Charles Baldwin

Quantum process tomography of unitary and near-unitary maps

Center for Quantum Information and Control, MSC07{4220,University of New Mexico, Albuquerque, New Mexico 87131-0001, USA(Dated: July 25, 2014)We study quantum process tomography given the prior information that the map is a unitary orclose to a unitary process. We show that a unitary map on a d-level system is completely char-acterized by a minimal set of d

Strictly-complete measurements for bounded-rank quantum-state tomography

We study the problem of quantum-state tomography under the assumption that the state of the system is close to pure. In this context, an efficient measurements that one typically formulates uniquely identify a pure state from within the set of other pure states. In general such measurements are not robust in the presence of measurement noise and other imperfections, and therefore are less practical for tomography. We argue here that state tomography experiments should instead be done using measurements that can distinguish a pure state from {\em any} other quantum state, of any rank. We show that such nontrivial measurements follows from the physical constraint that the density matrix is positive semidefinite and prove that these measurements yield a robust estimation of the state. We assert that one can implement such tomography relatively simply by measuring only a few random orthonormal bases; our conjecture is supported by numerical evidence. These results are generalized for estimation of states close to bounded-rank.We consider the problem of quantum-state tomography under the assumption that the state is pure, and more generally that its rank is bounded by a given value. In this scenario, new notions of informationally complete POVMs emerge, which allow for high-fidelity state estimation with fewer measurement outcomes than are required for an arbitrary rank state. We study this in the context of matrix completion, where the POVM outcomes determine only a few of the density matrix elements. We give an analytic solution that fully characterizes informational completeness and elucidates the important role that the positive-semidefinite property of density matrices plays in tomography. We show how positivity can impose a stricter notion of information completeness and allow us to use convex optimization programs to robustly estimate bounded-rank density matrices in the presence of statistical noise.We consider the problem of quantum-state tomography under the assumption that the state is pure, and more generally that its rank is bounded by a given value

The power of being positive: Robust state estimation made possible by quantum mechanics

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Informational completeness in bounded-rank quantum-state tomography

. In this scenario two notions of informationally complete measurements emerge: rank-

Arbitrary Dicke-State Control of Symmetric Rydberg Ensembles

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Joint quantum-state and measurement tomography with incomplete measurements

-complete measurements and rank-

Quantum tomography of near-unitary processes in high-dimensional quantum systems

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Quantum State Tomography of Cold Atom Qudits

strictly-complete measurements. Whereas in the first notion, a rank-

360-degree quantum tomography of a qudit

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The Role of the Global Phase in Optimal Quantum Control to Implement Partial Isometries.

state is uniquely identified from within the set of rank-