Transcript Document
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)