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Note on the saturation of the norm inequalities between diamond and nuclear norm
Ulrich Michel, Martin Kliesch, Richard Kueng +1
The diamond norm plays an important role in quantum information and operator theory. Recently, it has also been proposed as a regularizer for low-rank matrix recovery. The norm con…
Low rank matrix recovery from Clifford orbits
Richard Kueng, Huangjun Zhu, David Gross
We prove that low-rank matrices can be recovered efficiently from a small number of measurements that are sampled from orbits of a certain matrix group. As a special case, our theo…
Distinguishing quantum states using Clifford orbits
Richard Kueng, Huangjun Zhu, David Gross
It is a fundamental property of quantum mechanics that information is lost as a result of performing measurements. Indeed, with every quantum measurement one can associate a number…
The Clifford group fails gracefully to be a unitary 4-design
Huangjun Zhu, Richard Kueng, Markus Grassl +1
A unitary t-design is a set of unitaries that is "evenly distributed" in the sense that the average of any t-th order polynomial over the design equals the average over the entire…
Explaining quantum correlations through evolution of causal models
Robin Harper, Robert J. Chapman, Christopher Ferrie +5
We propose a framework for the systematic and quantitative generalization of Bell's theorem using causal networks. We first consider the multi-objective optimization problem of mat…
Robust Nonnegative Sparse Recovery and the Nullspace Property of 0/1 Measurements
Richard Kueng, Peter Jung
We investigate recovery of nonnegative vectors from non-adaptive compressive measurements in the presence of noise of unknown power. In the absence of noise, existing results in th…