Probabilistic Cloning and Quantum Computation

We discuss the usefulness of quantum cloning and present examples of quantum computation tasks for which thecloning offers an advantage which cannot be matched by any approach that does not resort to quantum cloning.In these quantum computations, we need to distribute quantum information contained in the states about whichwe have some partial information. To perform quantum computations, we use a state-dependent probabilistic quantum cloning procedure to distribute quantum information in the middle of a quantum computation.     

Quantum Computation and Entangled-State Generation Through Photon Emission and Absorption Processes in Separated Cavities

We propose a scheme to implement a two-bit conditional quantum phase gate and generate a multi-atom cluster state and a two-atom three-dimensional entangled state based on photon emission and absorption processes. In the scheme, a Λ-type atom and a V-type atom are individually trapped in two spatially separated cavities connected by an optical fiber. By choosing the interaction time and the ratio of coupling parameters appropriately, the gate operation and entanglement generation can be determinately achieved. We also discuss the influence of photon Leakage on the fidelities of the gate and entanglement and show that the scheme is scalable and feasible in the experimental realization and further utilization.     

Note on Generalized Quantum Gates and Quantum Operations

Recently, Gudder proved that the set of all generalized quantum gates coincides the set of all contractions in a finite-dimensional Hilbert space (S. Gudder, Int. J. Theor. Phys. 47:268–279, 2008). In this note, we proved that the set of all generalized quantum gates is a proper subset of the set of all contractions on an infinite dimensional separable Hilbert space ℋ. Meanwhile, we proved that the quantum operation deduced by an isometry is an extreme point of the set of all quantum operations on ℋ. This subject is supported by NSF of China (10571113).     

Quantum Physics and Classical Physics—In the Light of Quantum Logic

In contrast to the Copenhagen interpretation we consider quantum mechanics as universally valid and query whether classical physics is really intuitive and plausible. We discuss these problems within the quantum logic approach to quantum mechanics where the classical ontology is relaxed by reducing metaphysical hypotheses. On the basis of this weak ontology a formal logic of quantum physics can be established which is given by an orthomodular lattice. By means of the Solèr condition and Piron's result one obtains the classical Hilbert spaces. However, this approach is not fully convincing. There is no plausible justification of Solèr's law and the quantum ontology is partly too weak and partly too strong. We propose to replace this ontology by an ontology of unsharp properties and conclude that quantum mechanics is more intuitive than classical mechanics and that classical mechanics is not the macroscopic limit of quantum mechanics.     

Nonadiabatic Geometric Quantum Computation by Straightway Varying Parameters of Magnetic: A New Design

The approach to implement nonadiabatic geometric quantum computation by controlling the magnetic fields is applied to construct single-qubit noncommutable geometric quantum gates. The results show that it is helpful for experimenters to realize the geometric quantum gates by adjusting the external parameters.     

Quantum Computation on a Silicon Chip

We propose a potential quantum-computer hardware-architecture model on a silicon chip in which the basic cell gate is the atom-photon controlled phase flip gate. This gate can be implemented through a single-photon pulses scattering by a toroidal microcavity trapping a neutral atom, and it does not require very strict strong-coupling regime and can work beyond the Lamb-Dicke limit with high fidelity and success probability under practical noise environments. Especially, good and bad losses of the toroidal cavity are discussed in detail. Finally, a possibly simple experiment based on current experimental technology is proposed to demonstrate our scheme.     

Hamiltonian and Thermodynamic Modeling of Quantum Turbulence

The state variables in the novel model introduced in this paper are the fields playing this role in the classical Landau-Tisza model and additional fields of mass, entropy (or temperature), superfluid velocity, and gradient of the superfluid velocity, all depending on the position vector and another tree dimensional vector labeling the scale, describing the small-scale structure developed in ⁴He superfluid experiencing turbulent motion. The fluxes of mass, momentum, energy, and entropy in the position space as well as the fluxes of energy and entropy in scales, appear in the time evolution equations as explicit functions of the state variables and of their conjugates. The fundamental thermodynamic relation relating the fields to their conjugates is left in this paper undetermined. The GENERIC structure of the equations serves two purposes: (i) it guarantees that solutions to the governing equations, independently of the choice of the fundamental thermodynamic relation, agree with the observed compatibility with thermodynamics, and (ii) it is used as a guide in the construction of the novel model.     

Nonadiabatic Geometric Quantum Computation with Asymmetric Superconducting Quantum Interference Device

We propose a method of controlling the dc-SQUID(superconductiong quantum interference device)system by changing the gate voltages,which controls the amplitude of the fictitious magnetic fields Bz,and the externally applied current that produces the piercing magnetic flux Φx for the dc-SQUID system,we have also introduced a physical model for the dc-SQUID system.Using this physical model,one can obtain the non-adiabatic geometric phase gate for the single qubit and the non-adiabatic conditional geometric phase gate (controlled NOT gate) for the two qubits.It is shown that when the gate voltage and the externally applied current of the dc-SQUID system satisfies an appropriate constraint condition,the charge state evolution can be controlled exactly on a dynamic phase free path.The non-adiabatic evolution of the charge states is given as well.     

Formalism and Interpretation in Quantum Theory

Quantum Mechanics can be viewed as a linear dynamical theory having a familiar mathematical framework but a mysterious probabilistic interpretation, or as a probabilistic theory having a familiar interpretation but a mysterious formal framework. These points of view are usually taken to be somewhat in tension with one another. The first has generated a vast literature aiming at a “realistic” and “collapse-free” interpretation of quantum mechanics that will account for its statistical predictions. The second has generated an at least equally large literature aiming to derive, or at any rate motivate, the formal structure of quantum theory in probabilistically intelligible terms. In this paper I explore, in a preliminary way, the possibility that these two programmes have something to offer one another. In particular, I show that a version of the measurement problem occurs in essentially any non-classical probabilistic theory, and ask to what extent various interpretations of quantum mechanics continue to make sense in such a general setting. I make a start on answering this question in the case of a rudimentary version of the Everett interpretation.     

