exploring finite-dimensional hilbert spaces by quantum optics fileexploring finite-dimensional...
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Exploring finite-dimensional Hilbert spaces by Quantum Optics
PhD Candidate: Andrea ChiuriPhD Supervisor: Prof. Paolo Mataloni
Dottorato in Fisica XXV cicloSeminario Finale – 17 Ottobre 2012
About my PhD...
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
Dicke states✔ Engineering ✔ Characterization✔ Quantum protocols✔ ...
Noisy channel✔ Noise parameter
estimation✔ Maximum channel capacity achievement
Other studies✔ Quantum correlations✔ Quantum gates✔ Quantum protocols
multi-qubitmulti degree of freedomphotonic quantum states
QuantumSimulation
...about my talk
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
Dicke states✔ ✔ ✔ Quantum protocols✔ ...
QuantumSimulation
Quantum Optics
Introduction to Quantum Optics
Physical systems behavingas predicted by quantum mechanics
Atoms Ions QED circuits
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
Introduction to Quantum Optics
Atoms Ions QED circuits
Quantum Optics
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
Photons many degrees of freedom (DOFs)
Introduction to Quantum Optics
Quantum Optics
Atoms Ions QED circuits
Quantum Information
Quantum Computation
Experiments demonstrating the laws of Quantum Mechanics
(e.g. Non-Locality Test...)
Algorithms based on quantumstates encoded in quantum systems
Encode the Information(qubit → quantum bit) in
quantum system
What can be done with Quantum Optics?
Quantum Mechanics Experiments
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
Quantum Simulation
Use quantum systems to explore physics
never "seen" before (Planck scale, anyons...)
Photons many degrees of freedom (DOFs)
Hyperentanglement
Hyperentanglement:
System composed by two (or more) subsystems A and B:
Separable state Entangled state
Multi particle approach:1 particle 1 qubit
Quantum states of higher dimensionality (i.e. higer dimensionality of the Hilbert space), are a fundamental resource for quantum tasks !How to increase the dimensionality of the space? How can we generate multi-qubit states??
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
✔ 2 photons✔ each Bell state encoded in one DOF
We are able to generate up to 6-qubit HE states:
4-qubit HE states:
6-qubit HE states:
Path Entanglement
Experimental realization of HE statesH-cone
Experimental realization of HE states
V-coneBBO
mirror
QWP
L
H-coneH-cone
Experimental realization of HE statesExperimental realization of HE states
L
Holedmask
Polarization Entanglement
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
Advantages of HE states:
Path Entanglement
Experimental realization of HE statesH-cone
Experimental realization of HE states
V-coneBBO
mirror
QWP
L
H-coneH-cone
Experimental realization of HE statesExperimental realization of HE states
L
Holedmask
Polarization Entanglement
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
✔ Easy implementation of two qubit gates
✔ High generation rate
✔ High fidelity of the engineered states
✔ High flexibility of the source: allows to suitably manipulate the quantum state
Quantum Networking
Dicke states: useful resource for Quantum Telecloning and Open Destination Teleportation
2 quantum networking protocols
Sender Receiver 1
Receiver 2
Receiver 3
Dicke states
A. Chiuri et al., to appear on PRL
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
Quantum Networking - Quantum Telecloning
Sender
Receiver 1
Receiver 2
Receiver 3
Output: an optimal copy of the input
InputOutput
Output
Output
A. Chiuri et al., to appear on PRL
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
Dicke states
Quantum Networking - Open Destination Teleportation
Receiver 1
Receiver 2
Receiver 3
The sender can choose one channel to teleport its information
Receiver 1
Receiver 2
Receiver 3
Input
Input
Output
Output
A. Chiuri et al., to appear on PRL
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
The sender can choose one channel to teleport its information
Dicke states
Quantum Telecloning via Dicke states
Dicke states: quantum resource for 1→3 Quantum Telecloning
Murao et al. PRA 59, 156 (1999)
Quantum worldQubit
Qubit 1Qubit 2
Qubit 3
Qubit 4
Bell Measurement Quantum resource
Dicke states
0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0
0 . 7 5
0 . 8 0
Quantum Telecloning via Dicke states
Fidelity between the input state X and the 3 copies
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
Dicke states
Quantum Telecloning
Bell Measurement
Quantum resource(use different DOFs
of each photon)
Dicke states: useful resource for 1→3 Quantum Telecloning
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
Dicke states: useful resource for 1→3 Quantum Telecloning
Dicke states
Multi-qubit states based on Hyperentanglement: Dicke states
1) Seed state: (built on the hyperentangled state )
How to generate a Hyperentangled Dicke state?
