Exact properties of the chemical potential-density relation at finite temperature in the Hubbard model

We draw some rigorous conclusions about the functional properties of the $\mu-\rho$ relation in the Hubbard model based on symmetry considerations and unitary transformations. It is shown that the charge susceptibility reaches its local extreme at half-filling. Exact expressions are obtained in two limiting cases

Construction of Equientangled Bases in Arbitrary Dimensions via Quadratic Gauss Sums and Graph States

Recently [Karimipour and Memarzadeh, Phys. Rev. A 73, 012329 (2006)] studied the problem of finding a family of orthonormal bases in a bipartite space each of dimension $D$ with the following properties: (i) The family continuously interpolates between the product basis and the maximally entangled basis as some parameter $t$ is varied, and (ii) for a fixed $t$, all basis states have the same amount of entanglement. The authors derived a necessary condition and provided explicit solutions for $D \leq 5$ but the existence of a solution for arbitrary dimensions remained an open problem. We prove that such families exist in arbitrary dimensions by providing two simple solutions, one employing the properties of quadratic Gauss sums and the other using graph states. The latter can be generalized to multipartite equientangled bases with more than two parties.Comment: Minor changes, replaced by the published version. Any comments are welcome

A note on the proof of magnetic flux quantization from ODLRO

It is noticed that the excellent proof of the connection of magnetic flux quantization and off-diagonal long range order (ODLRO) presented recently by Nieh, Su and Zhao suffers from an imperfection, namely, the f-factors in the case of finite translation do not satisfy $f(a)f(b)=f(a+b)$, which was employed in the proof. A corrected proof is proposed to remedy this point.Comment: 6 pages, LATEX, no figure

Tripartite Entanglement in Qudit Stabilizer States and Application in Quantum Error Correction

Consider a stabilizer state on $n$ qudits, each of dimension $D$ with $D$ being a prime or a squarefree integer, divided into three mutually disjoint sets or parts. Generalizing a result of Bravyi et al. [J. Math. Phys. \textbf{47}, 062106 (2006)] for qubits (D=2), we show that up to local unitaries on the three parts the state can be written as a tensor product of unentangled single-qudit states, maximally entangled EPR pairs, and tripartite GHZ states. We employ this result to obtain a complete characterization of the properties of a class of channels associated with stabilizer error-correcting codes, along with their complementary channels.Comment: 15 pages, 2 figure