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 Chiuri PhD Supervisor: Prof. Paolo Mataloni Dottorato in Fisica XXV ciclo Seminario Finale – 17 Ottobre 2012

Transcript of Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional...

Page 1: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

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

Page 2: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

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

Page 3: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

...about my talk

Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012

Dicke states✔ ✔ ✔ Quantum protocols✔ ...

QuantumSimulation

Page 4: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

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

Page 5: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

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)

Page 6: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

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)

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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

Page 8: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

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

Page 9: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

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

Page 10: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

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

Page 11: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

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

Page 12: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

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

Page 13: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

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

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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

Page 15: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

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

Page 16: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

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

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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

Page 18: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

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

Page 19: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

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

Page 20: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

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

Page 21: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

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

Page 22: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

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

Page 23: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

Quantum simulation of Non- Markovianity

Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012

NON-MARKOVIAN

SYSTEM

ENVIRONMENT

MARKOVIAN

SYSTEM

ENVIRONMENT

QuantumSimulation

Page 24: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

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

Page 25: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

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)

Page 26: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

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)

Page 27: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

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)

Page 28: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

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

Page 29: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

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)

Page 30: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

The experimental results

Andrea Chiuri Seminario Finale di Dottorato | XXV ciclo 17/10/2012

Entropy

QuantumSimulation

A. Chiuri, et al., arXiv:1208.1630 (2012)

Page 31: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

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

Page 32: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

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

Page 33: Exploring finite-dimensional Hilbert spaces by Quantum Optics fileExploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: Andrea Chiuri PhD Supervisor: Prof. Paolo

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