Related papers: Parallel distinguishability of quantum operations
A distinguishability operator is defined for the continuous-time quantum walk (CTQW) of a bipartite quantum walker on two simply connected graphs, $W_{G_i,G_j} = U_{G_i}\left(t\right) \otimes U_{G_j}\left(t'\right) - U_{G_j}\left(t'\right)…
On classical phase spaces admitting just one complex-differentiable structure, there is no indeterminacy in the choice of the creation operators that create quanta out of a given vacuum. In these cases the notion of a quantum is universal,…
We investigate the necessary and sufficient condition for a convex cone of positive semidefinite operators to be fixed by a unital quantum operation $\phi$ acting on finite-dimensional quantum states. By reducing this problem to the problem…
Within context of quantum logic, it is possible to assign dispersion-free probabilities to experimental propositions pertaining to qubits. This makes qubits distinct from the rest of quantum systems since the latter do not admit…
Quantum state discrimination is a fundamental primitive in quantum statistics where one has to correctly identify the state of a system that is in one of two possible known states. A programmable discrimination machine performs this task…
We establish a spectral duality for certain unbounded operators in Hilbert space. The class of operators includes discrete graph Laplacians arising from infinite weighted graphs. The problem in this context is to establish a practical…
We analyze some features of alternative Hermitian and quasi-Hermitian quantum descriptions of simple and bipartite compound systems. We show that alternative descriptions of two interacting subsystems are possible if and only if the metric…
Clarifying the relation between the whole and its parts is crucial for many problems in science. In quantum mechanics, this question manifests itself in the quantum marginal problem, which asks whether there is a global pure quantum state…
We study two subspace systems in a separable infinite-dimensional Hilbert space up to (bounded) isomorphism. One of the main result of this paper is the following: Isomorphism classes of two subspace systems given by graphs of bounded…
We give an example of an operator with different weak and strong absolutely continuous subspaces, and a counterexample to the duality problem for the spectral components. Both examples are optimal in the scale of compact operators.
Quantum coherence, a basic feature of quantum mechanics residing in superpositions of quantum states, is a resource for quantum information processing. Coherence emerges in a fundamentally different way for nonidentical and identical…
It is shown that the dimension of the multilinear quantum Lie operations space is either equal to zero or included between $(n-2)!$ and $(n-1)!.$ The lower bound is achieved if the intersection of all conforming subsets is nonempty, while…
We extend the formulation of pseudo-Hermitian quantum mechanics to eta-pseudo-Hermitian Hamiltonian operators H with an unbounded metric operator eta. In particular, we give the details of the construction of the physical Hilbert space,…
One says that a pair (P,Q) of ordinary differential operators specify a quantum curve if [P,Q]=const. If a pair of difference operators (K,L) obey the relation KL=const LK we say that they specify a discrete quantum curve. This terminology…
We give a simple proof of the fact that every diagonalizable operator that has a real spectrum is quasi-Hermitian and show how the metric operators associated with a quasi-Hermitian Hamiltonian are related to the symmetry generators of an…
Quantum logic gates can perform calculations much more efficiently than their classical counterparts. However, the level of control needed to obtain a reliable quantum operation is correspondingly higher. In order to evaluate the…
Quantum connections are defined by parallel transport operators acting on a Hilbert space. They transport tangent operators along paths in parameter space. The metric tensor of a Riemannian manifold is replaced by an inner product of pairs…
The distinguishability between two quantum states can be defined in terms of their trace distance. The operational meaning of this definition involves a maximization over measurement projectors. Here we introduce an alternative definition…
In this work we present an algorithm to perform algorithmic differentiation in the context of quantum computing. We present two versions of the algorithm, one which is fully quantum and one which employees a classical step (hybrid…
In this work we will advance farther along a line previously developed concerning our proposal of a time interval operator, on finite dimensional spaces. The time interval operator is Hermitian, and its eigenvalues are time values with a…