# Representation of Quantum States as Points in a Probability Simplex Associated to a SIC-POVM

@article{Rosado2011RepresentationOQ,
title={Representation of Quantum States as Points in a Probability Simplex Associated to a SIC-POVM},
journal={Foundations of Physics},
year={2011},
volume={41},
pages={1200-1213}
}
• Published 5 July 2010
• Mathematics
• Foundations of Physics
The quantum state of a d-dimensional system can be represented by a probability distribution over the d2 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 (d2−1)-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…
12 Citations
Geometry of Quantum States from Symmetric Informationally Complete Probabilities
It is usually taken for granted that the natural mathematical framework for quantum mechanics is the theory of Hilbert spaces, where pure states of a quantum system correspond to complex vectors of
PROBING THE GEOMETRY OF QUANTUM STATES WITH SYMMETRIC POVMS
The geometry of the Quantum State Space, described by Bloch vectors, is a very intricate one. A deeper understanding of this geometry could lead to the solution of some difficult problems in Quantum
Exploring the geometry of qutrit state space using symmetric informationally complete probabilities
• Mathematics
• 2013
We examine the geometric structure of qutrit state space by identifying the outcome probabilities of symmetric informationally complete (SIC) measurements with quantum states. We categorize the
The SIC Question: History and State of Play
• Computer Science
Axioms
• 2017
Computer calculations have now furnished solutions in all dimensions up to 151, and in several cases beyond that, as large as dimension 844.
Some Negative Remarks on Operational Approaches to Quantum Theory
• Art
• 2014
This talk hopes to expand on points and convey some sense of why the author is fascinated with the problem of the symmetric informationally complete POVMs to an extent greater than axiomatic reconstructions.
The similarity to quantum state space, generalised qplexes and 2-designs
• Mathematics
• 2019
We study the class of quantum measurements with the property that the image of the set of quantum states under the measurement map is similar to this set. This leads to the notion of generalised
Morphophoric POVMs, generalised qplexes,ewline and 2-designs
• Mathematics
• 2020
We study the class of quantum measurements with the property that the image of the set of quantum states under the measurement map transforming states into probability distributions is similar to
Relaxation equations for the qubit in the tomographic representation
• Physics, Mathematics
• 2011
Within the framework of the tomographic-probability representation of quantum mechanics, we revisit the problem of the qubit evolution and show that the dynamics can be efficiently separated into two
A Mathematical Framework of Human Thought Process: Rectifying Software Construction Inefficiency and Identifying Characteristic Efficiencies of Networked Systems Via Problem-solution Cycle
A MATHEMATICAL FRAMEWORK OF HUMAN THOUGHT PROCESS: RECTIFYING SOFTWARE CONSTRUCTION INEFFICIENCY AND IDENTIFYING CHARACTERISTIC EFFICIENCIES OF NETWORKED SYSTEMS VIA PROBLEM-SOLUTION CYCLE by
Multiclass classification of dephasing channels
• Physics
Physical Review A
• 2021
Adriano M. Palmieri, ∗ Federico Bianchi, † Matteo G. A. Paris, 4, ‡ and Claudia Benedetti § Skolkovo Institute of Science and Technology, 121205 Moscow, Russia Bocconi University, I-20136 Milan,

## References

SHOWING 1-9 OF 9 REFERENCES
A Quantum-Bayesian Route to Quantum-State Space
• Physics
• 2011
In the quantum-Bayesian approach to quantum foundations, a quantum state is viewed as an expression of an agent’s personalist Bayesian degrees of belief, or probabilities, concerning the results of
Properties of QBist State Spaces
• Mathematics
• 2009
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.
Symmetric informationally complete quantum measurements
• Mathematics
• 2003
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.
Quantum Mechanics as Quantum Information
This thesis analyzes the epistemological implications and the role of basic concepts like information, physical law and matter in characterizing the physical reality. The key point will be a quantum
Geometry of Quantum States
• Physics
• 2007
a ) p. 131 The discussion between eqs. (5.14) and (5.15) is incorrect (dA should be made as large as possible!). b ) p. 256 In the figure, the numbers 6) and 7) occur twice. c ) p. 292 At the end of
The Bloch-Vector Space for N-Level Systems: the Spherical-Coordinate Point of View
• Mathematics
Open Syst. Inf. Dyn.
• 2005
A dual property of the space is found which provides an overall picture of thespace and three classes of quantum-state representations based on actual measurements and discuss their state-spaces are provided.
Quantum Mechanics as Quantum Information (and only a little more)
In this paper, I try once again to cause some good-natured trouble. The issue remains, when will we ever stop burdening the taxpayer with conferences devoted to the quantum foundations? The suspicion