Cet ouvrage fait partie de la bibliothèque YouScribe
Obtenez un accès à la bibliothèque pour le lire en ligne
En savoir plus

Entanglement evolution for quantum trajectories Dominique Spehner

De
29 pages
Entanglement evolution for quantum trajectories Dominique Spehner Laboratoire de Physique et Modelisation des Milieux Condenses & Institut Fourier, Grenoble, France Quantum Optics V, Cozumel, Mexico 16/11/2010 – p. 1

  • modelisation des milieux condenses

  • convex decompositions

  • e?

  • quantum optics

  • over all

  • optimal decomposition

  • joint work


Voir plus Voir moins

Entanglement evolution for quantum trajectories
Dominique Spehner
´ ´
Laboratoire de Physique et Modelisation des Milieux Condenses
& Institut Fourier, Grenoble, France
Quantum Optics V, Cozumel, Mexico 16/11/2010 – p. 1Outlines
• Evolution of entanglement in the presence of couplings
with an environment
• Average concurrence for quantum trajectories
• Conclusions & Perspectives
Jointwork with: Sylvain Vogelsberger (I.F. Grenoble)
Ref.: arXiv:1006.1317 [quant-ph]
Quantum Optics V, Cozumel, Mexico 16/11/2010 – p. 2Evolution of entanglement
EntanglementofformationE between 2 subsystemsA &B
ρ
in amixedstateρ: by definition,E is aninfimum over all
ρ
P
convex decompositionsρ = p |ψ ihψ | (withp ≥ 0),
k k k k
k
X

E = inf p E , E =S tr|ψ ihψ |
ρ k ψ ψ vonNeuman k k
k k
A
k
[Bennett et al. PRA 54 (’96)].
Ifρ evolves with time, so does the optimal decomposition
{p ,|ψ i} realizing the minimum.
k k
Quantum Optics V, Cozumel, Mexico 16/11/2010 – p. 3Evolution of entanglement
EntanglementofformationE between 2 subsystemsA &B
ρ
in amixedstateρ: by definition,E is aninfimum over all
ρ
P
convex decompositionsρ = p |ψ ihψ | (withp ≥ 0),
k k k k
k
X

E = inf p E , E =S tr|ψ ihψ |
ρ k ψ ψ vonNeuman k k
k k
A
k
[Bennett et al. PRA 54 (’96)].
Ifρ evolves with time, so does the optimal decomposition
{p ,|ψ i} realizing the minimum.
k k
When the 2 subsystemsinteractwiththeirenvironment, the
entanglement getsshared betweenA,B, and the environment
֒→E typically decreases (entanglement loss betweenA &B).
ρ
Quantum Optics V, Cozumel, Mexico 16/11/2010 – p. 3Evolution of entanglement
EntanglementofformationE between 2 subsystemsA &B
ρ
in amixedstateρ: by definition,E is aninfimum over all
ρ
P
convex decompositionsρ = p |ψ ihψ | (withp ≥ 0),
k k k k
k
X

E = inf p E , E =S tr|ψ ihψ |
ρ k ψ ψ vonNeuman k k
k k
A
k
[Bennett et al. PRA 54 (’96)].
Ifρ evolves with time, so does the optimal decomposition
{p ,|ψ i} realizing the minimum.
k k
When the 2 subsystemsinteractwiththeirenvironment, the
entanglement getsshared betweenA,B, and the environment
֒→E typically decreases (entanglement loss betweenA &B).
ρ
Q1: Can theA-B entanglement disappear completely?
Quantum Optics V, Cozumel, Mexico 16/11/2010 – p. 3Evolution of entanglement
EntanglementofformationE between 2 subsystemsA &B
ρ
in amixedstateρ: by definition,E is aninfimum over all
ρ
P
convex decompositionsρ = p |ψ ihψ | (withp ≥ 0),
k k k k
k
X

E = inf p E , E =S tr|ψ ihψ |
ρ k ψ ψ vonNeuman k k
k k
A
k
[Bennett et al. PRA 54 (’96)].
Ifρ evolves with time, so does the optimal decomposition
{p ,|ψ i} realizing the minimum.
k k
When the 2 subsystemsinteractwiththeirenvironment, the
entanglement getsshared betweenA,B, and the environment
֒→E typically decreases (entanglement loss betweenA &B).
ρ
Q1: Can theA-B entanglement disappear completely?
Q2: Can one extract information from the environment (by mea-
suring it) in order to “know” the optimal decomposition?
Quantum Optics V, Cozumel, Mexico 16/11/2010 – p. 3Entanglement sudden death
ENTANGLEMENT TYPICALLY DISAPPEARS BEFORE COHERENCES ARE LOST!
ρ
It can disappear after a finite time
T=0
ρ
S
• always the case if the qubits relax to a
common
bath
Gibbsstateρ atpositivetemperature

T>0
• otherwise depends on the initial state.
ρ
0
[Diosi ’03], [Dodd & Halliwell PRA 69 (’04)], [Yu et Eberly PRL 93 (’04)]
Quantum Optics V, Cozumel, Mexico 16/11/2010 – p. 4Entanglement sudden death
ENTANGLEMENT TYPICALLY DISAPPEARS BEFORE COHERENCES ARE LOST!
ρ
It can disappear after a finite time
T=0
ρ
S
• always the case if the qubits relax to a
common
bath
Gibbsstateρ atpositivetemperature

T>0
• otherwise depends on the initial state.
ρ
0
[Diosi ’03], [Dodd & Halliwell PRA 69 (’04)], [Yu et Eberly PRL 93 (’04)]
C(t)
If the two qubits are coupled to a
1
common bath, entanglement can
also suddently reappear
due to effective (bath-mediated) qubit
interaction creating entanglement
t
t
t
ESD ESD
sudden birth
[Ficek & Tana´s PRA 74 (’06)], [Hernandez &
Orszag PRA 78 (’08)], [Mazzola et al. PRA (’09)]
Quantum Optics V, Cozumel, Mexico 16/11/2010 – p. 4Quantum trajectories
As a result of continuous measurements on the environment, the
bipartite system remains in a pure state|ψ(t)i at all timest> 0
t∈R 7!|ψ(t)i quantum trajectory
+
Reason: each measurement disentangle the system and the
environment (by wavepacket reduction).
Quantum Optics V, Cozumel, Mexico 16/11/2010 – p. 5Quantum trajectories
As a result of continuous measurements on the environment, the
bipartite system remains in a pure state|ψ(t)i at all timest> 0
t∈R 7!|ψ(t)i quantum trajectory
+
Reason: each measurement disentangle the system and the
environment (by wavepacket reduction).
Averaging over the measurements, one gets the density matrix:
Z
ρ(t) =|ψ(t)ihψ(t)| = dp[ψ]|ψ(t)ihψ(t)| .
Quantum Optics V, Cozumel, Mexico 16/11/2010 – p. 5

Un pour Un
Permettre à tous d'accéder à la lecture
Pour chaque accès à la bibliothèque, YouScribe donne un accès à une personne dans le besoin