Mutually unbiased product bases for multiple qudits

Journal Article · Tue Mar 15 00:00:00 EDT 2016 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4943301· OSTI ID:22597047

McNulty, Daniel ^[1]; Pammer, Bogdan ^[2]; Weigert, Stefan ^[3]

---

1. Department of Optics, Palacký University, 17. listopadu 12, 771 46 Olomouc, Czech Republic and Department of Applied Mathematics, Hanyang University (ERICA), 55 Hanyangdaehak-ro, Ansan, Gyeonggi-do 426-791 (Korea, Republic of)
2. Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna (Austria)
3. Department of Mathematics, University of York, York YO10 5DD (United Kingdom)

We investigate the interplay between mutual unbiasedness and product bases for multiple qudits of possibly different dimensions. A product state of such a system is shown to be mutually unbiased to a product basis only if each of its factors is mutually unbiased to all the states which occur in the corresponding factors of the product basis. This result implies both a tight limit on the number of mutually unbiased product bases which the system can support and a complete classification of mutually unbiased product bases for multiple qubits or qutrits. In addition, only maximally entangled states can be mutually unbiased to a maximal set of mutually unbiased product bases.

• OSTI ID: 22597047
• Journal Information: Journal of Mathematical Physics, Vol. 57, Issue 3; Other Information: (c) 2016 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
QUANTUM ENTANGLEMENT
QUANTUM INFORMATION
QUANTUM SYSTEMS