New operator-ordering identities and associative integration formulas of two-variable Hermite polynomials for constructing non-Gaussian states

For directly normalizing the photon non-Gaussian states(e.g., photon added and subtracted squeezed states), we use the method of integration within an ordered product(IWOP) of operators to derive some new bosonic operator-ordering identities. We also derive some new integration transformation formulas about one- and two-variable Hermite polynomials in complex function space. These operator identities and associative integration formulas provide much convenience for constructing non-Gaussian states in quantum engineering.     

Locally Performing an Inner Product Modification on Remote Qubit Product States via Partially Entangled Qubit Pairs

We give a scheme for locally implementing an inner product modification onto remote qubit product states using partially entangled states, which is designed for obtaining conclusive result with optimal success probability. We exemplify this remote inner product modification (RIPM) by applying it to two-qubit product states via three partially entangled qubit pairs and, additionally, we construct a quantum network to implement this RIPM. It is interesting that our treatment can save entanglement resources.     

New Represent at ion for Squeezing-Rot at ing Entangled Unitary Transformation

We introduce a new unitary operator U which can engender a squeezing and rotating entangled transformation. The U operator has a concise expression in a new representation in two-mode Fock space. The normally ordered form of U can be derived by using the technique of integration within an ordered product of operators. The fluctuation in quadrature phases for these squeezing-rotating entangled states are analyzed.     

Unextendible Product Bases,Uncompletable Product Bases and Bound Entanglement

We report new results and generalizations of our work on unextendible product bases (UPB), uncompletable product bases and bound entanglement. We present a new construction for bound entangled states based on product bases which are only completable in a locally extended Hilbert space. We introduce a very useful representation of a product basis, an orthogonality graph. Using this representation we give a complete characterization of unextendible product bases for two qutrits. We present several generalizations of UPBs to arbitrary high dimensions and multipartite systems. We present a sufficient condition for sets of orthogonal product states to be distinguishable by separable superoperators. We prove that bound entangled states cannot help increase the distillable entanglement of a state beyond its regularized entanglement of formation assisted by bound entanglement.     

Coherent state polarons in quantum wells

We investigate the polaronic effects of an electron confined in a quantum well, which we describe through its algebraic properties using su(1,1), taking into account the electron-bulk longitudinal-optical phonon interaction. We construct the variational wave function as the direct product of an electronic part and a part describing coherent phonons generated by the Low–Lee–Pines transformation from the vacuum state. We use two explicit forms of coherent states, Perelomov and Barut-Girardello states, to represent the electronic part in the quantum well spectrum. Our results show that in a coherent state basis for electrons the basic polaron parameters such as the energy gap shift and effective mass are further enhanced compared to those obtained with the conventional sinusoidal form of the basis. The difference between the two types of quantum well coherent states appears in polaronic interactions in quantum wells. We extend the calculations in order to estimate polaron lifetimes for a variety of different material systems.     

Stochastic resonance in neuron models

We study Axiom A flows and introduce a new definition of Gibbs states which is modeled after a current one for diffeomorphisms and by which Gibbs states are locally characterized by their transformation when pulled back by conjugating homeomorphisms. We show that Gibbs states are equilibrium states and vice versa. We also show that for subshifts this equivalence can be strengthened.     

Multipartite State Representations in Multi-mode Fock Space and Their Squeezing Transformations

We present the continuous state vector of the total coordinate of multi-partlcle and the state vector of their total momentum, respectively, which possess completeness relation in multi-mode Fock space by virtue of the integration within an order product （IWOP） technique. We also calculate the transition from classical transformation of variables in the states to quantum unitary operator, deduce a new multi-mode squeezing operator, and discuss its squeezing effect. In progress, it indicates that the IWOP technique provides a convenient way to construct new representation in quantum mechanics.     

Energy states of colored particle in a chromomagnetic field

The unitary transformation which diagonalizes the squared Dirac equation in a constant chromomagnetic field is found. Applying this transformation, we find the eigenfunctions of the diagonalized Hamiltonian, that describes the states with a definite value of energy, and we call them energy states. It is pointed out that the energy states are determined by the color interaction term of the particle with the background chromofield, and this term is responsible for the splitting of the energy spectrum. We construct supercharge operators for the diagonal Hamiltonian that ensure the superpartner property of the energy states. PACS 03.65.-w An erratum to this article can be found at     

Joint Wavelet-Fractional Fourier Transform

Based on Dirac's representation theory and the technique of integration within an ordered product of operators,we put forward the joint wavelet-fractional Fourier transform in the context of quantum mechanics.Its corresponding transformation operator is found and the normally ordered form is deduced.This kind of transformation may be applied to analyzing and identifying quantum states.     

Computing scalar products via a two-terminal quantum transmission line

The scalar product of two vectors with K real components can be computed using two quantum channels, that is, information transmission lines in the form of spin-1/2 XX chains. Each channel has its own K-qubit sender and both channels share a single two-qubit receiver. The K elements of each vector are encoded in the pure single-excitation initial states of the senders. After time evolution, a bi-linear combination of these elements appears in the only matrix element of the second-order coherence matrix of the receiver state. An appropriate local unitary transformation of the extended receiver turns this combination into a renormalized version of the scalar product of the original vectors. The squared absolute value of this scaled scalar product is the intensity of the second-order coherence which consequently can be measured, for instance, employing multiple-quantum NMR. The unitary transformation generating the scalar product of two-element vectors is presented as an example.     

