Related papers: Solution to the King's problem with observables be…
In this paper, we suggest an alternative interpretation for the quantum state vector, which, by considering temporal parts for physical objects, aims to give an intelligible account of measurement problem in quantum mechanics. We examine…
It is shown that the full unknown state of a spin-1/2 system, S, which, within Born's statistical interpretation, is meant as the state of an ensamble of identically prepared systems, can be determined with a simultaneous measurement with…
For a pair of observables, they are called "incompatible", if and only if the commutator between them does not vanish, which represents one of the key features in quantum mechanics. The question is, how can we characterize the…
The measurement problem is to explain why a system which is in a linear combination of states appears, upon measurement, to be in just one of those states. The solution given here is to first show that if one assumes linear, unitary, no…
The Mean King's problem asks to determine the outcome of a measurement that is randomly selected from a set of complementary observables. We review this problem and offer a combinatorial solution. More generally, we show that whenever an…
Three-dimensional Chern-Simons vector models display an approximate higher spin symmetry in the large $N$ limit. Their single-trace operators consist of a tower of weakly broken currents, as well as a scalar $\sigma$ of approximate twist…
We generalize entanglement detection with covariance matrices for an arbitrary set of observables. A generalized uncertainty relation is constructed using the covariance and commutation matrices, then a criterion is established by…
We explore the joint measurability of incompatible qubit observables on ensembles of parallel and antiparallel spin-1/2 pairs. In parallel configuration, both spins are prepared in the same state, whereas in antiparallel case, each spin is…
We explore the possibility of achieving optimal joint measurements of noncommuting observables on a single quantum system by performing conventional measurements of commuting self adjoint operators on optimal clones of the original quantum…
We analyze the physical meaning of a possible experiment aimed at the simultaneous measurement of two non-commuting spin components. We demonstrate that switching of a strong spin-orbit interaction, e.g., in a solid state or a cold-atom…
In the King's Problem, a physicist is asked to prepare a d-state quantum system in any state of her choosing and give it to a king who measures one of (d+1) sets of mutually unbiased observables on it. The physicist is then allowed to make…
The vector transform operators are investigated; these operators are used at the solution of boundary value problems in piecewise homogeneous spherically symmetric areas. In particular, examples of transformation operators for vector…
We show how one can ascertain the values of four mutually complementary observables of a spin-1 degree of freedom.
We study various optimality criteria for quantum observables. Observables are represented as covariant positive operator valued measures and we consider the case when the symmetry group is compact. Phase observables are examined as an…
During the recent developments of quantum theory it has been clarified that the observable quantities (like energy or position) may be represented by operators (with real spectra) which are manifestly non-Hermitian. The mathematical…
The two observables are complementary if they cannot be measured simultaneously, however they become maximally complementary if their eigenstates are mutually unbiased. Only then the measurement of one observable gives no information about…
Operators that are associated with several important quantities, like angular momentum, play a double role: they are both generators of the symmetry group and ``observables.'' The analysis of different splittings of angular momentum into…
In quantum theory, the retrodiction problem is not as clear as its classical counterpart because of the uncertainty principle of quantum mechanics. In classical physics, the measurement outcomes of the present state can be used directly for…
The situation of two independent observers conducting measurements on a joint quantum system is usually modelled using a Hilbert space of tensor product form, each factor associated to one observer. Correspondingly, the operators describing…
We present two examples of non-Hermitian Hamiltonians which consist of an unperturbed part plus a perturbation that behaves like a vector, in the framework of PT quantum mechanics. The first example is a generalization of the recent work by…