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It has been proposed recently \cite{son} that excitations in Spin Ice can be of the form of magnetic monopoles that does not obey the Dirac Quantization Condition. It is also well known \cite{rj} that the above scenario leads to non-associativity among translation generators. It will be interesting to see how the monopole picture in Spin Ice survives in the light of the latter observation.
According to the widely accepted notion, the Schr{ö}dinger equation (SE) is not derivable in principle. Contrary to this belief, we present here a straightforward derivation of SE. It is based on only two fundamentals of mechanics: the classical Hamilton-Jacobi equation(HJE) and the Planck postulate about the discrete transfer of energy at micro-scales. Our approach is drastically different from the other published derivations of SE which either employ an ad hoc underlying assumption about the probabilistic or the statistical nature of the micro-scale phenomena, or rely on the prior knowledge of SE and arrive at it by introducing a new postulate - neither present in classical mechanics nor following from experiments - with a suitable but physically unjustifiable choice of a key arbitrary constant.
Conventional approaches for controlling open quantum systems use coherent control which affects the system's evolution through the Hamiltonian part of the dynamics. Such control, although being extremely efficient for a large variety of problems, has limited capabilities, e.g., if the initial and desired target states have density matrices with different spectra or if a control field needs to be designed to optimally transfer different initial states to the same target state. Recent research works suggest extending coherent control by including active manipulation of the non-unitary (i.e., incoherent) part of the evolution. This paper summarizes recent results specifically for incoherent control by the environment (e.g., incoherent radiation or a gaseous medium) with a kinematic description of controllability and landscape analysis.
We study the coherent exciton transport of continuous-time quantum walks (CTQWs) on Erdos-Renyi networks. The Erdos-Renyi network of N nodes is constructed by connecting every pair of nodes with probability $p$. We numerically calculate the ensemble averaged transition probability of quantum transport between two nodes of the networks. For finite networks, we find that the limiting transition probability is reached very quickly. For infinite networks whose spectral density follows the semicircle law, the efficiencies of the classical and quantum-mechanical transport are compared on networks of different average degree. In the long time limiting, we consider the distribution of the ensemble averaged transition probabilities, and show that there is a high probability to find the exciton at the initial node. Such high return probability almost do not alter in a wide range of connection probability p but increases rapidly when the network approaches to be fully connected. For networks whose topology is not extremely connected, the return probability is inversely proportional to the network size N. Furthermore, the transport dynamics are compared with that on a random graph model in which the degree of each node equals to the average degree of the Erdos-Renyi networks.
We study numerically the Casimir interaction between dielectrics in both two and three dimensions. We demonstrate how sparse matrix factorizations enable one to study torsional interactions in three dimensions. In two dimensions we study the full cross-over between non-retarded and retarded interactions as a function of separation. We use constrained factorizations in order to measure the interaction of a particle with a rough dielectric surface and compare with a scaling argument.
We investigate the possibility to have electron-pairs in dephasing-free subspace (DFS), by means of the quantum-dot cellular automata (QCA) and single-spin rotations, to carry out a high-fidelity and deterministic universal quantum computation. We show that our QCA device with electrons tunneling two dimensionally is very suitable for DFS encoding, and argue that our design favors a scalable quantum computation robust to collective dephasing errors.
In this paper it is shown that an equivalent to the complex Klein-Gordon equation can be obtained from the (2+3) dimensional Einstein equations coupled to a conserved energy momentum tensor. In an explicit toy model we give matching conditions for what corresponds to the phase, the amplitude, and the mass of the complex wave function.
Quantum trajectory theory is the best mathematical set up to model continual observations of a quantum system and feedback based on the observed output. Inside this framework, we study how to enhance the squeezing of the fluorescence light emitted by a two-level atom, stimulated by a coherent monochromatic laser. In the presence of a Wiseman-Milburn feedback scheme, based on the homodyne detection of a fraction of the emitted light, we analyze the squeezing dependence on the various control parameters.
We describe a method to axiomatize computations in deterministic Turing machines. When applied to computations in non-deterministic Turing machines, this method may produce contradictory (and therefore trivial) theories, considering classical logic as the underlying logic. By substituting in such theories the underlying logic by a paraconsistent logic we define a new computation model, the paraconsistent Turing machine. This model allows a partial simulation of superposed states of quantum computing. Such a feature allows the definition of paraconsistent algorithms which solve (with some restrictions) the well-known Deutsch's and Deutsch-Jozsa problems. This first model of computation, however, does not adequately represent the notions of entangled states and relative phase, which are key features in quantum computing. In this way, a more sharpened model of paraconsistent Turing machines is defined, which better approaches quantum computing features. Finally, we define complexity classes for such models, and establish some relationships with classical complexity classes.
We give a representation for entanglement-breaking channels in separable Hilbert space that generalizes the "Kraus decomposition with rank one operators" and use it to describe the complementary channels. We also give necessary and sufficient condition of entanglement-breaking for a general quantum Gaussian channel. Application of this condition to one-mode channels provides several new cases where the additivity conjecture holds in full generality.
