Fundamental Problems in Quantum Physics

Steve Campbell

Fundamental Problems in Quantum Physics

Involves units across Italy based in Milano, Pavia, Genova, Trieste Trento and Cozenza

Milano hosted representatives of all units for a workshop recently in June:

http://www.mi.infn.it/~vacchini/workshopBELL17.html

Members of the Milan unit

Linked projects:

• COST Action MP1209:Thermodynamics in the Quantum Regime

• FIRB 2010: Semigruppi Quantistici Markoviani e loro stima empirica

Fundamental Problems in Quantum Physics

Alberto Barchielli (PO, PoliMi)

Alessandro Toigo (RTDb, PoliMi)

Steve Campbell (INFN Fellow)

Bassano Vacchini (PA, UniMi)

Giovanni Salesi(PA, UniBg)

• EU Collaborative project QuProCS: Quantum Probes for Complex Systems

• UniMI H2020 Transition Grant

Giacomo Guarnieri (Former PhD UniMi)

Who are we?

•Quantum Spin Chains •UltraCold Quantum Gases •Quantum Thermodynamics •Open Quantum Systems •Coherent Control •Quantum Information

•Open Quantum Systems •Markovian vs non-Markovian •Quantum Information

Steve Campbell (INFN Fellow)

Bassano Vacchini (PA, UniMi)

Giacomo Guarnieri (Former PhD UniMi

now PostDoc Olomouc)

•Quantum Thermodynamics •Open Quantum Systems •Light-matter interactions

Open Quantum Systems

environment! open systemHilbert space HE

Hamiltonian HE

environment state ⇢E

Hilbert space HS

Hamiltonian HS

system state ⇢S

interaction HI

• Markovian and non-Markovian environments • Quantifying non-Markovianity • Information backflow and the role of correlations • Formal tools (generalised master equations)

Quantum Thermodynamics

• Quantum cycles & engines (controlling quantum systems) • (Re-)Definition of work, heat, entropy production • Thermalisation and equilibration of quantum systems • Ergodicity and eigenstate thermalisation hypothesis

So what have we been doing?Landauer’s Principle

…holds that "any logically irreversible manipulation of information, such as the erasure of a bit or the merging of two computation paths, must be accompanied by a corresponding entropy increase in non-information-bearing degrees of freedom of the information-processing apparatus or its environment".

Endows information with strong evidence that it is a physical resource and not just some abstract entity

One of the most remarkable outcomes is the exorcism of Maxwell’s Demon

Why would we care?

Information erasure goes hand in hand with a irreversible process, which leads us to think about thermodynamics and the second law

C. H. Bennet, “Notes on Landauer’s principle, reversible computation, and Maxwell’s Demon”, Studies in History and Philosophy of Modern Physics 34, 501–510 (2003)

Landauer’s bound is interesting but does not ask (what we think is an important question):

does the presence of quantumness change things?

Landauer’s bound has direct consequence in the context of computation, but our focus is more toward a thermodynamic viewpoint

We examined two alternative formulations of Landauer bounds and examining the thermodynamics of the open quantum system contrasted their tightness

A simple model to explore Landauer-like Bounds

|0iS

|1iS

|0iE

|1iE

�

H

%S %E =e��HE

Z

B > �S

�S > B

�!

0

We find the details of the initial state play a delicate role in dictating the tightness of Landauer like bounds

Clausius’ Law

�⌦Q↵� 0 ↵2 1

2 [1 + tanh(�)]

|0iS

|1iS

|0iE

|1iE

�

H

� = 1 � = 0.1

It is easy to find that Clausius’ statement of the second law holds for

We know both bounds can be negative and therefore fail to accurately capture the behaviour of the heat

Clausius

Entropic

Thermodynamic

Quantum Speed Limits

This relation is also another statement of the energy-time uncertainty principle

�E�t � ~2

“lifetime”/duration

How long does it take for a state to evolve into an orthogonal state?

The Margolus-Levitin inequality shows

t? � ~2E

E = hHiwhere

This sets a fundamental upper bound on the rate of change of a state

The time taken is then understood as a “quantum speed limit time” ⌧QSL

N. Margolus and L. B. Levitin, “The maximal speed of dynamical evoluation”, Phys. D Nonlinear Phenom. 120, 188 (1998) L. Mandelstam and I Tamm, “The uncertainty relation between energy and time in non relativistic quantum mechanics”, J. Phys. (USSR) 9, 249 (1945)

A few other interests

It is fundamental in assessing the control of quantum systems

Our Recent Works

Generalized master equations leading to completely positive dynamics Bassano VacchiniPhys. Rev. Lett. 117, 230401 (2016)

All-optical quantum simulator of qubit noisy channels Simone Cialdi, Matteo A. C. Rossi, Claudia Benedetti, Bassano Vacchini, Dario Tamascelli, Stefano Olivares, Matteo G. A. Paris Appl. Phys. Lett. 110, 081107 (2017)

Full counting statistics approach to the quantum non-equilibrium Landauer bound Giacomo Guarnieri, Steve Campbell, John Goold, Simon Pigeon, Bassano Vacchini, Mauro Paternostro arXiv:1704.01078

Non-Markovianity by undersampling Matteo A. C. Rossi, Claudia Benedetti, Simone Cialdi, Dario Tamascelli, Stefano Olivares, Bassano Vacchini, Matteo G. A. Paris arXiv:1705.05852

Trade-off between speed and cost in shortcuts to adiabaticity Steve Campbell, Sebastian Deffner Phys. Rev. Lett. 118, 100601 (2017)

Dynamics and Asymptotics of Correlations in a Many-Body Localized System Steve Campbell, Matthew J. M. Power, Gabriele De Chiara To Appear Eur. Phys. J. D (2017)

Global and local thermometry schemes in coupled quantum systems Steve Campbell, Mohammad Mehboudi, Gabriele De Chiara, Mauro Paternostro To Appear New J. Phys. (2017)

Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control Sebastian Deffner, Steve Campbell arXiv:1705.08023

Initial state dependence of non-equilibrium quantum Landauer bounds Steve Campbell, Giacomo Guarnieri, Mauro Paternostro, Bassano Vacchini

To Appear July 2017

Our Recent Works