Related papers: Notes on super-operator norms induced by Schatten …

We present new conditions for semigroups of positive operators to converge strongly as time tends to infinity. Our proofs are based on a novel approach combining the well-known splitting theorem by Jacobs, de Leeuw and Glicksberg with a…

Pseudo-random operators consist of sets of operators that exhibit many of the important statistical features of uniformly distributed random operators. Such pseudo-random sets of operators are most useful whey they may be parameterized and…

This paper communicates recent results in theory of complex symmetric operators and shows, through two non-trivial examples, their potential usefulness in the study of Schr\"odinger operators. In particular, we propose a formula for…

We define a natural ensemble of trace preserving, completely positive quantum maps and present algorithms to generate them at random. Spectral properties of the superoperator Phi associated with a given quantum map are investigated and a…

The Hamiltonian H specifies the energy levels and the time evolution of a quantum theory. It is an axiom of quantum mechanics that H be Hermitian because Hermiticity guarantees that the energy spectrum is real and that the time evolution is…

It is shown how the results in the theory of determinants and traces as well as in the theory of quasi-normed tensor products can be applied for getting new theorems on distribution of eigenvalues of nuclear operators in Banach spaces and…

A general strategy is provided to identify the most general metric for diagonalizable pseudo-Hermitian and anti-pseudo-Hermitian Hamilton operators represented by two-dimensional matrices. It is investigated how a permutation of the…

We formalize the correspondence between quantum states and quantum operations isometrically, and harness its consequences. This correspondence was already implicit in the various proofs of the operator sum representation of Completely…

We characterize the membership of Hankel operators with general symbols in the Schatten Classes $S^p,\, p\in(0,1),$ of the large Bergman spaces $A^2_{\omega}$. The case $p\geq 1$ was proved by Lin and Rochberg.

We introduce a weakened notion of norm attainment for bounded linear operators between Banach spaces which we call \emph{quasi norm attaining operators}. An operator $T\colon X \longrightarrow Y$ between the Banach spaces $X$ and $Y$ is…

This paper derives an inequality relating the p-norm of a positive 2 x 2 block matrix to the p-norm of the 2 x 2 matrix obtained by replacing each block by its p-norm. The inequality had been known for integer values of p, so the main…

We analyze some aspects of quantum computing with super-qubits (squbits). We propose the analogue of a superfield formalism, and give a physical interpretation for the Grassmann coefficients in the squbit expansion as fermionic creation…

We consider random linear operators $\Omega \to \mathcal{L}(\mathcal{T}_p, \mathcal{T}_p)$ acting in a $p$-th Schatten class $\mathcal{T}_p$ in a separable Hilbert space $\mathcal{H}$ for some $1 \leqslant p < \infty$. Such a superoperator…

Extending classical results of Janson and Peetre (1988) on the Schatten class $S^p$ membership of commutators of Riesz potentials on the Euclidean space, we obtain analogous results for commutators $[b,T]$, where…

We investigate and ascertain the ideal inputs to any finite-time thermodynamic process. We demonstrate that the expectation values of entropy flow, heat, and work can all be determined via Hermitian observables of the initial state. These…

In the Schroedinger formulation of non-Hermitian quantum theories a positive-definite metric operator $\eta\equiv e^{-Q}$ must be introduced in order to ensure their probabilistic interpretation. This operator also gives an equivalent…

Let $H_1$, $H_2$ be complex Hilbert spaces. A bounded linear operator $T : H_1 \to H_2$ is said to be norm attaining if there exists a unit vector $x \in H_1$ such that $\|Tx\| = \|T\|$. If $T|_{M} : M \to H_2$ is norm attaining for every…

In most introductory courses on quantum mechanics one is taught that the Hamiltonian operator must be Hermitian in order that the energy levels be real and that the theory be unitary (probability conserving). To express the Hermiticity of a…

Quantum coherence is a fundamental feature of quantum physics and plays a significant role in quantum information processing. By generalizing the resource theory of coherence from von Neumann measurements to positive operator-valued…

We develop numerous results that characterize when a complex Hermitian matrix is Birkhoff-James orthogonal, in the trace norm, to a (Hermitian) positive semidefinite matrix or set of positive semidefinite matrices. For example, we develop a…