The bilinear-biquadratic model on the complete graph

We study the spin-1 bilinear-biquadratic model on the complete graph of N sites, i.e., when each spin is interacting with every other spin with the same strength. Because of its complete permutation invariance, this Hamiltonian can be rewritten as the linear combination of the quadratic Casimir operators of su(3) and su(2). Using group representation theory, we explicitly diagonalize the Hamiltonian and map out the ground-state phase diagram of the model. Furthermore, the complete energy spectrum, with degeneracies, is obtained analytically for any number of sites

Temperature driven quenches in the Ising model: appearance of negative Rényi mutual information

We study the dynamics of the transverse field Ising chain after a local quench in which two independently thermalised chains are joined together and are left to evolve unitarily. In the emerging non-equilibrium steady state the Rényi mutual information with different indices are calculated between two adjacent segments of the chain, and are found to scale logarithmically in the subsystem size. Surprisingly, for Rényi indices > 2 we find cases where the prefactor of the logarithmic dependence is negative. The fact that the naively defined Rényi mutual information might be negative has been pointed out before, however, we provide the first example for this scenario in a realistic many-body setup. Our numerical and analytical results indicate that in this setup it can be negative for any index > 2 while it is always positive for < 2. Interestingly, even for > 2 the calculated prefactors show some universal features: for example, the same prefactor is also shown to govern the logarithmic time dependence of the Rényi mutual information before the system relaxes locally to the steady state. In particular, it can decrease in the non-equilibrium evolution after the quench

Entanglement negativity in two-dimensional free lattice models

We study the scaling properties of the ground-state entanglement between finite subsystems of infinite two-dimensional free lattice models, as measured by the logarithmic negativity. For adjacent regions with a common boundary, we observe that the negativity follows a strict area law for a lattice of harmonic oscillators, whereas for fermionic hopping models the numerical results indicate a multiplicative logarithmic correction. In this latter case, we conjecture a formula for the prefactor of the area-law violating term, which is entirely determined by the geometries of the Fermi surface and the boundary between the subsystems. The conjecture is tested against numerical results and a good agreement is found.Comment: 11 pages, 6 figures, published versio

Extendibility of Werner States

We investigate the two-sided symmetric extendibility problem of Werner states. The interplay of the unitary symmetry of these states and the inherent bipartite permutation symmetry of the extendibility scenario allows us to map this problem into the ground state problem of a highly symmetric spin-model Hamiltonian. We solve this ground state problem analytically by utilizing the representation theory of SU(d), in particular a result related to the dominance order of Young diagrams in Littlewood-Richarson decompositions. As a result, we obtain necessary and sufficient conditions for the extendibility of Werner states for arbitrary extension size and local dimension. Interestingly, the range of extendible states has a non-trivial trade-off between the extension sizes on the two sides. We compare our result with the two-sided extendibility problem of isotropic states, where there is no such trade-off.Comment: 5+5 pages, 4 fig

Mitigation of readout noise in near-term quantum devices by classical post-processing based on detector tomography

We propose a simple scheme to reduce readout errors in experiments on quantum systems with finite number of measurement outcomes. Our method relies on performing classical post-processing which is preceded by Quantum Detector Tomography, i.e., the reconstruction of a Positive-Operator Valued Measure (POVM) describing the given quantum measurement device. If the measurement device is affected only by an invertible classical noise, it is possible to correct the outcome statistics of future experiments performed on the same device. To support the practical applicability of this scheme for near-term quantum devices, we characterize measurements implemented in IBM's and Rigetti's quantum processors. We find that for these devices, based on superconducting transmon qubits, classical noise is indeed the dominant source of readout errors. Moreover, we analyze the influence of the presence of coherent errors and finite statistics on the performance of our error-mitigation procedure. Applying our scheme on the IBM's 5-qubit device, we observe a significant improvement of the results of a number of single- and two-qubit tasks including Quantum State Tomography (QST), Quantum Process Tomography (QPT), the implementation of non-projective measurements, and certain quantum algorithms (Grover's search and the Bernstein-Vazirani algorithm). Finally, we present results showing improvement for the implementation of certain probability distributions in the case of five qubits.Comment: 18 + 5 pages, 11+2 figures, 5+1 tables, comments and suggestions are welcome; v2: version accepted in Quantum, updated references, fixed figures formatting, improved style and narrative in the main text, added note about code availabilit