Quantum is Generic

Fernando G.S.L. Brandão University College London

Joint work with Marco Piani and Pawel Horodecki

arXiv:1310.8640

February 2014

Classical from

How the classical world we perceive emerges from ?

Decoherence: lost of due to interacons with environment

Classical from Quantum

How the classical world we perceive emerges from quantum mechanics?

Decoherence: lost of coherence due to interacons with environment

We only learn informaon about a quantum system indirectly by accessing a small part of its environment.

E.g. we see an object by observing a ny fracon of its photon environment Quantum Darwinism in a Nutshell (Zurek ’02; Blume-Kohout, Poulin, Riedel, Zwolak, ….) Objecvity of : Observers accessing a quantum system by probing part of its environment can only learn about the measurement of a preferred

Quantum Darwinism in a Nutshell (Zurek ’02; Blume-Kohout, Poulin, Riedel, Zwolak, ….) Objecvity of observables: Observers accessing a quantum system by probing part of its environment can only learn about the measurement of a preferred observable

Objecvity of outcomes: Different observes accessing different parts of the environment have almost full informaon about the preferred observable and agree on what they observe Quantum Darwinism in a Nutshell (Zurek ’02; Blume-Kohout, Poulin, Riedel, Zwolak, ….) Objecvity of observables: Observers accessing a quantum system by probing part of its environment can only learn about the measurement of a preferred observable

Objecvity of outcomes: Different observes accessing different parts of the environment have almost full informaon about the preferred observable and agree on what they observe

itH := e SE 0 | iB1,...,Bk | iS ⌦ | iE Bj only contains informaon about the measurement of on Mk k S { } | i

And almost all Bj have close to full informaon about the outcome of the measurement Mk k { }

Quantum Darwinism: Examples

(Riedel, Zurek ‘10) Dieletric sphere interacng with photon bath: Proliferaon of informaon about the posion of the sphere

…

(Blume-Kohout, Zurek ‘07) Parcle in brownian moon (bosonic bath): Proliferaon of informaon about posion of the parcle

Is quantum Darwinism a general feature of quantum mechanics?

itHSE No: Let B1,...,Bk := e S 0 E | i | i ⌦ | i -i t H For very mixing evoluons U = e , is almost maximally mixed Bj for Bj as big as half total system size

Informaon is hidden (again, QECC is an example) Is quantum Darwinism a general feature of quantum mechanics?

itHSE No: Let B1,...,Bk := e S 0 E | i | i ⌦ | i -i t H For very mixing evoluons U = e , is almost maximally mixed Bj for Bj as big as half total system size

Informaon is hidden (again, QECC is an example) Objecvity of Observables is Generic

thm (B., Piani, Horodecki ‘13) For every , there ⇤ : S B1,...,Bn exists a measurement {M_k} on S such that for almost all ! j,

⇤j(⇢):=tr B ⇤(⇢) tr(Mj⇢)j,k \ j ⇡ j 3 1/3X O(ds n )

Proof by monogamy of entanglement and quantum informaon-theorec techniques (blackboard) Thanks!