REVIEW 2 cited by
An Analysis of Completely-Positive Trace-Preserving Maps on 2x2 Matrices
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
read the original abstract
We give a useful new characterization of the set of all completely positive, trace-preserving (i.e., stochastic) maps from 2x2 matrices to 2x2 matrices. These conditions allow one to easily check any trace-preserving map for complete positivity. We also determine explicitly all extreme points of this set, and give a useful parameterization after reduction to a certain canonical form. This allows a detailed examination of an important class of non-unital extreme points which can be characterized as having exactly two images on the Bloch sphere. We also discuss a number of related issues about the images and the geometry of the set of stochastic maps, and show that any stochastic map on 2x2 matrices can be written as a convex combination of two "generalized" extreme points.
Forward citations
Cited by 2 Pith papers
-
Efficient simulation of parametrized quantum circuits under non-unital noise through Pauli backpropagation
Pauli backpropagation classically simulates parameterized quantum circuits under non-unital noise in polynomial time in the average (L2) sense over the parameter landscape.
-
Quantum communication and fault-tolerance
The thesis proves that fault-tolerant encoder and decoder circuits can achieve entanglement-assisted communication rates close to the ideal capacity, and reports trapped-ion error-detection experiments plus a new boun...
Discussion (0). Continue with ORCID to comment.