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
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)
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