Properties of QBist State Spaces

@article{Appleby2009PropertiesOQ,
  title={Properties of QBist State Spaces},
  author={David Marcus Appleby and {\AA}sa Ericsson and Christopher A. Fuchs},
  journal={Foundations of Physics},
  year={2009},
  volume={41},
  pages={564-579}
}
Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought of as a restricted subset of all potentially available probabilities. A recent publication (Fuchs and Schack, arXiv:0906.2187v1, 2009) advocates such a representation using symmetric informationally complete (SIC) measurements. Building upon this work we study… 
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References

SHOWING 1-10 OF 17 REFERENCES
Symmetric informationally complete quantum measurements
TLDR
It is conjecture that a particular kind of group-covariant SIC–POVM exists in arbitrary dimensions, providing numerical results up to dimension 45 to bolster this claim.
Tight informationally complete quantum measurements
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…
Parts of quantum states
It is shown that generic N-party pure quantum states (with equidimensional subsystems) are uniquely determined by their reduced states of just over half the parties; in other words, all the…
Information processing in generalized probabilistic theories
TLDR
A framework in which a variety of probabilistic theories can be defined, including classical and quantum theories, and many others, is introduced, and a tensor product rule for combining separate systems can be derived.
Quantum-Bayesian Coherence
TLDR
It is argued that the Born Rule should be seen as an empirical addition to Bayesian reasoning itself, and how to view it as a normative rule in addition to usual Dutch-book coherence is shown.
Tomography of Quantum States in Small Dimensions
  • M. Grassl
  • Mathematics
    Electron. Notes Discret. Math.
  • 2005
About SIC POVMs and discrete Wigner distributions
A set of d2 vectors in a Hilbert space of dimension d is called equiangular if each pair of vectors encloses the same angle. The projection operators onto these vectors define a POVM which is…
Symmetric Informationally Complete POVM tomography: theory and applications.
Quantum Tomography is a branch of Quantum Information Theory that deals with the recognition and estimation of quantum states. Our aim is to present a new technique for quantum tomography of quantum…
Cloning and Broadcasting in Generic Probabilistic Theories
We prove generic versions of the no-cloning and no-broadcasting theorems, applicable to essentially {\em any} non-classical finite-dimensional probabilistic model that satisfies a no-signaling…
SIC-POVMs: A new computer study
We report on a new computer study into the existence of d2 equiangular lines in d complex dimensions. Such maximal complex projective codes are conjectured to exist in all finite dimensions and are…
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