Entropy and specific heat for open systems in steady states

The fundamental assumption of statistical mechanics is that the system is equally likely in any of the accessible microstates. Based on this assumption, the Boltzmann distribution is derived and the full theory of statistical thermodynamics can be built. In this paper, we show that the Boltzmann distribution in general can not describe the steady state of open system. Based on the effective Hamiltonian approach, we calculate the specific heat, the free energy and the entropy for an open system in steady states. Examples are illustrated and discussed.Comment: 4 pages, 7 figure

Nonequilibrium thermal entanglement in three-qubit XXXX model

Making use of the master equation and effective Hamiltonian approach, we investigate the steady state entanglement in a three-qubit $XX$ model. Both symmetric and nonsymmetric qubit-qubit couplings are considered. The system (the three qubits) is coupled to two bosonic baths at different temperatures. We calculate the steady state by the effective Hamiltonian approach and discuss the dependence of the steady state entanglement on the temperatures and couplings. The results show that for symmetric qubit-qubit couplings, the entanglements between the nearest neighbor are equal, independent of the temperatures of the two baths. The maximum of the entanglement arrives at $T_L=T_R$. For nonsymmetric qubit-qubit couplings, however, the situation is totally different. The baths at different temperatures would benefit the entanglement and the entanglements between the nearest neighbors are no longer equal. By examining the probability distribution of each eigenstate in the steady state, we present an explanation for these observations. These results suggest that the steady entanglement can be controlled by the temperature of the two baths.Comment: Comments are welcom

Entanglement in Anderson Nanoclusters

We investigate the two-particle spin entanglement in magnetic nanoclusters described by the periodic Anderson model. An entanglement phase diagram is obtained, providing a novel perspective on a central property of magnetic nanoclusters, namely the temperature dependent competition between local Kondo screening and nonlocal Ruderman-Kittel-Kasuya-Yoshida spin ordering. We find that multiparticle entangled states are present for finite magnetic field as well as in the mixed valence regime and away from half filling. Our results emphasize the role of charge fluctuations.Comment: 5 pages, 3 figure

Quantum correlations in a cluster-like system

We discuss a cluster-like 1D system with triplet interaction. We study the topological properties of this system. We find that the degeneracy depends on the topology of the system, and well protected against external local perturbations. All these facts show that the system is topologically ordered. We also find a string order parameter to characterize the quantum phase transition. Besides, we investigate two-site correlations including entanglement, quantum discord and mutual information. We study the different divergency behaviour of the correlations. The quantum correlation decays exponentially in both topological and magnetic phases, and diverges in reversed power law at the critical point. And we find that in TQPT systems, the global difference of topology induced by dimension can be reflected in local quantum correlations.Comment: 7 pages, 6 figure

Scalable gate architecture for densely packed semiconductor spin qubits

We demonstrate a 12 quantum dot device fabricated on an undoped Si/SiGe heterostructure as a proof-of-concept for a scalable, linear gate architecture for semiconductor quantum dots. The device consists of 9 quantum dots in a linear array and 3 single quantum dot charge sensors. We show reproducible single quantum dot charging and orbital energies, with standard deviations less than 20% relative to the mean across the 9 dot array. The single quantum dot charge sensors have a charge sensitivity of 8.2 x 10^{-4} e/root(Hz) and allow the investigation of real-time charge dynamics. As a demonstration of the versatility of this device, we use single-shot readout to measure a spin relaxation time T1 = 170 ms at a magnetic field B = 1 T. By reconfiguring the device, we form two capacitively coupled double quantum dots and extract a mutual charging energy of 200 microeV, which indicates that 50 GHz two-qubit gate operation speeds are feasible

Maximal Entanglement of Two-qubit States Constructed by Linearly Independent Coherent States

In this paper, we find the necessary and sufficient condition for the maximal entanglement of the state, $|\psi>=\mu|\alpha>|\beta>+\lambda|\alpha>|\delta>+ \rho|\gamma>|\beta>+\nu|\gamma>|\delta>,$ constructed by linearly independent coherent states with \emph{real parameters} when $=$. This is a further generalization of the classified nonorthogonal states discussed in Ref. Physics Letters A {\bf{291}}, 73-76 (2001).Comment: some examples added; Int J Theor Phys 201

Method for classifying multiqubit states via the rank of the coefficient matrix and its application to four-qubit states

We construct coefficient matrices of size 2^l by 2^{n-l} associated with pure n-qubit states and prove the invariance of the ranks of the coefficient matrices under stochastic local operations and classical communication (SLOCC). The ranks give rise to a simple way of partitioning pure n-qubit states into inequivalent families and distinguishing degenerate families from one another under SLOCC. Moreover, the classification scheme via the ranks of coefficient matrices can be combined with other schemes to build a more refined classification scheme. To exemplify we classify the nine families of four qubits introduced by Verstraete et al. [Phys. Rev. A 65, 052112 (2002)] further into inequivalent subfamilies via the ranks of coefficient matrices, and as a result, we find 28 genuinely entangled families and all the degenerate classes can be distinguished up to permutations of the four qubits. We also discuss the completeness of the classification of four qubits into nine families

Enhancement of quantum correlations for the system of cavity QED by applying bang-bang pulses

We propose a scheme of increasing quantum correlations for the cavity quantum electrodynamics system consisting of two noninteracting two-level atoms each locally interacting with its own quantized field mode by bang-bang pulses. We investigate the influence of the bang-bang pulses on the dynamics of quantum discord, entanglement, quantum mutual information and classical correlation between the two atoms. It is shown that the amount of quantum discord and entanglement of the two atoms can be improved by applying the bang-bang pulses.Comment: 6 pages, 5 figure

Quantum information approach to the quantum phase transition in the Kitaev honeycomb model

Kitaev honeycomb model with topological phase transition at zero temperature is studied using quantum information method. Based on the exact solution of the ground state, the mutual information between two nearest sites and between two bonds with longest distance are obtained. It is found that the mutual information show some singularities at the critical point where the ground state of the system transits from gapless phase to gapped phase. The finite-size effects and scalar behavior are also studied. The mutual information can serve as good indicators of the topological phase transition, since the mutual information catches some global correlation properties of the system. Meanwhile, this method has other advantages such that the phase transition can be determined easily and the order parameters are not required previously, for the order parameters of some topological phase transitions are hard to know.Comment: 8 pages, 7 figures, published versio

Entanglement in SU(2)-invariant quantum systems: The positive partial transpose criterion and others

We study entanglement in mixed bipartite quantum states which are invariant under simultaneous SU(2) transformations in both subsystems. Previous results on the behavior of such states under partial transposition are substantially extended. The spectrum of the partial transpose of a given SU(2)-invariant density matrix $\rho$ is entirely determined by the diagonal elements of $\rho$ in a basis of tensor-product states of both spins with respect to a common quantization axis. We construct a set of operators which act as entanglement witnesses on SU(2)-invariant states. A sufficient criterion for $\rho$ having a negative partial transpose is derived in terms of a simple spin correlator. The same condition is a necessary criterion for the partial transpose to have the maximum number of negative eigenvalues. Moreover, we derive a series of sum rules which uniquely determine the eigenvalues of the partial transpose in terms of a system of linear equations. Finally we compare our findings with other entanglement criteria including the reduction criterion, the majorization criterion, and the recently proposed local uncertainty relations.Comment: 7 pages, no figures, version to appear in Phys. Rev.