Cloning of observables, unlike standard cloning of states, aims at copying the information encoded in the statistics of a class of observables rather then on quantum states themselves. In such a process the emphasis is on the quantum operation (evolution plus measurement) necessary to retrieve the original information. We analyze, for qubit systems, the cloning of a class generated by two nonco...

Coherence of a quantum state intrinsically depends on the choice of the reference basis. A natural question to ask is the following: if we use two or more incompatible reference bases, can there be some trade-off relation between the coherence measures in different reference bases? We show that the quantum coherence of a state as quantified by the relative entropy of coherence in two or more no...

We show that all the coefficients of the polynomial tr((A+ tB)) ∈ R[t] are nonnegative whenever m ≤ 13 is a nonnegative integer and A and B are positive semidefinite matrices of the same size. This has previously been known only for m ≤ 7. The validity of the statement for arbitrary m has recently been shown to be equivalent to the Bessis-Moussa-Villani conjecture from theoretical physics. In o...

We show how one can use superconductors and Josephson junctions to create a laboratory system which can explore the groundstates of the free electromagnetic field in a 3-manifold with torsion in its cohomology.

Let S ∪ {f} be a set of symmetric polynomials in noncommuting variables. If f satisfies a polynomial identity P i h ∗ i fhi = 1 + P i g ∗ i sigi for some si ∈ S ∪ {1}, then f is obviously nowhere negative semidefinite on the class of tuples of non-zero operators defined by the system of inequalities s ≥ 0 (s ∈ S). We prove the converse under the additional assumption that the quadratic module g...

We study mixing properties of epimorphisms of a compact connected finite-dimensional abelian group X . In particular, we show that a set F , |F | > dimX , of epimorphisms of X is mixing iff every subset of F of cardinality (dimX)+1 is mixing. We also construct examples of free nonabelian groups of automorphisms of tori which are mixing, but not mixing of order 3, and show that, under some irred...