Quasi-probability representations of quantum theory with applications to quantum information science

By C. Ferrie. 2010

188 citations recorded by the source corpus.

This paper comprises a review of both the quasi-probability representations of infinite-dimensional quantum theory (including the Wigner function) and the more recently defined quasi-probability representations of finite-dimensional quantum theory. We focus on both the characteristics and applications of these representations with an emphasis toward quantum information theory. We discuss the recently proposed unification of the set of possible quasi-probability representations via frame theory and then discuss the practical relevance of negativity in such representations as a criteria for quantumness.

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

View Paper: https://www.semanticscholar.org/paper/e1d64e5083df01db0a8df96a4c00de601ac6a8c4

How researchers see this paper

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

In Applied Mathematics

1. David Gross
2. Victor Veitch
3. Joseph Emerson
4. C. Ferrie

In Artificial Intelligence

1. Joseph Emerson
2. Victor Veitch
3. David Gross
4. C. Ferrie
5. E.J. Candes
6. Justin K. Romberg
7. B. Recht
8. John Wright

In Atomic and Molecular Physics, and Optics

1. Victor Veitch
2. Joseph Emerson
3. David Gross
4. C. Ferrie
5. Gilad Gour
6. Andreas J. Winter
7. Zi-Wen Liu
8. Eric Chitambar

Citations in the corpus

• Negative quasi-probability as a resource for quantum computation (2012, methodology): “Our approach is to exploit the freedom in choice of quasi-probability representations (Ferrie 2011) in order to align the positive subtheory with the operational restriction defining the error-free resources in the magic state model.”
• Corrigendum: Negative quasi-probability as a resource for quantum computation (2012, methodology): “Our approach is to exploit the freedom in choice of quasi-probability representations [18] in order to align the positive subtheory with the operational restriction defining the error-free resources in the magic-state model.”