progress in the understanding of the emergence of quantum probabilities and the objectification of observables. We conclude that it is not only viable, but moreover compelling to regard a minimal no-collapse quantum theory as a leading candidate for a physically motivated and empirically consistent interpretation of quantum mechanics.     

Quantum decision theory as quantum theory of measurement

We present a general theory of quantum information processing devices, that can be applied to human decision makers, to atomic multimode registers, or to molecular high-spin registers. Our quantum decision theory is a generalization of the quantum theory of measurement, endowed with an action ring, a prospect lattice and a probability operator measure. The algebra of probability operators plays the role of the algebra of local observables. Because of the composite nature of prospects and of the entangling properties of the probability operators, quantum interference terms appear, which make actions noncommutative and the prospect probabilities nonadditive. The theory provides the basis for explaining a variety of paradoxes typical of the application of classical utility theory to real human decision making. The principal advantage of our approach is that it is formulated as a self-consistent mathematical theory, which allows us to explain not just one effect but actually all known paradoxes in human decision making. Being general, the approach can serve as a tool for characterizing quantum information processing by means of atomic, molecular, and condensed-matter systems.     

Electron self-trapping at quantum and classical critical points

Using Feynman path integral technique estimations of the ground state energy have been found for a conduction electron interacting with order parameter fluctuations near quantum critical points. In some cases only singular perturbation theory in the coupling constant emerges for the electron ground state energy. It is shown that an autolocalized state (quantum fluctuon) can be formed and its characteristics have been calculated depending on critical exponents for both weak and strong coupling regimes. The concept of fluctuon is considered also for the classical critical point (at finite temperatures) and the difference between quantum and classical cases has been investigated. It is shown that, whereas the quantum fluctuon energy is connected with a true boundary of the energy spectrum, for classical fluctuon it is just a saddle-point solution for the chemical potential in the exponential density of states fluctuation tail.     

Realization of Arbitrary Inverse Unitary Transformation of Single Mode Fibre by Using Three Wave Plates

We report a method to realize the arbitrary inverse unitary transformation imposed by a single-mode fibre on photon＇s polarization by the succession of two quarter-wave plates and a half-wave plate. The process of realization is analysed on a Poincar6 sphere due to the fact that unitary transformation does not change the angle formed by polarization state vector. The method is meaningful in quantum communication experiment such as quantum teleportation, in which an unknown arbitrary quantum state should be kept to be unchanged in the case of using a single-mode fibre for time delay.[第一段]