arXiv subjects

Asa Ericsson

Publications and source records attributed to Asa Ericsson.

7 recordsLinked to original sources

arXiv2011

Properties of QBist State Spaces

Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought of as a restricted subset of all potentially available probabilities. A recent publication [1] advocates such a representation using symmetric informationally complete (SIC) measurements. Building upon this work we study how this subset--quantum-state space--might be characterized. Our leading characteristic is that the inner products of the probabilities are bounded, a simple condition with nontrivial consequences. To get quantum-state space something more detailed about the extreme points is needed. No definitive characterization is reached, but we see several new interesting features over those in [1], and all in conformity with quantum theory.

quant-ph↗

arXiv2008

Effects of the $g$-factor in semi-classical kinetic plasma theory

A kinetic theory for spin plasmas is put forward, generalizing those of previous authors. In the model, the ordinary phase space is extended to include the spin degrees of freedom. Together with Maxwell's equations, the system is shown to be energy conserving. Analysing the linear properties, it is found that new types of wave-particle resonances are possible, that depend directly on the anomalous magnetic moment of the electron. As a result new wave modes, not present in the absence of spin, appear. The implications of our results are discussed.

physics.plasm-ph↗

arXiv2006

Mubs and Hadamards of Order Six

We report on a search for mutually unbiased bases (MUBs) in 6 dimensions. We find only triplets of MUBs, and thus do not come close to the theoretical upper bound 7. However, we point out that the natural habitat for sets of MUBs is the set of all complex Hadamard matrices of the given order, and we introduce a natural notion of distance between bases in Hilbert space. This allows us to draw a detailed map of where in the landscape the MUB triplets are situated. We use available tools, such as the theory of the discrete Fourier transform, to organise our results. Finally we present some evidence for the conjecture that there exists a four dimensional family of complex Hadamard matrices of order 6. If this conjecture is true the landscape in which one may search for MUBs is much larger than previously thought.

quant-ph↗

arXiv2005

Geodesics and the best measurement for distinguishing quantum states

From statistical distinguishability of probability distributions, one can define distinguishability of quantum states. A corresponding measurement to perform, optimal in a definite sense, for distinguishing between two given states rho_A and rho_B, has been derived by Fuchs and Caves. We show that the Bures-Uhlmann geodesic through the two states singles out this measurement. The geodesic `bounces' at the boundary of the set of quantum states. Whenever the geodesic hits the boundary, the state orthogonal to that boundary state is one of the basis states for the measurement.

quant-ph↗

arXiv2004

Mutually Unbiased Bases and The Complementarity Polytope

A complete set of N+1 mutually unbiased bases (MUBs) forms a convex polytope in the N^2-1 dimensional space of NxN Hermitian matrices of unit trace. As a geometrical object such a polytope exists for all values of N, while it is unknown whether it can be made to lie within the body of density matrices unless N=p^k, where p is prime. We investigate the polytope in order to see if some values of N are geometrically singled out. One such feature is found: It is possible to select N^2 facets in such a way that their centers form a regular simplex if and only if there exists an affine plane of order N. Affine planes of order N are known to exist if N=p^k; perhaps they do not exist otherwise. However, the link to the existence of MUBs--if any--remains to be found.

quant-ph↗

arXiv2004

Birkhoff's polytope and unistochastic matrices, N=3 and N=4

The set of bistochastic or doubly stochastic N by N matrices form a convex set called Birkhoff's polytope, that we describe in some detail. Our problem is to characterize the set of unistochastic matrices as a subset of Birkhoff's polytope. For N=3 we present fairly complete results. For N=4 partial results are obtained. An interesting difference between the two cases is that there is a ball of unistochastic matrices around the van der Waerden matrix for N=3, while this is not the case for N=4.

math.CO↗

arXiv2003

How to mix a density matrix

A given density matrix may be represented in many ways as a mixture of pure states. We show how any density matrix may be realized as a uniform ensemble. It has been conjectured that one may realize all probability distributions that are majorized by the vector of eigenvalues of the density matrix. We show that if the states in the ensemble are assumed to be distinct then it is not true, but a marginally weaker statement may still be true.

quant-ph↗