The dynamics of quantum correlation with two controlled qubits under classical dephasing environment

We discuss the quantum correlation dynamics of two qubits controlled through the application of π$\pi$-pulses under classical dephasing non-Markovian environment. It is shown that the quantum discord (QD) and one-norm geometric quantum discord (one-norm GQD) between the two qubits, which are prepared initially in the three-parameter-X$X$-type quantum states, depend strongly on non-Markovian properties and the time difference between adjacent pulses. The freezing time of discord and one-norm GQD can be lengthened for appropriate pulse separate time and pulse numbers. And the freezing time of one-norm GQD is longer slightly than QD for both Markovian and non-Markovian cases. What is more, we find that double sudden changes of one-norm GQD can appear only for some initial parameters when π$\pi$-pulses are applied.     

Coherent superpositions of states in coupled Hilbert-space using step by step Morris–Shore transformation

Creation of coherent superpositions in quantum systems with N_a$N_a$ states in the lower set and N_b$N_b$ states in the upper set is presented. The solution is drived by using the Morris–Shore transformation, which step by step reduces the fully coupled system to a three-state Λ$\Lambda$-like system and a set of decoupled states. It is shown that, for properly timed pulse, robust population transfer from an initial ground state (or superposition of M$M$ ground states) to an arbitrary coherent superposition of the ground states can be achieved by coincident pulses and/or STIRAP techniques.     

Geometric measure of pairwise quantum discord for superpositions of multipartite generalized coherent states

We give the explicit expressions of the pairwise quantum correlations present in superpositions of multipartite coherent states. A special attention is devoted to the evaluation of the geometric quantum discord. The dynamics of quantum correlations under a dephasing channel is analyzed. A comparison of geometric measure of quantum discord with that of concurrence shows that quantum discord in multipartite coherent states is more resilient to dissipative environments than is quantum entanglement. To illustrate our results, we consider some special superpositions of Weyl–Heisenberg, SU(2)$\mathit{SU}(2)$ and SU(1,1)$\mathit{SU}(1,1)$ coherent states which interpolate between Werner and Greenberger–Horne–Zeilinger states.     

Random matrix theory for transition strength densities in finite quantum systems: Results from embedded unitary ensembles

Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless fermion (or boson) systems, with say m$m$ fermions (or bosons) in N$N$ single particle states and interacting via k$k$-body interactions, we have EGUE(k$k$) [embedded GUE of k$k$-body interactions] with GUE embedding and the embedding algebra is U(N)$U\left(N\right)$. A finite quantum system, induced by a transition operator, makes transitions from its states to the states of the same system or to those of another system. Examples are electromagnetic transitions (then the initial and final systems are same), nuclear beta and double beta decay (then the initial and final systems are different), particle addition to or removal from a given system and so on. Towards developing a complete statistical theory for transition strength densities (transition strengths multiplied by the density of states at the initial and final energies), we have derived formulas for the lower order bivariate moments of the strength densities generated by a variety of transition operators. Firstly, for a spinless fermion system, using EGUE(k$k$) representation for a Hamiltonian that is k$k$-body and an independent EGUE(t$t$) representation for a transition operator that is t$t$-body and employing the embedding U(N)$U\left(N\right)$ algebra, finite-N$N$ formulas for moments up to order four are derived, for the first time, for the transition strength densities. Secondly, formulas for the moments up to order four are also derived for systems with two types of spinless fermions and a transition operator similar to beta decay and neutrinoless beta decay operators. In addition, moments formulas are also derived for a transition operator that removes k₀$k_0$ number of particles from a system of m$m$ spinless fermions. In the dilute limit, these formulas are shown to reduce to those for the EGOE version derived using the asymptotic limit theory of Mon and French (1975). Numerical results obtained using the exact formulas for two-body (k=2$k=2$) Hamiltonians (in some examples for k=3$k=3$ and 4$4$) and the asymptotic formulas clearly establish that in general the smoothed (with respect to energy) form of the bivariate transition strength densities take bivariate Gaussian form for isolated finite quantum systems. Extensions of these results to bosonic systems and EGUE ensembles with further symmetries are discussed.     

Divergence of fermionic correlations under non-Markovian noise in a non-inertial frame

Non-Markovian dynamics of correlations of fermionic systems is investigated beyond the single-mode approximations in a non-inertial frame. Two well known correlation measures, quantum discord and geometric quantum discord, are analyzed for the fermionic states influenced by the non-Markovian noise. Persistence of discord is seen for longer times depending upon the level of mixedness of the fermionic system. The dynamics of the fermionic systems heavily depends upon the degree of white noise. It is shown that fermionic systems remain dependent upon the choice of Unruh modes (_qR$q_R$) beyond the single-mode approximations under non-Markovian noise. Quantum discord is found to be more robust as compared to the geometric quantum discord. Furthermore, the non-Markovian effects are more stronger than the acceleration of Bob, the accelerated partner.     

Supersymmetric quantum mechanics of magnetic monopoles: A case study

We study, in detail, the supersymmetric quantum mechanics of charge-(1,1)$(1,1)$ monopoles in N=2$N=2$ supersymmetric Yang–Mills–Higgs theory with gauge group SU(3)$\mathit{SU}(3)$ spontaneously broken to U(1)×U(1)$U(1)\times U(1)$. We use the moduli space approximation of the quantised dynamics, which can be expressed in two equivalent formalisms: either one describes quantum states by Dirac spinors on the moduli space, in which case the Hamiltonian is the square of the Dirac operator, or one works with anti-holomorphic forms on the moduli space, in which case the Hamiltonian is the Laplacian acting on forms. We review the derivation of both formalisms, explicitly exhibit their equivalence and derive general expressions for the supercharges as differential operators in both formalisms. We propose a general expression for the total angular momentum operator as a differential operator, and check its commutation relations with the supercharges. Using the known metric structure of the moduli space of charge-(1,1)$(1,1)$ monopoles we show that there are no quantum bound states of such monopoles in the moduli space approximation. We exhibit scattering states and compute corresponding differential cross sections.     

On the group-theoretic structure of a class of quantum dialogue protocols

A sufficient condition for implementation of the quantum dialogue protocol is obtained and it is shown that the set of unitary operators used for the purpose must form a group under multiplication. A generalized protocol of quantum dialogue is obtained using the sufficient condition. Further, several examples of possible groups of unitary operators and quantum states that may be used for implementation of quantum dialogue are systematically generated. As examples, it is shown that GHZ state, GHZ-like state, W state, 4 and 5-qubit Cluster states, Ω   state, Brown state, _Q4$Q_4$ state and _Q5$Q_5$ state can be used to implement quantum dialogue protocol. It is also shown that if a quantum system is found to be suitable for quantum dialogue then that can provide solution of the socialist millionaire problem too.     

Excited-state quantum phase transitions in systems with two degrees of freedom: Level density,level dynamics,thermal properties

Quantum systems with a finite number of freedom degrees f$f$ develop robust singularities in the energy spectrum of excited states as the system’s size increases to infinity. We analyze the general form of these singularities for low f$f$, particularly f=2$f=2$, clarifying the relation to classical stationary points of the corresponding potential. Signatures in the smoothed energy dependence of the quantum state density and in the flow of energy levels with an arbitrary control parameter are described along with the relevant thermodynamical consequences. The general analysis is illustrated with specific examples of excited-state singularities accompanying the first-order quantum phase transition.