1) Seed state: (built on the hyperentangled state )
2) Implementing the Unitary Transformation
A. Chiuri et al., Phys. Rev. Lett. 105, 250501 (2010)
Few changes performed on
QWP
1) Seed state: (built on the hyperentangled state )
Few changes performed on
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
Quantum Telecloning: Experimental Scheme
Photon B
BS1
BS2
HWP @ 45° HWP @ 0°
Photon B
Photon A
BS1
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
Dicke states
Quantum Telecloning: Results
Qubit X always in the same state
(Qubit 4)
(Qubit 3)
(Qubit 2)
3 qubits → 3 copies
Qubit X:
0
1
0
1
0
0 . 2 5
0 . 5
0 . 7 5
1
0
1
0
1
0
1
0
1
0
0 . 2
0 . 4
0 . 6
0
1
0
1
0
1
0
1
0
0 . 2
0 . 4
0 . 6
0
1
0
1
BM:
Expected state for 2,3,4:
Telecloned copies
0
1
0
1
0
0 . 2
0 . 4
0 . 6
0
1
0
1
0
1
0
1
0
0 . 2
0 . 4
0 . 6
0
1
0
1
BM:
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
Qubit X always in the same state
Dicke states
Quantum Telecloning: Results
Qubit X in 3 different states → measure always the same telecloned qubit:
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
Dicke states
Open Destination Teleportation: experimental results
0
1
0
1
0
0 . 2
0 . 4
0 . 6
0 . 8
0
1
0
1
Qubit X:Teleported qubit
Qubit 1Qubit 2Qubit X:
Teleported qubitQubit 1Qubit 2
0
1
0
1
0
0 . 2 5
0 . 5
0 . 7 5
1
0
1
0
1
0 . 7 5
0 . 2 5
0
1
0
1
0
0 . 2 5
0 . 5
0 . 7 5
1
0
1
0
1
0
1
0
1
0
0 . 2 5
0 . 5
0 . 7 5
0
1
0
1
0
1
0
1
0
0 . 2
0 . 4
0 . 6
0 . 8
0
1
0
1
0
1
0
1
0
0 . 2
0. 4
0 . 6
0 . 8
0
1
0
1
0
1
0
1
0
0 . 2 5
0 . 5
0 . 7 5
0
1
0
1
0
1
0
1
0
0 . 2
0 . 4
0 . 6
0 . 8
0
1
0
1
0
1
0
1
0
0 . 2 5
0 . 5
0 . 7 5
0
1
0
1
0
1
0
1
0
0 . 2 5
0 . 5
0 . 7 5
0
1
0
1
Qubit 1: Qubit 1: Qubit 2:
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
Dicke states
Open Destination Teleportation: experimental results
0
1
0
1
0
0 . 2
0 . 4
0 . 6
0
1
0
1
0
1
0
1
0
0 . 2
0 . 4
0
1
0
1
Teleported qubitQubit 1Qubit 2
Qubit X:Teleported qubit
Qubit 1Qubit 2Qubit X:
0
1
0
1
0
0 . 2
0 . 4
0
1
0
1
0
1
0
1
0
0 . 2
0 . 4
0
1
0
1
0
1
0
1
0
0 . 2
0 . 4
0
1
0
1
0
1
0
1
0
0 . 2
0 . 4
0
1
0
1
Qubit 1: Qubit 1: Qubit 2:
0 . 4
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
Dicke states
Quantum simulation: brief introduction
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
QuantumSimulation
“A digital quantum simulator is an envisioned quantum device that can be programmed to efficiently simulate any other local system.” B. P. Lanyon, et al. Science (2011)
based on a quantum system
It behaves as the desired system. This allows to study physics never seen or that cannot be explored with the actual technology
Quantum simulation of Non- Markovianity
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
NON-MARKOVIAN
SYSTEM
ENVIRONMENT
MARKOVIAN
SYSTEM
ENVIRONMENT
QuantumSimulation
Quantum simulation: how to detect Non-Markovianity?
