Quantum InformationQuantum Information: Quantum Mechanics SecondYouthQuantum Mechanics SecondYouth

Quantum EntanglementQuantum Entanglement

Quantum NoiseQuantum Noise

Fabio Benatti, Roberto FloreaniniFabio Benatti, Roberto Floreanini

Dipartimento di Fisica Teorica, INFNDipartimento 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 DFTThe Group at DFT

Quantum Information:Quantum Information:fromfrom bitsbits toto qubits qubits

• Bits : 0,1

• Qubits :

0077!! jj00ii ==1100

;; 1177!! jj11ii ==0011

jjªª ii == ®®jj00ii ++ ¯̄jj11ii ==®®¯̄

;; jj®®jj22 ++ jj¯̄ jj22 == 11

THE QUANTUM SKIERTHE QUANTUM SKIER

(Charles Addams)

IN THE QUANTUM WORLD STRANGE THINGS HAPPENIN THE QUANTUM WORLD STRANGE THINGS HAPPEN

Quantum EntanglementQuantum Entanglement

Alice and Bob share 2 qubits in

• Separable states

• Entangled States

j0iA j0iB + j1iA j1iBp2

j0iA j0iB ; j1iA j1iB

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 EntanglementQuantum Entanglement: from Magic to a Physical ResourcePhysical 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 NoiseQuantum Noise

• Reversible Quantum Time Evolution:

vector states remain vector states

• Irreversible Quantum Time Evolution

vector states turned into mixtures

@@tt½½tt == ¡¡ii~~[[HH ;; ½½tt]]

½7! N[½]=X

i

Ai ½Ayi

jÃihÃj

jÃihÃj

Open Quantum SystemsOpen Quantum Systems

Quantum systemsQuantum systems immersed in theirimmersed in their environmentenvironment

E S@@tt½½tt == ¡¡

ii~~[[HH ;; ½½tt]]

++XX

ii

AAii ½½tt AAyyii

DissipationDissipation

NoiseNoise

¡¡1122

XX

ii

ffAAyyii AAii ;;½½ttgg

affected by affected by

Open Quantum Systems and NoiseOpen Quantum Systems and Noise

• DecoherenceDecoherence: : interference effects eliminatedinterference effects eliminated

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

• Extremely dangerous inExtremely dangerous in quantum information quantum information andand computation computation based on persistencebased on persistence of linear of linear superpositionssuperpositions

®®jjªª ii ++ ¯̄jj©©ii 77!! jj®®jj22jjªª iihhªª jj ++ jj¯̄ jj22jj©©iihh©©jj

NoiseNoise can also can also entangleentangle

• non-directly interacting non-directly interacting quantum systemsquantum systems in a in a same environmentsame environment may interactmay interact through the environmentthrough the environment andand become become entangledentangled

EES1S1

S2S2

A Theoretical and Experimental ScenarioA Theoretical and Experimental Scenario: Bose-Einstein Condensates (BEC)Bose-Einstein Condensates (BEC)

• Laser coolingLaser cooling• Magnetic trappingMagnetic trapping• Evaporative coolingEvaporative cooling

• Rubidium-87 atomsRubidium-87 atoms condensed condensed at the temperature ofat the temperature of in in 1D1D wells of width wells of width

105

50nK10¹m

400400 nK nK

200200 nK nK

5050 nK nK

BEC BEC in Double Well TrapsDouble Well Traps

Noise on the tunneling barrierNoise on the tunneling barrier

BEC Entangled StatesBEC Entangled States

Well 1: Well 1:

K atomsK atoms

Well 2: Well 2:

N-K atomsN-K atoms

jjªª ii == ®®jjKK;;NN ¡¡ KK ii

++¯̄jjQQ;;NN ¡¡ QQii

jjKK;;NN ¡¡ KK ii

Atom Chips

What are the effects of the environment?What are the effects of the environment?It decoheres, but not only. On short times,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)