MAWI Trieste Conference

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Tuesday 18th February

Luca Pezze

This is a continuation of similar seminars done in MAWI’s Grenoble Conference. Similar in nature to the Quantum theory of phase estimation.

We have:

• $J_z=\frac{N_a-N_b}{2}$ as the number difference between the two arms of the Mach-Zehnder interferometer
• $\theta :={\theta }_a-{\theta }_b$ as our relative phase.
• $⟨J_z⟩=\frac{N}{2}\cos (\theta )$
• $(\Delta \theta {)}^2=\frac{(\Delta J_z{)}_{out}^2}{m(\frac{(J_z{)}_{out}}{\theta }{)}^2}=\frac{1}{mN}$.

Goal: We want to generalize the approach given in MAWI’s Grenoble Conference to other systems.

We describe our system with three components:

1. A Probe state $\rho$ describing the initial state of the system.
2. A transformation ${\Lambda }_{\theta }$ describing a Unitary Operator parameterized by $\theta$. This leads to a final state ${\rho }_{\theta }={\Lambda }_{\theta }[\rho ]$, which formally is equivalent to ${\rho }_{\theta }=e^{-i{H}_{\theta }}\rho e^{iH\theta }$.
3. A measurement $E_{\mu }$,, described as a POVM.

With the above setup, we are able to build an estimator for $\theta$ based on our measurements $E_{\mu }$. For example, we can have ${\theta }_{EST}={\sum }_{\mu }\mathbb{P}[\mu |\theta ]{\theta }_{est}(\mu )$ and associated variance $(\Delta {\theta }_{EST}{)}^2={\sum }_{\mu }\mathbb{P}(\mu |\theta )({\theta }_{EST}(\mu )-{\bar{\theta }}_{EST}{)}^2$. We aim to choose among all possible statistical estimators, probes and Measurements, the one that minimizes our uncertainty $(\Delta {\theta }_{EST}{)}^2$. Our ability to minimize this is bounded by the Cramer Rao bound.

Natalia Bruno

Experimental Quantum Optics and Quantum Information Keywords: Photon bunching See: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.39.691

Marco Fattori

Dell’antonio

Calabrese

Perrin

Fabio Benatti

Keywords: Back-flow of information, Super activation of BFI, Collisional models. Very similar in content to the Complete Positivity and Quantum Information Systems class :)

Thomas Fernholz

Blas

Wednesday 19th February

Luca Pezze ( continuation )

Keywords: Quantum Fisher information Matrix,

Christian Koller

Hsu Chung Chuan ( Michael)

Keywords: LIGO

Greta Firenze

Keywords: Gradiometry

Angelo Bassi

Keywords: Continuous Spontaneous Localization See: Collapse dynamics are diffusive

Amtmann

Francesco Scazza

Biella

Franchini

Thursday 20th

Krueger

Mairhofer