One of the central tasks in quantum error-correction is to construct quantum codes that have good parameters. In this paper, we construct three new classes of quantum MDS codes from classical Hermitian self-orthogonal generalized Reed-Solomon codes. We also present some classes of quantum codes from matrix-product codes. It turns out that many of our quantum codes are new in the sense that the ...

We introduce the notion of pseudo-Hermiticity and show that every Hamiltonian with a real spectrum is pseudo-Hermitian. We point out that all the PT -symmetric non-Hermitian Hamiltonians studied in the literature are pseudo-Hermitian and argue that the structure responsible for the reality of the spectrum of these Hamiltonian is their pseudo-Hermiticity not PT -symmetry. We explore the basic pr...

Abstract In this work, we study the non-Hermitian Swanson Hamiltonian, particularly non-parity-time symmetry phase. We use formalism of Gel’fand triplet to construct generalized eigenfunctions and corresponding spectrum. Depending on region parameter model space, show that Hamiltonian represents different physical systems, i.e. parabolic barrier, negative mass oscillators. also discussed presen...

For an arbitrary possibly non-Hermitian matrix Hamiltonian H, that might involve exceptional points, we construct an appropriate parameter space M and a lines bundle Ln over M such that the adiabatic geometric phases associated with the eigenstates of the initial Hamiltonian coincide with the holonomies of Ln. We examine the case of 2× 2 matrix Hamiltonians in detail and show that, contrary to ...

Abstract It is shown that for a given hermitian Hamiltonian possessing supersymmetry, there is always a non-hermitian Jaynes-Cummings-type Hamiltonian(JCTH) admitting entirely real spectra. The parent supersymmetric Hamiltonian and the corresponding non-hermitian JCTH are simultaneously diagonalizable. The exact eigenstates of these non-hermitian Hamiltonians are constructed algebraically for c...

Non-Hermitian systems in condensed matter Physics are well studied recent years. In conventional viewpoint, the non-Hermiticity of a Hamiltonian is obtained by dissipative or gain and loss. Recently, some people investigate from other perspective, which point out that may come curved space. this letter, we derive duality between generalized non-Hermitian HN model $d$-dimensional flat space Herm...

In quantum mechanics it is well known that observables are represented by hermitian matrices (or operators). Uncertainty relations are represented as some kinds of trace inequalities satisfied by two observables and one density matrix (or operator). Now we try to release the hermitian restriction on observables. This is only a mathematical interest. In this case we give several non-hermitian ex...

in this paper‎, ‎we study the extremal‎ ‎ranks and inertias of the hermitian matrix expression $$‎ ‎f(x,y)=c_{4}-b_{4}y-(b_{4}y)^{*}-a_{4}xa_{4}^{*},$$ where $c_{4}$ is‎ ‎hermitian‎, ‎$*$ denotes the conjugate transpose‎, ‎$x$ and $y$ satisfy‎ ‎the following consistent system of matrix equations $a_{3}y=c_{3}‎, ‎a_{1}x=c_{1},xb_{1}=d_{1},a_{2}xa_{2}^{*}=c_{2},x=x^{*}.$ as‎ ‎consequences‎, ‎we g...