Quantum Information Information Quantum Mechanics Second Youth Quantum

Quantum Information: Information Quantum Mechanics Second. Youth Quantum Entanglement Quantum Noise Fabio Benatti, Roberto Floreanini Dipartimento di Fisica Teorica, INFN

The Group at DFT • • • Petra SCUDO (Post Doc, DFT) Sebastiano ANDERLONI (dottorando Uni. Ts) Alexandra LIGUORI (dottoranda Uni. Ts) Adam NAGY (dottorando TU Budapest) Ugo MARZOLINO (dottorando Uni. Ts) Pierfrancesco ROSINI (Laureato 2008) Giovanni MORAS (Laureato 2008) Giangiacomo GUERRESCHI (Laureando 2008) Mauro TONON (Laureando 2008)

Quantum Information: from bits to qubits • Bits : 0, 1 1 0 ! 7 = 7 ! = 0 ; 1 j 0 i j 1 i 0 1 • Qubits : ® jª i = ®j 0 i + ¯ j 1 i = ; ¯ j®j 2 + j¯ j 2 = 1

IN THE QUANTUM WORLD STRANGE THINGS HAPPEN THE QUANTUM SKIER (Charles Addams)

Quantum Entanglement Alice and Bob share 2 qubits in • Separable states j 0 i A j 0 i B ; j 1 i A j 1 i B • Entangled States j 0 i A j 0 i B + j 1 i A j 1 i B p 2

Quantum Entanglement: an epistemological riddle • Einstein-Podolski-Rosen: An entangled wavefunction does not describe the physical reality in a complete way • Schroedinger: For an entangled state the best possible knowledge of the whole does not include the best possible knowledge of its parts • Mermin: a correlation that contradicts theory of elements of reality • Peres: a trick that quantum magicians use to produce phenomena that cannot be imitated by classical magicians

Quantum Entanglement: Entanglement from Magic to a Physical Resource • Bell : a correlation that is stronger than any classical correlation • Bennett : a resource that enables quantum teleportation • Shor : a global structure of the wavefunction that allows for faster algorithms • Ekert : a tool for secure communication

Quantum Noise • Reversible Quantum Time Evolution: i @t ½t = ¡ [H ; ½t ] ~ vector states jÃi hÃj remain vector states • Irreversible Quantum Time Evolution ! N [½] = ½ 7 X A i ½A iy i Ãj jÃi h vector states turned into mixtures

Open Quantum Systems Quantum systems immersed in their environment E S affected by i @t ½t = ¡ [H ; ½t ] ~ 1 X y ¡ A f Dissipation 2 i A i ; ½t g Noise + X i i A i ½t A iy

Open Quantum Systems and Noise • Decoherence: interference effects eliminated ! j®j 2 jª i hª j + j¯ j 2 j©i h©j ®jª i + ¯ j©i 7 • Extremely useful to derive the classical macrodynamics from the quantum microdynamics (Ghiradi-Rimini. Weber) • Extremely dangerous in quantum information and computation based on persistence of linear superpositions

Noise can also entangle • non-directly interacting quantum systems in a same environment may interact through the environment and become entangled S 1 E S 2

A Theoretical and Experimental Scenario: Scenario Bose-Einstein Condensates (BEC) • • • Laser cooling Magnetic trapping Evaporative cooling 5 10 • Rubidium-87 atoms condensed at the temperature of 50 n. K in 1 D wells of width 10¹ m

50 n. K 200 n. K 400 n. K

BEC in Double Well Traps Atom Chips Noise on the tunneling barrier j. K ; N ¡ K i BEC Entangled States jª i = ®j. K ; N ¡ K i Well 1: Well 2: K atoms N-K atoms + ¯ j. Q ; N ¡ Q i

What are the effects of the environment? It decoheres, but not only. On short times, • It can generate a current in an otherwise insulating state (poster S. Anderloni); • it can generate entanglement in an otherwise separable state (poster A. M. Liguori); • It can measurably alter transmission and reflection coefficients (poster G. Moras); • it allows to study the wave packet reduction in an almost mesoscopic context: currently under study together with the experimental group of M. Inguscio at LENS (Florence)