Abstract
The quantum state of a d-dimensional system can be represented by a probability distribution over the d 2 outcomes of a Symmetric Informationally Complete Positive Operator Valued Measure (SIC-POVM), and then this probability distribution can be represented by a vector of \(\mathbb {R}^{d^{2}-1}\) in a (d 2−1)-dimensional simplex, we will call this set of vectors \(\mathcal{Q}\). Other way of represent a d-dimensional system is by the corresponding Bloch vector also in \(\mathbb {R}^{d^{2}-1}\), we will call this set of vectors \(\mathcal{B}\). In this paper it is proved that with the adequate scaling \(\mathcal{B}=\mathcal{Q}\). Also we indicate some features of the shape of \(\mathcal{Q}\).
Similar content being viewed by others
References
Appleby, D.M., Ericsson, A., Fuchs, C.A.: Properties of qbist state spaces. http://arxiv.org/abs/0910.2750
Bengtsson, I., Życzkowski, K.: Geometry of Quantum States. Cambridge University Press, Cambridge (2006)
Fuchs, C.A.: Quantum mechanics as quantum information (and only a little more). http://arxiv.org/abs/quant-ph/0205039 (2002)
Fuchs, C.A., Schack, R.: A quantum-Bayesian route to quantum-state space. Foundations of Physics (2010)
Keyl, M.: Fundamentals of quantum information theory. Phys. Rep. 369, 431–548 (2002)
Kimura, G.: The Bloch vector for n-level systems. Phys. Lett. A 314, 339–349 (2003)
Kimura, G., Kossakowski, A.: The Bloch-vector space for n-level systems: the spherical-coordinate point of view. Open Syst. Inf. Dyn. 12, 207–229 (2005)
Renes, J.M., Blume-Kohout, R., Scott, A.J., Caves, C.M.: Symmetric informationally complete quantum measurements. J. Math. Phys. 45, 2171–2180 (2004)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rosado, J.I. Representation of Quantum States as Points in a Probability Simplex Associated to a SIC-POVM. Found Phys 41, 1200–1213 (2011). https://doi.org/10.1007/s10701-011-9540-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10701-011-9540-9