Related Experiment Video
Updated: May 18, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
Published on: May 30, 2014
Optimal unambiguous discrimination of pure quantum states
János A Bergou1, Ulrike Futschik, Edgar Feldman
1Department of Physics and Astronomy, CUNY Hunter College, 695 Park Avenue, New York, New York 10065, USA.
Abstract:
A complete geometric view is presented for the optimal unambiguous discrimination among N > 2 pure states. A single intuitive picture contains all aspects of the problem: linear independence of the states, positivity of the detection operators, and a graphic method for finding and classifying the optimal solutions. The method is illustrated on the example of three states. We show that the problem depends on the phases of the complex inner products only through an invariant combination, the Berry phase φ, and present complete analytical results for φ = 0 and φ = π. The optimal solution exhibits full permutational symmetry and is single valued for a large range of parameters. However, for φ = 0 it can be bivalued: beyond a critical value of the parameters a second, less symmetric solution becomes optimal. The bifurcation is analogous to a second-order symmetry-breaking phase transition. We conclude with a discussion of the unambiguous discrimination of N > 3 states.
Related Concept Videos
The Uncertainty Principle
The Pauli Exclusion Principle
¹H NMR: Interpreting Distorted and Overlapping Signals
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
Atomic Nuclei: Nuclear Spin State Overview
Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule
UV–Vis Spectroscopy: Molecular Electronic Transitions
