Secure quantum channels with correlated twin laser beams

A quantum cryptographic protocol based on the use of a strongly correlated pair of laser beams is proposed. The properties of the corresponding states are described in detail. The protocol is based on the strong correlation of photon numbers in both beams in each measurement. The protocol stability against basic interception attempts is analyzed.     

Robustness of two-qubit and three-qubit states in correlated quantum channels

We investigate how the correlated actions of quantum channels affect the robustness of entangled states. We consider the Bell-like state and random two-qubit pure states in the correlated depolarizing, bit flip, bit-phase flip, and phase flip channels. It is found that the robustness of two-qubit pure states can be noticeably enhanced due to the correlations between consecutive actions of these noisy channels, and the Bell-like state is always the most robust one. We also consider the robustness of three-qubit pure states in correlated noisy channels. For the correlated bit flip and phase flip channels, the result shows that although the most robust and most fragile states are locally unitary equivalent, they exhibit different robustness in different correlated channels, and the effect of channel correlations on them is also significantly different. However, for the correlated depolarizing and bit-phase flip channels, the robustness of two special three-qubit pure states is exactly the same. Moreover, compared with the random three-qubit pure states, they are neither the most robust states nor the most fragile states.     

Master equations for magnons

The connection between the Liouville and Master equation for a dynamic spin system is established by using Hubbard type spin-lattice coupling.     

Master equations for subordinated processes

We study Markov jump processes constructed by subordination of diffusion processes. The procedure can be viewed as a randomization or a coarse graining of time. We construct the master equation for the cases of finite and infinite total jump rates, and give a collection of explicitly solvable examples.     

Master equations for coupled systems

A formalism to cope with the problem of dynamically coupled systems is developed. A time-dependent projection operator of the type given by Willis-Picard and Grabert-Weidlich is used to derive a time-convolutionless master equation from the Liouville equation for the total composite system. A systematic perturbational expansion formula with respect to the interaction between systems is also given. Finally, the comparison with the usual non-Markoffian master equation is discussed.     

Scale-renormalized matrix-product states for correlated quantum systems

A generalization of matrix product states (MPS) for interacting quantum systems in two and three dimensions is introduced. These scale-renormalized matrix-product states (SR-MPS) are based on a coarse graining of the lattice in which the blocks at each level are associated with matrix products that are further transformed (scale renormalized) with other matrices before they are assembled to form blocks at the next level. Using the two-dimensional transverse-field Ising model as a test, it is shown that the SR-MPS converge much more rapidly with the matrix size than a standard MPS. It is also shown that the use of lattice symmetries speeds up the convergence very significantly.     

Green function equations for correlated cooper pairs

The simplest self-consistent Green functions equations for a system with correlated Cooper pairs are considered. Possible applications of the results obtained to superconductors and to the B-phase of superfluid He³ are discussed.     

Master equation for retrodiction of quantum communication signals

We derive the master equation that governs the evolution of the measured state backwards in time in an open system. This allows us to determine probabilities for a given set of preparation events from the results of subsequent measurements, which has particular relevance to quantum communication.     

Degenerate quantum codes for Pauli channels

A striking feature of quantum error correcting codes is that they can sometimes be used to correct more errors than they can uniquely identify. Such degenerate codes have long been known, but have remained poorly understood. We provide a heuristic for designing degenerate quantum codes for high noise rates, which is applied to generate codes that can be used to communicate over almost any Pauli channel at rates that are impossible for a nondegenerate code. The gap between nondegenerate and degenerate code performance is quite large, in contrast to the tiny magnitude of the only previous demonstration of this effect. We also identify a channel for which none of our codes outperform the best nondegenerate code and show that it is nevertheless quite unlike any channel for which nondegenerate codes are known to be optimal.     

