Coherence migration in high-dimensional bipartite systems

The conservation law for first-order coherence and mutual correlation of a bipartite qubit state is first proposed by Svozilík et al. [Phys. Rev. Lett. 115, 220501 (2015)], and their theories laid the foundation for the study of coherence migration under unitary transformations. In this paper, we generalize the framework of first-order coherence and mutual correlation to an arbitrary $(m \otimes n)$-dimensional bipartite composite state by introducing an extended Bloch decomposition form of the state. We also generalize two kinds of unitary operators in high-dimensional systems, which can bring about coherence migration and help to obtain the maximum or minimum first-order coherence. Meanwhile, coherence migration in open quantum systems are investigated. We take depolarizing channels as examples and establish that the reduced first-order coherence of the principal system over time is completely transformed into mutual correlation of the $(2 \otimes 4)$-dimensional system-environment bipartite composite state. It is expected that our results may provide a valuable idea or method for controlling the quantum resource such as coherence and quantum correlations.

A Highly Scalable Method for Extractive Text Summarization Using Convex Optimization

The paper describes a convex optimization formulation of the extractive text summarization problem and a simple and scalable algorithm to solve it. The optimization program is constructed as a convex relaxation of an intuitive but computationally hard integer programming problem. The objective function is highly symmetric, being invariant under unitary transformations of the text representations. Another key idea is to replace the constraint on the number of sentences in the summary with a convex surrogate. For solving the program we have designed a specific projected gradient descent algorithm and analyzed its performance in terms of execution time and quality of the approximation. Using the datasets DUC 2005 and Cornell Newsroom Summarization Dataset, we have shown empirically that the algorithm can provide competitive results for single document summarization and multi-document query-based summarization. On the Cornell Newsroom Summarization Dataset, it ranked second among the unsupervised methods tested. For the more challenging task of multi-document query-based summarization, the method was tested on the DUC 2005 Dataset. Our algorithm surpassed the other reported methods with respect to the ROUGE-SU4 metric, and it was at less than 0.01 from the top performing algorithms with respect to ROUGE-1 and ROUGE-2 metrics.

Solving Dirac oscillator in commutative and noncommutative planes by supersymmetry structures

Based on the supersymmetry structures, we propose to solve the model of a charged Dirac oscillator interacting with a uniform perpendicular magnetic field on both commutative and noncommutative planes in a unified way by employing unitary transformations. The unitary operators are constructed out of the generators of the supersymmetry structures of the model.

Causal and compositional structure of unitary transformations

The causal structure of a unitary transformation is the set of relations of possible influence between any input subsystem and any output subsystem. We study whether such causal structure can be understood in terms of compositional structure of the unitary. Given a quantum circuit with no path from input system A to output system B, system A cannot influence system B. Conversely, given a unitary U with a no-influence relation from input A to output B, it follows from [B. Schumacher and M. D. Westmoreland, Quantum Information Processing 4 no. 1, (Feb, 2005)] that there exists a circuit decomposition of U with no path from A to B. However, as we argue, there are unitaries for which there does not exist a circuit decomposition that makes all causal constraints evident simultaneously. To address this, we introduce a new formalism of `extended circuit diagrams', which goes beyond what is expressible with quantum circuits, with the core new feature being the ability to represent direct sum structures in addition to sequential and tensor product composition. A causally faithful extended circuit decomposition, representing a unitary U, is then one for which there is a path from an input A to an output B if and only if there actually is influence from A to B in U. We derive causally faithful extended circuit decompositions for a large class of unitaries, where in each case, the decomposition is implied by the unitary's respective causal structure. We hypothesize that every finite-dimensional unitary transformation has a causally faithful extended circuit decomposition.

A semi exact solution for a metallic phase in a Holstein-Hubbard chain at half filling with Gaussian anharmonic phonons

The nature of phase transition from an antiferromagnetic SDW polaronic Mott insulator to the paramagnetic bipolaronic CDW Peierls insulator is studied for the half-filled Holstein-Hubbard model in one dimension in the presence of Gaussian phonon anharmonicity. A number of unitary transformations performed in succession on the Hamiltonian followed by a general many-phonon averaging leads to an effective electronic Hamiltonian which is then treated exactly by using the Bethe-Ansatz technique of Lieb and Wu to determine the energy of the ground state of the system. Next using the Mott–Hubbard metallicity condition, local spin-moment calculation, and the concept of quantum entanglement entropy and double occupancy, it is shown that in a plane spanned by the electron–phonon coupling coefficient and onsite Coulomb correlation energy, there exists a window in which the SDW and CDW phases are separated by an intermediate phase that is metallic.

Quantum Control Landscapes Beyond the Dipole Approximation: Controllability, Singular Controls, and Resources

We investigate the control landscapes of closed n-level quantum systems beyond the dipole approximation by including a polarizability term in the Hamiltonian. The latter term is quadratic in the control field. Theoretical analysis of singular controls is presented, which are candidates for producing landscape traps. The results for considering the presence of singular controls are compared to their counterparts in the dipole approximation (i.e., without polarizability). A numerical analysis of the existence of traps in control landscapes for generating unitary transformations beyond the dipole approximation is made upon including the polarizability term. An extensive exploration of these control landscapes is achieved by creating many random Hamiltonians which include terms linear and quadratic in a single control field. The discovered singular controls are all found not to be local optima. This result extends a great body of recent work on typical landscapes of quantum systems where the dipole approximation is made. We further investigate the relationship between the magnitude of the polarizability and the fluence of the control resulting from optimization. It is also shown that including a polarizability term in an otherwise uncontrollable dipole coupled system removes traps from the corresponding control landscape by restoring controllability. We numerically assess the effect of a polarizability term on a known example of a particular three-level Λ-system with a second order trap in its control landscape. It is found that the addition of the polarizability removes the trap from the landscape. The general practical control implications of these simulations are discussed.

Tripartite entanglement and quantum correlation

We provide an analytical tripartite-study from the generalized R-matrix. It provides the upper bound of the maximum violation of Mermin’s inequality. For a generic 2-qubit pure state, the concurrence or R-matrix characterizes the maximum violation of Bell’s inequality. Therefore, people expect that the maximum violation should be proper to quantify Quantum Entanglement. The R-matrix gives the maximum violation of Bell’s inequality. For a general 3-qubit state, we have five invariant entanglement quantities up to local unitary transformations. We show that the five invariant quantities describe the correlation in the generalized R-matrix. The violation of Mermin’s inequality is not a proper diagnosis due to the non-monotonic behavior. We then classify 3-qubit quantum states. Each classification quantifies Quantum Entanglement by the total concurrence. In the end, we relate the experiment correlators to Quantum Entanglement.