A robust and efficient implementation of LOBPCG

Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is widely used to compute eigenvalues of large sparse symmetric matrices. The algorithm can suffer from numerical instability if it is not implemented with care. This is especially problematic when the number of eigenpairs to be computed is relatively large. In this paper we propose an improved basis selection strategy based on earlier work by Hetmaniuk and Lehoucq as well as a robust convergence criterion which is backward stable to enhance the robustness. We also suggest several algorithmic optimizations that improve performance of practical LOBPCG implementations. Numerical examples confirm that our approach consistently and significantly outperforms previous competing approaches in both stability and speed

The equation of state for scalar-tensor gravity

We show that the field equation of Brans-Dicke gravity and scalar-tensor gravity can be derived as the equation of state of Rindler spacetime, where the local thermodynamic equilibrium is maintained. Our derivation implies that the effective energy can not feel the heat flow across the Rindler horizon.Comment: 6 pages, to be published in Prog. Theor. Phy

Nonlocal Properties and Local Invariants for Bipartite Systems

The nonlocal properties for a kind of generic N-dimensional bipartite quantum systems are investigated. A complete set of invariants under local unitary transformations is presented. It is shown that two generic density matrices are locally equivalent if and only if all these invariants have equal values in these density matrices.Comment: Latex, 9 page

Tighter weighted polygamy inequalities of multipartite entanglement in arbitrary-dimensional quantum systems

We investigate polygamy relations of multipartite entanglement in arbitrary-dimensional quantum systems. By improving an inequality and using the $\beta$th ($0\leq\beta\leq1$) power of entanglement of assistance, we provide a new class of weighted polygamy inequalities of multipartite entanglement in arbitrary-dimensional quantum systems. We show that these new polygamy relations are tighter than the ones given in [Phys. Rev. A 97, 042332 (2018)]

Ordering states with various coherence measures

Quantum coherence is one of the most significant theories in quantum physics. Ordering states with various coherence measures is an intriguing task in quantification theory of coherence. In this paper, we study this problem by use of four important coherence measures -- the $l_1$ norm of coherence, the relative entropy of coherence, the geometric measure of coherence and the modified trace distance measure of coherence. We show that each pair of these measures give a different ordering of qudit states when $d\geq 3$. However, for single-qubit states, the $l_1$ norm of coherence and the geometric coherence provide the same ordering. We also show that the relative entropy of coherence and the geometric coherence give a different ordering for single-qubit states. Then we partially answer the open question proposed in [Quantum Inf. Process. 15, 4189 (2016)] whether all the coherence measures give a different ordering of states.Comment: 12 page

Two-copy Quantum Teleportation

We investigate two-copy scenario of quantum teleportation based on Bell measurements. The detailed protocol is presented and the general expression of the corresponding optimal teleportation delity is derived, which is given by the two-copy fully entangled fraction that is invariant under local unitary transformations. We prove that under a speci c case of the protocol, which is signi cant for improving the optimal delity, the set of states with their two-copy fully entangled fractions bounded by a threshold value that required for useful two-copy teleportation is convex and compact. Hence the witness operators exist to separate states that are useful for two-copy teleportation from the rest ones. Moreover, we show that the optimal delity of two-copy teleportation surpasses that of the original one copy teleportation.Comment: 8 pages, 2 figure