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 how this subset—quantum-state space—might be characterized. Our leading characteristic is that the inner products of the probabilities are bounded, a simple condition with nontrivial consequences. To get quantum-state space something more detailed about the extreme points is needed. No definitive characterization is reached, but we see several new interesting features over those in Fuchs and Schack (arXiv:0906.2187v1, 2009), and all in conformity with quantum theory.
KeywordsQuantum-state space SIC-POVM Bayesian Interpretation
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- 1.Fuchs, C.A., Schack, R.: Quantum-Bayesian coherence. arXiv:0906.2187v1 [quant-ph] (2009)
- 3.Barnum, H., Barrett, J., Leifer, M., Wilce, A.: Cloning and broadcasting in generic probabilistic models. arXiv:quant-ph/0611295v1 (2006)
- 4.Barnum, H., Barrett, J., Leifer, M., Wilce, A.: Teleportation in general probabilistic theories. 0805.3553v1 [quant-ph] (2008)
- 5.Fuchs, C.A., Schack, R.: A quantum-Bayesian route to quantum-state space. arXiv:0912.4252v1 [quant-ph] (2009)
- 6.Sullivant, S.: Statistical models are algebraic varieties. Posted at http://www.math.harvard.edu/~seths/lecture1.pdf
- 7.Caves, C.M.: Symmetric informationally complete POVMs. Internal report 9 September 1999, posted at http://info.phys.unm.edu/~caves/reports/infopovm.pdf
- 13.Appleby, D.M., Dang, H.B., Fuchs, C.A.: Physical significance of symmetric informationally-complete sets of quantum states. arXiv:0707.2071v1 [quant-ph] (2007)
- 14.Scott, A.J.: Ongoing web-document SIC-POVMs. Posted at http://www.cit.gu.edu.au/~ascott/sicpovms/ (2009)
- 15.Scott, A.J., Grassl, M.: SIC-POVMs: A new computer study. arXiv:0910.5784v2 [quant-ph] (2009)