Tight informationally complete quantum measurements
A. J. Scott
Abstract
We introduce a class of informationally complete positive-operator-valued measures which are, in analogy with a tight frame, "as close as possible" to orthonormal bases for the space of quantum states. These measures are distinguished by an exceptionally simple state-reconstruction formula which allows "painless" quantum state tomography. Complete sets of mutually unbiased bases and symmetric informationally complete positive-operator-valued measures are both members of this class, the latter being the unique minimal rank-one members. Recast as ensembles of pure quantum states, the rank-one members are in fact equivalent to weighted 2-designs in complex projective space. These measures are shown to be optimal for quantum cloning and linear quantum state tomography.
Create a lesson
Related papers
Approximate Synthetic Spectra of Quantum Systems Associated with Compact Lie Groups
Junyang Liu, Hang Wang, Houjin Wang et al.
An example of universal braiding in Links--Gould topological quantum computation
Matthew Harper, Ben-Michael Kohli
Reasoning about Shared-Qubit Concurrency in Quantum Computing
Mingsheng Ying
Information-Geometric Representation of Upper Bounds on Fluctuation Growth in Open Quantum Systems
Newshaw Bahreyni, Paul M. Alsing
Initialization-controlled fault sensitivity and force-balance plateaus in noisy variational quantum optimization
Longhui Shen, Fangzhou Jin, Bin Guo
Quantum identity authentication protocol via perturbed probability amplitudes
Xiangqun Fu, Zheng Han, Hongwei Li et al.