Transformation matrices for the Mueller-Jones formalism

The Mueller-Jones (MJ) or pure Mueller matrix formulation has been reported by using two different matrix transformations in a condensed representation. The possibility to find other transformation matrices is explored. A complete set of unitary operators (R) is found to be closely related with the MJ matrices and with the evolution of pure states on the Poincaré sphere surface. We propose an alternative deduction for the condensed representation of the MJ matrices, obtained by using the Kronecker product operation and use of R unitary matrices as a tool to combine different Mueller matrices and changes of polarized states on the Poincarè sphere surface. Finally, it is shown explicitly that the columns of the transformation matrices are the eigenvectors of the MJ matrix associated to a non-depolarizing optical system and a corollary is established as a criterion to differentiate a Mueller matrix from an MJ matrix.     

Relativistic quantum field theory with fractional spin and statistics

We construct a relativistic quantum field theory in 2 + 1 dimensions whose Fock states provide a multivalued representation of the Poincaré group. We add a topological term to the action of a scalar field theory and we show that this endows the path integral of the theory with an operator-valued cocycle which modifies the transformation properties of physical states. We demonstrate that one-particle states carry (in general) fractional spin. We determine the spin of many-particle states and we prove a generalized spin-statistics relation. We propose an equation of motion for on-shell states which generalizes naturally the Dirac equation.     

Norm-overlap formula for Hartree-Fock-Bogoliubov states with odd number parity

A formula to calculate the norm overlap between Hartree-Fock-Bogoliubov (HFB) states with odd number parity (one quasi-particle excited states) is derived with the help of Grassmann numbers and Fermion coherent states. The final formula is expressed in terms of a product of the Pfaffian for a neighboring even-even system (the zero quasi-particle state), and an extra factor consisting of the Bogoliubov transformation matrix and the anti-symmetric matrix in Thouless? HFB ansatz for the even-even system.     

Catalytic Coherence Transformation and Distillation for Special Mixed States

The coherence transformation and distillation for a class of special mixed coherent states of rank-2 under incoherent operations (IO) is discussed. Similar to the entanglement transformation for mixed entangled states, the catalytic coherence transformation for this class of special mixed coherent states is analyzed. On the one hand, it is found that some of the mixed coherent states can be converted into other mixed coherent states under IO. But for those mixed coherent states which fail in the coherence conversion under IO, the catalytic coherence manipulation can solve this problem. In this case, a mixed coherent state cannot be converted into another under IO, while the coherence transformation can be realized with the help of coherence-assisted incoherent operations, that is, catalytic coherence transformation. On the other hand, these special mixed coherent states can be distilled into the maximally pure coherent states or mixed states of arbitrary dimensions by strictly incoherent operations with certain probabilities. Finally, the coherence transformation of this type of mixed states can be generalized to the case of higher rank in a similar way, which is discussed at the end of this paper.     

Fidelity estimation between two finite ensembles of unknown pure equatorial qubit states

Suppose, we are given two finite ensembles of pure qubit states, so that the qubits in each ensemble are prepared in identical (but unknown for us) states lying on the equator of the Bloch sphere. What is the best strategy to estimate fidelity between these two finite ensembles of qubit states? We discuss three possible strategies for the fidelity estimation. We show that the best strategy includes two stages: a specific unitary transformation on two ensembles and state estimation of the output states of this transformation.     

Polarization transformers for optical anisotropy: II. Transformation of properties of optical anisotropy of reciprocal and nonreciprocal elements

The methods of transformation of an arbitrary phase optical anisotropy using a set of quarter-wave plates are considered. For this purpose, we use a formal analogy between the Jones matrices of these anisotropic elements and the matrices of transformation of the polarization basis states. We consider all types of reciprocal and nonreciprocal optical phase anisotropy. We show that the minimum set of anisotropic elements sufficient for such a transformation is a set of four quarter-wave plates. For nonreciprocal systems, this set should be complemented with Faraday rotators, whose number depends on the initial and final type of the nonreciprocity.     

Quantum State Identification of Qutrits via a Nonlinear Protocol

We propose a probabilistic quantum protocol to realize a nonlinear transformation of qutrit states, which by iterative applications on ensembles can be used to distinguish two types of pure states. The protocol involves single-qutrit and two-qutrit unitary operations as well as post-selection according to the results obtained in intermediate measurements. We utilize the nonlinear transformation in an algorithm to identify a quantum state provided it belongs to an arbitrary known finite set. The algorithm is based on dividing the known set of states into two appropriately designed subsets, which can be distinguished by the nonlinear protocol. In most cases, this is accompanied by the application of some properly defined physical (unitary) operation on the unknown state. Then, applying the nonlinear protocol, one can decide which of the two subsets the unknown state belongs to, thus reducing the number of possible candidates. By iteratively continuing this procedure until a single possible candidate remains, one can identify the unknown state.     

Commutativity equations and dressing transformations

We study dressing transformations that generate all solutions to commutativity equations and, after picking up special coordinates, all solutions to WDVV equations. We conjecture that the homological tensor product of solutions to the commutativity equations corresponds to the tensor product of matrices of the dressing transformation and check this in the first nontrivial case.     

Optimal eavesdropping in cryptography with three-dimensional quantum states

We study optimal eavesdropping in quantum cryptography with three-dimensional systems, and show that this scheme is more secure against symmetric attacks than protocols using two-dimensional states. We generalize the according eavesdropping transformation to arbitrary dimensions, and discuss the connection with optimal quantum cloning.