The **Workshop on Applied Quantum Mechanics**, organized by

Marco Genoni within the framework of the H2020 project ConAquMe (Quantum Control for Advanced Quantum Metrology), will take place at the Physics Department of Unimi, LITA building, fifth floor, on *Wednesday, 20th September *starting at *10:30*.

### Program

10:30 — Matteo Lostaglio (ICFO, Barcelona)

*Elementary Thermal Operations*

11:30 — Francesco Albarelli (UniMi)

*Resource theories of non-Gaussianity*

12:30 — Lunch break

14:30 — Jeongwoo Jae (Hanyang University, Seoul)

*Operational quasi-probability for continuous-variable systems*

15:30 — Luigi Seveso (UniMi)

*Building all orthogonal arrays from quantum theory*

### Abstracts

### Elementary Thermal Operations

Matteo Lostaglio (ICFO, Barcelona)

To what extent do thermodynamic resource theories capture physically relevant constraints? Inspired by quantum computation, we define a set of elementary thermodynamic gates that only act on 2 energy levels of a system at a time. We show that this theory is well reproduced by a Jaynes-Cummings interaction in rotating wave approximation and draw a connection to standard descriptions of thermalisation. We then prove that elementary thermal operations present tighter constraints on the allowed transformations than thermal operations. Mathematically, this illustrates the failure at finite temperature of fundamental theorems by Birkhoff and Muihead-Hardy-Littlewood-Polya concerning stochastic maps. Physically, this implies that stronger constraints can be given if we tailor a thermodynamic resource theory to the relevant experimental scenario. We provide new tools to do so, including necessary and sufficient conditions for a given change of the population to be possible. As an example, we describe the resource theory of the Jaynes-Cummings model. Finally, we initiate an investigation into how our resource theories can be applied to Heat Bath Algorithmic Cooling protocols.

#### Resource theories of non-Gaussianity

Francesco Albarelli (UniMI)

The quantum information community has devoted a lot of attention to resource theories related to many different tasks. I will present and discuss different resource theories for the non-Gaussian/nonclassical character of continuous variable (CV) quantum systems. In particular I will focus on a monotone derived from the volume of the negative part of the Wigner function, called “mana”, which can be computed for many states. The discrete variable (DV) version of this resource monotone was already introduced and studied in [NJP 16, 013009 (2014)] to address the problem of magic state distillation. Distillation of of magic states is one of the most important ingredients in a feasible path to fault-tolerant quantum computation, but a direct CV counterpart of this protocol is still lacking. Nonetheless I will show that this resource theoretical point of view can be useful to analyse protocols for probabilistic state engineering through Gaussian operations and I will present some results from this analysis.

#### Operational quasi-probability for continuous-variable systems

Jeongwoo Jae (Hanyang University, Seoul)

We generalize the operational quasi-probability involving sequential measurements proposed by Ryu et al. [Phys. Rev. A 88, 052123] to a continuous-variable system. The quasi-probabilities such as Wigner, Q-, P- function and their classical counterparts represent a given physical observation in different mathematical forms. Also, their negative values in quasi-probability can be positive in another. These may be regarded as obstacles in operationally interpreting the negative values and the former is called “incommensurability” of quasi-probabilities. The operational quasi-probability satisfies the commensurability, enabling to compare quantum and classical statistics on the same footing. We show that it can be negative for various states of light against the hypothesis of macroscopic realism. Quadrature variables of light are our examples of continuous variables. We also compare our approach to Glauber-Sudarshan P-function. In addition, we suggest an experimental scheme to sequentially measure the quadrature variables of light.

#### Building all orthogonal arrays from quantum theory

Luigi Seveso (UniMI)

Orthogonal arrays are combinatorial designs first introduced by Rao in 1947. Since then, they have found a wealth of applications in applied mathematics, ranging from cryptography and coding theory to the statistical design of experiments, software testing and quality control. Recently, orthogonal arrays have found a new surprising use in the characterization of entanglement in multipartite quantum systems.

In this talk, we further explore the connection between orthogonal arrays and quantum mechanics. We propose a constructive technique to represent the full set of orthogonal arrays in terms of a finite set of generators. The corresponding quantum states turn out to play an important role in quantum mechanics: they exhibit a high degree of multipartite entanglement and include the full set of maximum distance separable codes. We provide a general construction of the generators and show explicit solutions for orthogonal arrays composed of two, three and four columns and two symbols.