Tight informationally complete quantum measurements

By A. J. Scott. 2006

321 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/d2fbe9c92b841b161bee470cc7ceb76a6af54926

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Christopher A. Fuchs
2. C. Ferrie
3. Hsin-Yuan Huang
4. Ruediger Schack
5. Peter Zoller
6. Richard Kueng
7. A. J. Scott
8. John Preskill

In Atomic and Molecular Physics, and Optics

1. Christopher A. Fuchs
2. A. J. Scott
3. C. Ferrie
4. Hsin-Yuan Huang
5. Ruediger Schack
6. Peter Zoller
7. Richard Kueng
8. Steven T. Flammia

Citations in the corpus

• Optimizing quantum process tomography with unitary 2-designs (2007, background): “In this form it is clear that unitary 1-designs are equivalent to tight unitary frames [5, 30].”
• Quasi-probability representations of quantum theory with applications to quantum information science (2010, background): “This definition generalizes a defining condition for an orthogonal basis {Bk}d2k=1 d2∑ k=1 Tr[BkA] 2 = ‖A‖2, (66) 14 Frames have been considered in the context of quantum theory for other purposes in Bisio et al (2009) and Scott (2006). for all A ∈ H(H).”
• Quantum-Bayesian Coherence (2009, background): “ 8i = √1 2 0 1 ω , |ψ 9i = 1 √ 2 ω 0 1 . (24) One can check by quick inspection that this set of vectors satisfies Eq. (20). Do SICs exist for every finite dimension d? Despite much effort [60, 61, 62, 63, 64, 65, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98], no one pre”
• The randomized measurement toolbox (2022, background): “Single-qubit symmetric informationally complete measurements 157,158 seem an ideal candidate, because they may alleviate the need for choosing measurement settings at random while still allowing for fast state reconstruction and fast estimation of arbitrary polynomial functionals of the quantum…”