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

Transcription

1 Exploring finite-dimensional Hilbert spaces by Quantum Optics PhD Candidate: PhD Supervisor: Prof. Paolo Mataloni

2 Outline t Introduction to Quantum Optics t Entanglement and Hyperentanglement t Some Experiments t Perspectives

3 Introduction to Quantum Optics Quantum Optics Photons (many degrees of freedom DOF) Physical systems behaving as predicted by quantum mechanics Atoms Ions QED circuits What can be done with Quantum Optics? By encoding the Information (qubit quantum bit) in quantum system Quantum Teleportation... Quantum Information Quantum Computation Quantum Mechanics Experiment Algorithms based on quantum states encoded in quantum systems Experiments demonstrating the validity of the laws of the Quantum Mechanics (e.g. Non-Locality Test...)

4 Introduction to Quantum Optics Quantum Optics Photons (many degrees of freedom DOF) Atoms Ions QED circuits What can be done with Quantum Optics? In the computational basis By encoding the Information (qubit quantum bit) in quantum system Quantum Information Quantum Computation We can encode the qubit in different degrees of freedom of the photons: Quantum - polarization Mechanics - longitudinal momentum Experiment - emission time...

5 Outline Introduction to Quantum Optics t Entanglement and Hyperentanglement Some Experiments Perspectives

6 Entanglement and Hyperentanglement Let us consider a system composed by two (or more) subsystems A and B Entangled state Separable state Maximally Entangled two-qubit state 2 photons 1 DOF (polarization)!? Quantum states of higer dimensionality (i.e. higer dimensionality of the Hilbert space), represent fundamental resources for quantum tasks How to increase the dimensionality of the space? How can we generate multi-qubit states? Multi particle approach: 1 particle 1 qubit Hyperentanglement: 2 photons 2 qubit for each DOF

7 Experimental realization of the HE states H-cone Photon A Photon B QWP mirror BBO V-cone Polarization Entanglement Holed mask L Path Entanglement We can generate up to 6-qubit HE states: 4-qubit HE states: 6-qubit HE states:

8 Outline Introduction to Quantum Optics Entanglement and Hyperentanglement t Some Experiments : Dicke State Perspectives

9 Multi-qubit states based on Hyperentanglement: Dicke states How to generate an Hyperentangled Dicke state? 1) We found an equivalent state, up to Unitary Transformation (the entanglement doesn't change) Few changes performed in the hyperentangled state 2) We implemented the necessary Unitary Transformation Experimental setup DA C Z 12C Z 34 ' A. Chiuri et al., Phys. Rev. Lett. 105, (2010) BS C X 12 C X 34 DB

10 A structural operator to reveal Entanglement in Dicke state Toolbox Entanglement Witness Operator: non-negative expectation values for all separable states negative expectation values for at least one entangled state Decoherence (white noise): by introducing dechoerence, the coherent superposition in the state can be spoiled 1) We have been able to introduce white noise (decoherence) in the state in a controlled way 2) We measured a novel Entanglement Witness based on structural factor (wide range of applications!) i-th Pauli Operator (i = x,y,z) on the n-th qubit A. Chiuri et al., Phys. Rev. Lett. 105, (2010)

11 A structural operator to reveal Entanglement in Dicke state Toolbox Entanglement Witness Operator: non-negative expectation values for all separable states negative expectation values for at least one entangled state Decoherence (white noise): by introducing dechoerence, the coherent superposition in the state can be spoiled noise A. Chiuri et al., Phys. Rev. Lett. 105, (2010)

12 Outline Introduction to Quantum Optics Entanglement and Hyperentanglement t Some Experiments : New Non-classicality Indicator Perspectives

13 Exploring quantum correlations:introduction A B! An entangled state shows non-classical correlations between A and B (Quantum Correlations) BUT Entanglement Non-Classicality (Quantumness) A M ID :p os si bl e so lu tio n Several Non-Classicality Indicators have been proposed (Discord, MID...) BUT these have shown some problems A. Chiuri et al., arxiv:

14 Exploring quantum correlations:experiment Theoretical calculations Amid-Discord space Discord-Entropy space! The extremal states belong to several families of 2-qubit (mixed) quantum states! By suitably adapting the source of 4-qubit path-polarization entanglement (path DOF ancillary qubit) we have been able to engineer all of these families! A. Chiuri et al., arxiv:

15 Exploring quantum correlations:experiment Theoretical calculations Amid-Discord space Discord-Entropy space Experimentat Results Amid-Discord space Discord-Entropy space A. Chiuri et al., arxiv:

16 Other works... Optimal Noise Estimation We implemented a single qubit noisy channel (NC) We implemented an optimal protocol which allows to estimate how much noise p has been introduced in a single qubit state A. Chiuri et al., in preparation Fully Non-Local Quantum Correlations MAIN IDEA: In Quantum Mechanics, the results of distant experiments cannot always be understood in terms of local models (Quantum Non-Locality). BUT BUT In a typical non-locality test, however, some of the events still admit a local description We performed a Non-Locality Experiment showing the largest non-local quantum correlations ever reported: vs vs Previous experiments: L. Aolita, R. Gallego, A. Acín, A. Chiuri, G. Vallone, P. Mataloni, A. Cabello arxiv:

17 Perspectives Telecloning protocol based on Dicke states Higher dimensionality of the HE state by exploiting also other DOFs (time-energy) Integreted circuits by exploiting HE states Sansoni, L. et al. Phys. Rev. Lett. 105, (2010)