This tutorial is intended to give an accessible introduction to Hopf algebras. The mathematical context is that of representation theory, and we also illustrate the structures with examples taken from combinatorics and quantum physics, showing that in this latter case the axioms of Hopf algebra arise naturally. The text contains many exercises, some taken from physics, aimed at expanding and exemplifying the concepts introduced.
This paper has been withdrawn by the author, due a crucial error in the optimization. For the last one month I have been trying to remove the error, but it seems to take a lot of time so I decided to withdraw this paper for the moment.
Classical communications are used in the post-processing procedure of quantum key distribution. Since the security of quantum key distribution is based on the principles of quantum mechanics, intuitively the secret key can only be derived from the quantum states. We find that classical communications are incorrectly used in the so-called quantum dialogue type protocols. In these protocols, public communications are used to transmit secret messages. Our calculations show that half of Alice's and Bob's secret message is leaked through classical channel. By applying Holevo bound, we can see that the quantum efficiency claimed in the quantum dialogue type of protocols is not achievable.
We present a model which describes coherent and incoherent processes in continuous-variable atom-light interfaces. We assume Gaussian states for light and atoms and formulate the system dynamics in terms of first and second moments of the angular momentum operators. Spatial and temporal inhomogeneities in light and atom variables are incorporated by partitioning the system into small homogeneous segments. Furthermore, other experimental imperfections as for instance limited detector time-resolution and atomic motion are simulated. The model is capable of describing many experimental situations ranging from room temperature vapor cells to sub-mK atomic clouds. To illustrate the method, we calculate the effect of detector time-resolution, spatial inhomogeneities and atomic motion on the spin squeezing dynamics of rubidium 87 on the D2 transition.
We develop a scheme to construct the Hamiltonians of the lambda, vee and cascade type of three-level configurations using the generators of SU(3) group. It turns out that this approach provides a well defined selection rule to give different Hamitonians for each configurations. The lambda and vee type configurations are exactly solved with different initial conditions while taking the two-mode classical and quantized fields . For the classical field, it is shown that the Rabi oscillation of the lambda model is similar to that of the vee model and the dynamics of the vee model can be recovered from lambda model and vice versa simply by inversion. We then proceed to solve the quantized version of both models introducing a novel Euler matrix formalism. It is shown that this dynamical symmetry exhibited in the Rabi oscillation of two configurations for the semiclassical models is completely destroyed on quantization of the field modes. The symmetry can be restored within the quantized models when the field modes are both in the coherent states with large average photon number which is depicted through the collapse and revival of the Rabi oscillations.
We investigate the maximal violations for both sides of the $d$-dimensional CGLMP inequality by using the Bell operator method. It turns out that the maximal violations have a decelerating increase as the dimension increases and tend to a finite value at infinity. The numerical values are given out up to $d=10^6$ for positively maximal violations and $d=2\times 10^5$ for negatively maximal violations. Counterintuitively, the negatively maximal violations tend to be a little stronger than the positively maximal violations. Further we show the states corresponding to these maximal violations and compare them with the maximally entangled states by utilizing entangled degree defined by von Neumann entropy. It shows that their entangled degree tends to some nonmaximal value as the dimension increases.
For any arbitrary values of $n$ and $l$ quantum numbers, we present a simple exact analytical solution of the $D$-dimensional ($D\geq 2$) hyperradial Schr% ödinger equation with the Kratzer and the modified Kratzer potentials within the framework of the exact quantization rule (EQR) method. The exact energy levels $(E_{nl})$ of all the bound-states are easily calculated from this EQR method. The corresponding normalized hyperradial wave functions $% (ψ_{nl}(r))$ are also calculated. The exact energy eigenvalues for these Kratzer-type potentials are calculated numerically for the typical diatomic molecules $LiH,$ $CH,$ $HCl,$ $CO,$ $NO,$ $O_{2},$ $N_{2}$ and $I_{2}$ for various values of $n$ and $l$ quantum numbers. Numerical tests using the energy calculations for the interdimensional degeneracy ($D=2-4$) for $I_{2}, $ $LiH,$ $HCl,$ $O_{2},$ $NO$ and $CO$ are also given. Our results obtained by EQR are in exact agreement with those obtained by other methods.
The paper gives a short introduction to mutually unbiased bases and the Welch bounds and demonstrates that the latter is a good technical tool to explore the former. In particular, a criterion for a system of vectors to satisfy the Welch bounds with equality is given and applied for the case of MUBs. This yields a necessary and sufficient condition on a set of orthonormal bases to form a complete system of MUBs. This condition takes an especially elegant form in the case of homogeneous systems of MUBs. We express some known constructions of MUBs in this form. Also it is shown how recently obtained results binding MUBs and some combinatorial structures (such as perfect nonlinear functions and relative difference sets) naturally follow from this criterion. Some directions for proving non-existence results are sketched as well.