725 research outputs found

### Maps on density operators preserving quantum f-divergences

For an arbitrary strictly convex function f defined on the
non-negative real line we determine the structure of all transformations
on the set of density operators which preserve the quantum f-divergence

### Structure of sufficient quantum coarse-grainings

Let H and K be Hilbert spaces and T be a coarse-graining from B(H) to B(K).
Assume that density matrices D_1 and D_2 acting on H are given. In the paper
the consequences of the existence of a coarse-graining S from B(K) to B(H)
satisfying ST(D_1)=D_1 and ST(D_2)=D_2 are given. (This condition means the
sufficiency of T for D_1 and D_2.) Sufficiency implies a particular
decomposition of the density matrices. This decomposition allows to deduce the
exact condition for equality in the strong subadditivity of the von Neumann
entropy.Comment: 13 pages, LATE

### Complementarity and the algebraic structure of 4-level quantum systems

The history of complementary observables and mutual unbiased bases is
reviewed. A characterization is given in terms of conditional entropy of
subalgebras. The concept of complementarity is extended to non-commutative
subalgebras. Complementary decompositions of a 4-level quantum system are
described and a characterization of the Bell basis is obtained.Comment: 19 page

### Large deviations for functions of two random projection matrices

In this paper two independent and unitarily invariant projection matrices
P(N) and Q(N) are considered and the large deviation is proven for the
eigenvalue density of all polynomials of them as the matrix size $N$ converges
to infinity. The result is formulated on the tracial state space $TS({\cal A})$
of the universal $C^*$-algebra ${\cal A}$ generated by two selfadjoint
projections. The random pair $(P(N),Q(N))$ determines a random tracial state
$\tau_N \in TS({\cal A})$ and $\tau_N$ satisfies the large deviation. The rate
function is in close connection with Voiculescu's free entropy defined for
pairs of projections.Comment: 22 page

### Symmetry Reduction of Quasi-Free States

Given a group-invariant quasi-free state on the algebra of canonical
commutation relations (CCR), we show how group averaging techniques can be used
to obtain a symmetry reduced CCR algebra and reduced quasi-free state. When the
group is compact this method of symmetry reduction leads to standard results
which can be obtained using other methods. When the group is non-compact the
group averaging prescription relies upon technically favorable conditions which
we delineate. As an example, we consider symmetry reduction of the usual vacuum
state for a Klein-Gordon field on Minkowski spacetime by a non-compact subgroup
of the Poincar\'e group consisting of a 1-parameter family of boosts, a
1-parameter family of spatial translations and a set of discrete translations.
We show that the symmetry reduced CCR algebra and vacuum state correspond to
that used by each of Berger, Husain, and Pierri for the polarized Gowdy ${\bf
T}^3$ quantum gravity model.Comment: 18 page

### Point Estimation of States of Finite Quantum Systems

The estimation of the density matrix of a $k$-level quantum system is studied
when the parametrization is given by the real and imaginary part of the entries
and they are estimated by independent measurements. It is established that the
properties of the estimation procedure depend very much on the invertibility of
the true state. In particular, in case of a pure state the estimation is less
efficient. Moreover, several estimation schemes are compared for the unknown
state of a qubit when one copy is measured at a time. It is shown that the
average mean quadratic error matrix is the smallest if the applied observables
are complementary. The results are illustrated by computer simulations.Comment: 16 pages, 5 figure

### On Mutual Information in Multipartite Quantum States and Equality in Strong Subadditivity of Entropy

The challenge of equality in the strong subadditivity inequality of entropy
is approached via a general additivity of correlation information in terms of
nonoverlapping clusters of subsystems in multipartite states (density
operators). A family of tripartite states satisfying equality is derived.Comment: 8 pages; Latex2e and Revtex

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