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
signature of non-Markovianity
time
En
tan
gle
men
t S
-A
SYSTEM
ENVIRONMENT
ANCILLA
A. Rivas, S. F. Huelga, M. B. Plenio, Phys. Rev. Lett. 105, 050403 (2010)
Quantum simulation: how to detect Non-Markovianity? QuantumSimulation
Quantum simulation: our experiment
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
Qubit S
Qubit E
Qubit A
✔ Qubits S-A encoded in the polarization DOF of two photons
✔ Qubit E encoded in the longitudinal momentum of one of the two photons
QuantumSimulation
A. Chiuri, et al., arXiv:1208.1630 (2012)
Quantum simulation: our experiment
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
Qubit S
Qubit E
Qubit A
✔ Qubits S-E interact via two-qubit controlled gates
✔ Qubits S-E evolve after each interaction
✔ S-A entanglement monitored at each step of the experiment
QuantumSimulation
A. Chiuri, et al., arXiv:1208.1630 (2012)
Quantum simulation: our experiment
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
Qubit S
Qubit E
Qubit A
Simulated Hamiltonian
QuantumSimulation
✔ Qubits S-E interact via two-qubit controlled gates
✔ Qubits S-E evolve after each interaction
✔ S-A entanglement monitored at each step of the experiment
A. Chiuri, et al., arXiv:1208.1630 (2012)
The experimental scheme
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
A
S E
Input state:
t=0
t=1
t=2
t=3
t=4
S E
HWP @ 22,5°
HWP @ 0°
BS
time
2-qubit gates
Env.evolution
Sys.evolution
2-qubit gates
QuantumSimulation
The experimental results
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
Entanglement of Formation: allows to quantify the entanglement betweenSystem and Ancilla
QuantumSimulation
A. Chiuri, et al., arXiv:1208.1630 (2012)
The experimental results
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
Entropy
QuantumSimulation
A. Chiuri, et al., arXiv:1208.1630 (2012)
The experimental results
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
Simulating aMarkovian behaviour
QuantumSimulation
E reset into the mixed state at each step
NO possibility ofS-E correlations
Perspectives
Sansoni, L. et al. Phys. Rev. Lett. 105, 200503 (2010)
✔ Quantum Simulation based on multiDOF quantum states (several advantages!!!)
✔ Higher dimensionality of the HE state achievable by exploiting further DOFs (time-energy)
✔ Exploit HE states within Integrated photonic circuits (more powerful quantum simulation)
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012
List of Publications List of Conferences
✔ G. Vallone, et al., PRA 81, 050302(R) (2010).
✔ A. Chiuri, et al., PRL 105, 250501 (2010).
✔ A. Chiuri, et al., PRA 84, 020304(R) (2011).
✔ A. Chiuri, et al., PRL 107, 253602 (2011).
✔ L. Aolita, et al., PRA 85, 032107 (2012).
✔ A. Chiuri, et al., NJP 14, 085006 (2012).
✔ A. Chiuri, et al., to appear on PRL
✔ A. Chiuri, et al., EPJ D 66, 195 (2012).
✔ A. Chiuri, et al., arXiv:1206.6881 (2012).
✔ A. Chiuri, et al., arXiv:1208.1630 (2012).
a) Quantum 2012, Torino 20-26 Maggio 2012: “Experimental Realization of Optimal Noise Estimation for a General Pauli Channel” (talk)
b) Fotonica 2012 Firenze, 15-17 Maggio 2012: “Experimental Quantum Networking Protocols via 4-Qubit Hyperentangled Dicke States”, (invited talk)
c) Congresso SIF, L’Aquila, 26-30 Settembre 2011: “Experimental Realization of Optimal Noise Estimation for a General Pauli Channel” (talk)
d) CLEOEurope EQEC 2011, Monaco (Ger),22-26 Maggio 2011: “Extremal Quantum Correlations: Experimental Study with Two-qubit States” (poster)
e) Quantum Simulations, Benasque (Spa), Feb 28 – Mar 05 2011: “Decoherence Simulationin Hyperentangled Phased Dicke States” (poster)
f) Stockholm Summer School on Quantum Optics and Nanophotonics 2010, Stoccolma (Sve), 21-25 Giugno 2010: “Four-qubit two-photon Dicke states based on hyperentanglement” (poster)
Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012