Quantum Information

:

Quantum Mechanics SecondYouth

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 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 )

Quantum Information:

from

bits

to

qubits

•

Bits

:

0,1 j0i = 1 0

  •

Qubits : j ª i = ®j0i + ¯j1i =

 

® ¯ ; j1i = 0 1

 

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 j0i A j0i B ; j1i A j1i B

•

Entangled States j0i A j0i B p + j1i A 2 j1i 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

: 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: @ ½ t = ¡ i ~ [H ; ½ t ] j ÃihÃj

•

Irreversible Quantum Time Evolution X ½7! N [½] = A i ½A y i j ÃihÃj i

Open Quantum Systems

Quantum systems immersed in their environment E

S

affected by @ Noise ½ t = Dissipation ¡ ¡ + i ~ [H ; 1 X 2 ½ t ] f A y i A i i X A i ½ t A y i ; ½ t g i

Open Quantum Systems and Noise

•

Decoherence : interference effects eliminated ®jª i + ¯j©i 7! j®j 2 j ª i hª j + j¯j 2 j ©ih©j

•

Extremely useful to derive the from the classical macrodynamics quantum microdynamics (Ghiradi-Rimini Weber)

•

Extremely dangerous in computation quantum information and based on persistence superpositions of linear

Noise can also entangle

•

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

A Theoretical and Experimental Scenario

:

Bose-Einstein Condensates (BEC)

• • •

Laser cooling Magnetic trapping Evaporative cooling

•

10 5 Rubidium-87 atoms condensed at the temperature of in 1D wells of width 50 nK 10 ¹ m

400 nK 200 nK 50 nK

BEC in Double Well Traps

Atom Chips Noise on the tunneling barrier jK ; N ¡ K i BEC Entangled States Well 1: K atoms Well 2: N-K atoms j ª i = ®jK ; N ¡ K i + ¯jQ;N ¡ Qi

What are the effects of the environment?

It decoheres, but not only. On short times,

• It can

generate insulating

a state (

current

in an otherwise

poster S. Anderloni

); • it can

generate entanglement separable

state ( in an otherwise

poster A.M. Liguori

); • It can measurably alter

transmission

and

reflection coefficients

(

poster G. Moras

); • it allows to study the

wave packet reduction

an almost

mesoscopic

in context: currently under study together with the experimental group of M. Inguscio at

LENS (Florence)