Classical signal model for quantum channels

Recently it was shown that the main distinguishing features of quantum mechanics (QM) can be reproduced by a model based on classical random fields, the so-called prequantum classical statistical field theory (PCSFT). This model provides a possibility to represent averages of quantum observables, including correlations of observables on subsystems of a composite system (e.g., entangled systems), as averages with respect to fluctuations of classical (Gaussian) random fields. We consider some consequences of the PCSFT for quantum information theory. They are based on our previous observation that classical Gaussian channels (important in classical signal theory) can be represented as quantum channels. Now we show that quantum channels can be represented as classical linear transforms of classical Gaussian signals.     

Repetition versus noiseless quantum codes for correlated errors

We study the performance of simple quantum error correcting codes with respect to correlated noise errors characterized by a finite correlation strength μ. Specifically, we consider bit flip (phase flip) noisy quantum memory channels and use repetition and noiseless quantum codes. We characterize the performance of the codes by means of the entanglement fidelity F(μ,p) as function of the error probability p and degree of memory μ. Finally, comparing the entanglement fidelities of repetition and noiseless quantum codes, we find a threshold μ^*(p) for the correlation strength that allows to select the code with better performance.     

Coarse-grained kinetic equations for quantum systems

The nonequilibrium density matrix method is employed to derive a master equation for the averaged state populations of an open quantum system subjected to an external high frequency stochastic field. It is shown that if the characteristic time τ_stoch of the stochastic process is much lower than the characteristic time τ_steady of the establishment of the system steady state populations, then on the time scale Δt ～ τ_steady, the evolution of the system populations can be described by the coarse-grained kinetic equations with the averaged transition rates. As an example, the exact averaging is carried out for the dichotomous Markov process of the kangaroo type.     

Master equation for a quantum particle in a gas

The equation for the quantum motion of a Brownian particle in a gaseous environment is derived by means of S-matrix theory. This quantum version of the linear Boltzmann equation accounts nonperturbatively for the quantum effects of the scattering dynamics and describes decoherence and dissipation in a unified framework. As a completely positive master equation it incorporates both the known equation for an infinitely massive Brownian particle and the classical linear Boltzmann equation as limiting cases.     

Interference of quantum channels

We show how interferometry can be used to characterize certain aspects of general quantum processes and, in particular, the coherence of completely positive maps. We derive a measure of coherent fidelity, the maximum interference visibility, and the closest unitary operator to a given physical process under this measure.     

Charge frustration and quantum criticality for strongly correlated fermions

We study a model of strongly correlated electrons on the square lattice which exhibits charge frustration and quantum critical behavior. The potential is tuned to make the interactions supersymmetric. We establish a rigorous mathematical result which relates quantum ground states to certain tiling configurations on the square lattice. For periodic boundary conditions this relation implies that the number of ground states grows exponentially with the linear dimensions of the system. We present substantial analytic and numerical evidence that for open boundary conditions the system has gapless edge modes.     

An effective quantum parameter for strongly correlated metallic ferromagnets

The correlated motion of electrons in metallic ferromagnets is investigated in terms of a realistic interacting-electron model with N-fold orbital degeneracy and intra-orbital (U) and inter-orbital (J) Coulomb interactions. Correlation-induced self-energy and vertex corrections are incorporated systematically to provide a non-perturbative Goldstone-mode-preserving scheme. An effective quantum parameter [U2+(N-1)J2]/[U+(N-1)J]2 is obtained which determines, in analogy with 1/S for quantum spin systems and 1/N for the N-orbital Hubbard model, the strength of correlation-induced quantum corrections to magnetic excitations. The rapid suppression of this quantum parameter with Hund's coupling J, especially for large N, provides fundamental insight into the phenomenon of strong stabilization of metallic ferromagnetism by orbital degeneracy and Hund's coupling. Correlation effects are investigated for spin stiffness, magnon dispersion, electronic spectral function, density of states, and finite-temperature spin dynamics using realistic bandwidth, interaction, and lattice parameters for iron.     

Entangled finitely correlated quantum spin chains

We study the multipartite entanglement properties of translation-invariant states of infinite quantum spin chains with a valence-bond structure.