Reconciling Spacetime and the Quantum: Relational Blockworld and the Quantum Liar Paradox

The Relational Blockworld (RBW) interpretation of non-relativistic quantum mechanics (NRQM) is introduced. Accordingly, the spacetime of NRQM is a relational, non-separable blockworld whereby spatial distance is only defined between interacting trans-temporal objects. RBW is shown to provide a novel statistical interpretation of the wavefunction that deflates the measurement problem, as well as a geometric account of quantum entanglement and non-separability that satisfies locality per special relativity and is free of interpretative mystery. We present RBW’s acausal and adynamical resolution of the so-called “quantum liar paradox,” an experimental set-up alleged to be problematic for a spacetime conception of reality, and conclude by speculating on RBW’s implications for quantum gravity.     

Fluctuations of Quantum Currents and Unravelings of Master Equations

The very notion of a current fluctuation is problematic in the quantum context. We study that problem in the context of nonequilibrium statistical mechanics, both in a microscopic setup and in a Markovian model. Our answer is based on a rigorous result that relates the weak coupling limit of fluctuations of reservoir observables under a global unitary evolution with the statistics of the so-called quantum trajectories. These quantum trajectories are frequently considered in the context of quantum optics, but they remain useful for more general nonequilibrium systems. In contrast with the approaches found in the literature, we do not assume that the system is continuously monitored. Instead, our starting point is a relatively realistic unitary dynamics of the full system     

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.     

Two-Qubit Quantum Logic Gate in Molecular Magnets

We propose a scheme to realize a controlled-NOT quantum logic gate in a dimer of exchange coupled singlemolecule magnets, [Mn4]2. We chosen the ground state and the three low-lying excited states of a dimer in a finite longitudinal magnetic field as the quantum computing bases and introduced a pulsed transverse magnetic field with a special frequency. The pulsed transverse magnetic field induces the transitions between the quantum computing bases so as to realize a controlled-NOT quantum logic gate. The transition rates between a pair of the four quantum computing bases and between the quantum computing bases and excited states are evaluated and analysed.     

Probability Description and Entropy of Classical and Quantum Systems

Tomographic approach to describing both the states in classical statistical mechanics and the states in quantum mechanics using the fair probability distributions is reviewed. The entropy associated with the probability distribution (tomographic entropy) for classical and quantum systems is studied. The experimental possibility to check the inequalities like the position–momentum uncertainty relations and entropic uncertainty relations are considered.     

One Atom in an Optical Cavity： Entanglement and Applications to Quantum Computation

We propose a scheme to implement two-bit .quantum phase gates and one-bit unitary gates by using the two- mode two-photon Jaynes Cummings model. The entanglement between the atom and cavity is also investigated in the presence of phase decoherence. It is found that there is stationary entanglement that is sensitive with the detuning     

On the Discrimination Between Classical and Quantum States

With the purpose of introducing a useful tool for researches concerning foundations of quantum mechanics and applications to quantum technologies, here we address three quantumness quantifiers for bipartite optical systems: one is based on sub-shot-noise correlations, one is related to antibunching and one springs from entanglement determination. The specific cases of parametric downconversion seeded by thermal, coherent and squeezed states are discussed in detail.     

Neutrino Mixing Matrix and Leptogenesis from Quantum Gravity

We consider non renormalization 1/M _x interaction term as a perturbation of the neutrino mass matrix. We find that for the degenerate neutrino mass spectrum. We assume that the neutrino masses and mixing arise through physics at a scale intermediate between Planck Scale and the electroweak scale. We also assume, above the electroweak breaking scale, neutrino masses are nearly degenerate and their mixing is bimaximal. The perturbation generates a non zero value of θ ₁₃, which is within reach of the high performance neutrino factory. In this paper, we find that the non zero value of θ ₁₃ due to Planck scale effects indicates the possibility of CP violation.     

Undecidability and the Problem of Outcomes in Quantum Measurements

We argue that it is fundamentally impossible to recover information about quantum superpositions when a quantum system has interacted with a sufficiently large number of degrees of freedom of the environment. This is due to the fact that gravity imposes fundamental limitations on how accurate measurements can be. This leads to the notion of undecidability: there is no way to tell, due to fundamental limitations, if a quantum system evolved unitarily or suffered wavefunction collapse. This in turn provides a solution to the problem of outcomes in quantum measurement by providing a sharp criterion for defining when an event has taken place. We analyze in detail in examples two situations in which in principle one could recover information about quantum coherence: (a) “revivals” of coherence in the interaction of a system with the measurement apparatus and the environment and (b) the measurement of global observables of the system plus apparatus plus environment. We show in the examples that the fundamental limitations due to gravity and quantum mechanics in measurement prevent both revivals from occurring and the measurement of global observables. It can therefore be argued that the emerging picture provides a complete resolution to the measurement problem in quantum mechanics.     

Continuous-Time Quantum Walk on Integer Lattices and Homogeneous Trees

This paper is concerned with the continuous-time quantum walk on ℤ, ℤ ^d , and infinite homogeneous trees. By using the generating function method, we compute the limit of the average probability distribution for the general isotropic walk on ℤ, and for nearest-neighbor walks on ℤ ^d and infinite homogeneous trees. In addition, we compute the asymptotic approximation for the probability of the return to zero at time t in all these cases.