Two mode squeezing for multi-parameter metrology on a bosonic cQED platform

One of the fundamental principles of quantum mechanics is the Heisenberg uncertainty relation, which states that simultaneous knowledge of two non-commuting observables in any given state cannot be infinitely precise. Multi-parameter metrology aims to maximize the precision with which multiple observables can be measured. In this presentation, we introduce a scheme that leverages entanglement and squeezing in the form of a two-mode squeezed vacuum state (TMSV) to circumvent the Heisenberg uncertainty relation, enabling precise measurements of both position (x) and momentum (p). Furthermore, we propose an efficient and practical design for implementing this protocol using known elements in a bosonic cQED device.