Related papers: Not all pure states on B(H) are diagonalizable
We construct a pure state on the C*-algebra $\mathcal B(\ell_2)$ of all bounded linear operators on $\ell_2$ which is not diagonalizable, i.e., it is not of the form $\lim_u\langle T(e_k), e_k\rangle$ for any orthonormal basis $(e_k)_{k\in…
Experimental evidence, the heuristics of indistinguishability, and its logical inconsistency with quantum formalism all argue against the existence of a quantum mixture uncorrelated with the exterior, that is, argue for the postulate "The…
In quantum theory every state can be diagonalized, i.e. decomposed as a convex combination of perfectly distinguishable pure states. This elementary structure plays an ubiquitous role in quantum mechanics, quantum information theory, and…
We prove that all inseparable Gaussian states of two modes can be distilled into maximally entangled pure states by local operations. Using this result we show that a bipartite Gaussian state of arbitrarily many modes can be distilled if…
We argue that the notion of pure sate within Standard Quantum Mechanics is presently applied within the specialized literature in relation to two mutually inconsistent definitions. While the first (operational purity) provides a…
We study if all maximally entangled states are pure through several entanglement monotones. In the bipartite case, we find that the same conditions which lead to the uniqueness of the entropy of entanglement as a measure of entanglement,…
We prove that $i)$ if $\mathcal{A}$ is $\lambda $-accessible and it is axiomatizable in (finitary) coherent logic then $\lambda $-pure maps are strict monomorphisms and $ii)$ if there is a proper class of strongly compact cardinals and…
Consider a qubit-qutrit ($2 \times 3$) composite state space. Let $C(\{1}{2}I_2, \{1}{3}I_3)$ be a convex set of all possible states of composite system whose marginals are given by $\{1}{2}I_2$ and $\{1}{3}I_3$ in two and three dimensional…
Recently, the much-used trace distance of coherence was shown to not be a proper measure of coherence, so a modification of it was proposed. We derive an explicit formula for this modified trace distance of coherence on pure states. Our…
We give an informal overview of the Kadison-Singer extension problem with emphasis on its initial connections to Dirac's formulation of quantum mechanics. Let H be an infinite dimensional separable Hilbert space, and B(H) the algebra of all…
All the connections, pure toward the nilpotent structure, are found. Examples of manifolds, for which the curvature tensor is pure or hybrid, are given. For a manifold of B-type a necessary and sufficient condition for purity of the…
We show that pure states of multipartite quantum systems are multiseparable (i.e. give separable density matrices on tracing any party) if and only if they have a generalized Schmidt decomposition. Implications of this result for the…
We generalise Wigner's theorem to its most general form possible for B(h) in the sense of completely characterising those vector state transformations of B(h) that appear as restrictions of duals of linear operators on B(h). We then use…
We prove that all purifications of a non-factorable state (i.e., the state which cannot be expressed in a form $\rho_{AB}=\rho_A\otimes\rho_B$) are entangled. We also show that for any bipartite state there exists a pair of measurements…
Using the existing classification of all alternatives to the measurement postulates of quantum theory we study the properties of bi-partite systems in these alternative theories. We prove that in all these theories the purification…
The halting problem for Turing machines is decidable on a set of asymptotic probability one. Specifically, there is a set B of Turing machine programs such that (i) B has asymptotic probability one, so that as the number of states n…
The theory of generalised measurements is used to examine the problem of discriminating unambiguously between non-orthogonal pure quantum states. Measurements of this type never give erroneous results, although, in general, there will be a…
Having in mind present uncertainty of the experimental situation in respect to exotic hadrons, it is important to discuss any possible theoretical arguments, pro and contra. Up to now, there are no theoretical ideas which could forbid…
It is proven that the relativistic charged ball with its charge less than its mass (in natural units) cannot have a non-singular static configuration while its radius approaches its external horizon size. This conclusion does not depend on…
We study the problem of quantum-state tomography under the assumption that the state of the system is close to pure. In this context, an efficient measurements that one typically formulates uniquely identify a pure state from within the set…