Small sets of complementary observables

• Main Authors: Grassl, M., McNulty, D., Mišta, L., Paterek, Tomasz
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2017
• Subjects: Complementary observables; Quantum theory
• Online Access: https://hdl.handle.net/10356/84128; http://hdl.handle.net/10220/42938
• Institution: Nanyang Technological University

Two observables are called complementary if preparing a physical object in an eigenstate of one of them yields a completely random result in a measurement of the other. We investigate small sets of complementary observables that cannot be extended by yet another complementary observable. We construct explicit examples of unextendible sets up to dimension 16 and conjecture certain small sets to be unextendible in higher dimensions. Our constructions provide three complementary measurements, only one observable away from the ultimate minimum of two. Almost all our examples in finite dimensions are useful for discriminating pure states from some mixed states, and they help to shed light on the complex topology of the Bloch space of higher-dimensional quantum systems.