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

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

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

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

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

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 the theory of elements of reality Peres: a trick that quantum magicians use to produce phenomena that cannot be imitated by classical magicians

Quantum Entanglement Physical Resource Quantum 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: vector states remain vector states Irreversible Quantum Time Evolution vector states turned into t ½ t = ¡ i ~ [ H ; ½ t ] ½ 7! N [ ½ ] = X i A i ½ A y i j à ih à j j à ih à j

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

Open Quantum Systems and Noise Decoherence: interference effects eliminatedDecoherence: interference effects eliminated Extremely useful to derive the classical macrodynamics from the quantum microdynamics (Ghiradi-Rimini- Weber)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 superpositionsExtremely dangerous in quantum information and computation based on persistence of linear superpositions ® j ª i + ¯ j © i 7! j ® j2j ª ih ª j + j ¯ j2j © ih © j

Noise can also entangle non-directly interacting quantum systems in a same environment may interact through the environment and become entanglednon-directly interacting quantum systems in a same environment may interact through the environment and become entangled E S1 S2

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

400 nK 200 nK 50 nK

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

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)