3 research outputs found
Minimum error discrimination of Pauli channels
We solve the problem of discriminating with minimum error probability two
given Pauli channels. We show that, differently from the case of discrimination
between unitary transformations, the use of entanglement with an ancillary
system can strictly improve the discrimination, and any maximally entangled
state allows to achieve the optimal discrimination. We also provide a simple
necessary and sufficient condition in terms of the structure of the channels
for which the ultimate minimum error probability can be achieved without
entanglement assistance. When such a condition is satisfied, the optimal input
state is simply an eigenstate of one of the Pauli matrices.Comment: 8 pages, no figure
Trace distance from the viewpoint of quantum operation techniques
In the present paper, the trace distance is exposed within the quantum
operations formalism. The definition of the trace distance in terms of a
maximum over all quantum operations is given. It is shown that for any pair of
different states, there are an uncountably infinite number of maximizing
quantum operations. Conversely, for any operation of the described type, there
are an uncountably infinite number of those pairs of states that the maximum is
reached by the operation. A behavior of the trace distance under considered
operations is studied. Relations and distinctions between the trace distance
and the sine distance are discussed.Comment: 26 pages, no figures. The bibliography is extended, explanatory
improvement
Symmetry protection of measurement-based quantum computation in ground states
The two-dimensional cluster state, a universal resource for measurement-based
quantum computation, is also the gapped ground state of a short-ranged
Hamiltonian. Here, we examine the effect of perturbations to this Hamiltonian.
We prove that, provided the perturbation is sufficiently small and respects a
certain symmetry, the perturbed ground state remains a universal resource. We
do this by characterising the operation of an adaptive measurement protocol
throughout a suitable symmetry-protected quantum phase, relying on generic
properties of the phase rather than any analytic control over the ground state.Comment: 20 pages plus appendices, 11 figures, comments very welcome; v2 minor
corrections and additional references; v3 published version with minor
correction