# Seminar on Condensed Matter Theory

Group of Theoretical Physics at the Department of Condensed Matter Physics

of Charles University has a pleasure to invite you to attend the seminar

on 9th November 2023 at 13:00

at Faculty of Mathematics and Physics of Charles University, Ke Karlovu 5, 121 16 Praha 2

Seminar room **F 052**

### prof. RNDr. Zdenek Hradil, CSc.

#### Department of Optics, Palacky University, 17. listopadu 12, 771 46 Olomouc, Czech Republic

## Uncertainty relations, simultaneous measurement, and phase-space representation for angle and angular momentum: new twist for an old pair

# prof. RNDr. Zdenek Hradil, CSc. » Uncertainty relations, simultaneous measurement, and phase-space representation for angle and angular momentum: new twist for an old pair

*Department of Optics, Palacky University, 17. listopadu 12, 771 46 Olomouc, Czech Republic*

Location: Seminar room KFKL, MFF UK (room F052 - ground floor near the rear staircase, Ke Karlovu 5)

Reaching ultimate performance of quantum technologies requires the use of detection at quantum limits and access to all resources of the underlying physical system. We establish a full quantum analogy between the pair of angular momentum and exponential angular variable, and the structure of canonically conjugate position and momentum. This includes the notion of optimal simultaneous measurement of the angular momentum and angular variable, the identification of Einstein-Podolsky-Rosen-like variables and states, and, finally, a phase- space representation of quantum states. Our construction is based on close interconnection of the three concepts and may serve as a template for the treatment of other complementary observables. This theory also provides a test bed for implementation of quantum technologies combining discrete and continuous quantum variables.