Quantum Darwinism 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 Quantum How the classical world we perceive emerges from quantum mechanics? Decoherence: lost of coherence due to interacPons with environment Classical from Quantum How the classical world we perceive emerges from quantum mechanics? Decoherence: lost of coherence due to interacPons 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 Pny fracPon of its photon environment 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 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 φ := e− SE 0 | iB1,...,Bk | iS ⌦ | iE φ 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 interacPng with photon bath: Proliferaon of informaon about the posiPon of the sphere … (Blume-Kohout, Zurek ‘07) ParPcle in brownian moon (bosonic bath): Proliferaon of informaon about posiPon of the parPcle Is quantum Darwinism a general feature of quantum mechanics? itHSE No: Let φ B1,...,Bk := e− S 0 E | i | i ⌦ | i -i t H For very mixing evoluPons U = e , is almost maximally mixed φBj 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 φ B1,...,Bk := e− S 0 E | i | i ⌦ | i -i t H For very mixing evoluPons U = e , is almost maximally mixed φBj 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⇢)σj,k \ j ◦ ⇡ j 3 1/3X O(ds n− ) Proof by monogamy of entanglement and quantum informaon-theorePc techniques (blackboard) Thanks! .