# Davide Girolami

## Hi, interested reader!

I am a physicist working on quantum information theory. Currently, I am a J. R. Oppenheimer Fellow at Los Alamos National Laboratory. In the project *Optimal Control of Quantum Machines*, I develop methods to obtain optimal control of quantum systems by employing their very peculiar properties, quantum coherence and correlations. Generally, I am interested in the computational properties of quantum systems and the physical limits to information processing. While being a theoretician, I often collaborate with experimentalists in both design and data analysis of quantum information processing implementations.

## My work

For full details, see my CV.

You can find the links to my papers in my Google Scholar profile.

My most significant results answer questions about structure and computational power of quantum systems:

**How difficult is it to prepare a quantum state?**

It is given a quantum system in an input state. One wants to drive it into a target state. Assuming classical states and operations as free resources, I identify a geometric cost function which quantifies the difficulty of the state preparation in terms of how different it is from a classical process. The quantity determines a lower bound to the number of quantum operations, ie unitary transformations, required to complete the task. I then discuss the link between the quantumness of a state preparation and the amount of coherence and quantum correlations that are created in the target state.

*See arXiv:1808.01649 for details.*

**How to quantify genuine k-partite correlations in a system of N particles?**

This is a simple question to phrase, yet no answer was known even for classical systems. We propose an information-theoretic framework to quantify multipartite correlations in classical and quantum systems. We identify measures of genuine multipartite correlations, i.e., statistical dependencies that cannot be ascribed to bipartite correlations, satisfying a set of desirable properties. Inspired by ideas developed in complexity science, we then introduce the concept of weaving to classify states that display different correlation patterns, but cannot be distinguished by correlation measures. The weaving of a state is defined as the weighted sum of correlations of every order. Weaving measures are good descriptors of the complexity of correlation structures in multipartite systems*.*

*See Phys. Rev. Lett. 119, 140505 (2017) for details. *

**How to determine the speed of evolution of a many-body quantum system?**

It turns out that a few local measurements are sufficient! Important properties of a quantum system are not directly measurable, but they can be disclosed by how fast the system changes under controlled perturbations. In particular, asymmetry and entanglement can be verified by reconstructing the state of a quantum system. Yet, this usually requires experimental and computational resources which increase exponentially with the system size. We show how to detect metrologically useful asymmetry and entanglement by a limited number of measurements. This is achieved by studying how they affect the speed of evolution of a system under a unitary transformation. We show that the speed of multiqubit systems can be evaluated by measuring a set of local observables, providing exponential advantage with respect to state tomography. Indeed, the presented method requires neither the knowledge of the state and the parameter-encoding Hamiltonian nor global measurements performed on all the constituent subsystems. We implement the detection scheme in an all- optical experiment.

*See Phys. Rev. A 96, 042327 (2017) for details.*

**How to quantify the computational speed up given by coherence in a physics experiment?**

Quantum coherence is the key resource for quantum technology, with applications in quantum optics, information processing, metrology, and cryptography. Yet, there is no universally efficient method for quantifying coherence either in theoretical or in experimental practice. I introduce a framework for measuring quantum coherence in finite dimensional systems. I define a theoretical measure which satisfies the reliability criteria established in the context of quantum resource theories. Then, I present an experimental scheme implementable with current technology which evaluates the quantum coherence of an unknown state of a d-dimensional system by performing two programmable measurements on an ancillary qubit, in place of the O(d2) direct measurements required by full state reconstruction. The result yields a benchmark for monitoring quantum effects in complex systems, e.g., certifying nonclassicality in quantum protocols and probing the quantum behavior of biological complexes.

*See Phys. Rev. Lett. 113, 170401 (2014) for details.*

**Is there a link between quantum complementarity and quantum correlations? Is there an uncertainty principle for single quantum observables? **

Yes, and yes! Quantum mechanics predicts that measurements of incompatible observables carry a minimum uncertainty which is independent of technical deficiencies of the measurement apparatus or incomplete knowledge of the state of the system. Nothing yet seems to prevent a single physical quantity, such as one spin component, from being measured with arbitrary precision. Here, we show that an intrinsic quantum uncertainty on a single observable is ineludible in a number of physical situations. When revealed on local observables of a bipartite system, such uncertainty defines an entire class of bona fide measures of nonclassical correlations. For the case of 2×d systems, we find that a unique measure is defined, which we evaluate in closed form. We then discuss the role that these correlations, which are of the “discord” type, can play in the context of quantum metrology. We show in particular that the amount of discord present in a bipartite mixed probe state guarantees a minimum precision, as quantified by the quantum Fisher information, in the optimal phase estimation protocol.

*See Phys. Rev. Lett. 110, 240402 (2013) for details.*

## Career Summary

- January 2018 -- J. R. Oppenheimer Fellow at Los Alamos National Laboratory in the T-4 group
- July 2017 -- Director's Fellow at Los Alamos National Laboratory in the T-4 group
- March 2014 -- Oxford Martin fellow (from July 2014, EPSRC fellow) at the University of Oxford in the Frontiers of Quantum Physics group
- September 2013 - March 2014 -- Postdoc at the National University of Singapore in the Quantum Measurement group
- July 2013 -- PhD in Mathematics at The University of Nottingham in the Quantum Correlations group
- December 2009 -- M.Sc. in Theoretical Physics at the University of Torino
- September 2007 -- B.Sc. in Physics at the University of Torino

Contact

If you have some questions about my work, e-mail to __davegirolamiATgmailDOTcom__