Multipath and polarization entanglement of photons

Transcription

1 Multipath and polarization entanglement of photons. Chiuri, G. Vallone*, P. Mataloni Quantum Optics Group, Dipartimento di Fisica Sapienza Università di Roma, 0085, Italy INO CNR, 5025 Firenze, Italy * present address: Dipartimento di Fisica, Università di Padova

2 Path - polarization hyperentanglement of 2 photons (to create 4/6 qubits) Polarization entanglement E 2 2 H H V V 2 photons qubits

3 . + Path entanglement (right-left) E 4 2 H H V V 2 l r r l 2 photons 4 qubits

4 V V H H E Path entanglement (External-Internal) l r r l 2 2 photons 6 qubits I I E E 2

5 Experiments with path-polarization HE states 4-qubit & 6-qubit Cluster states: - Nonlocality tests (Growing with size nonlocality, VN, Fully nonlocal quantum correlations (L. olita s talk)) - One-Way quantum computation (Probabilistic/deterministic single qubit rotation, C-NOT, Grover s search algorithm, Deutsch-Jozsa algorithm) 4-qubit HE Dicke states: - Phased Dicke states (entanglement test by multipartite state Entanglement Witness, Resilience to decoherence) - Symmetric Dicke states ( 3 telecloning protocol)

6 b b a a b b a a b b a a b b a a V l r V r V l V l H r H r H l H 2 From hyperentangled to cluster states 4 qubits Vallone et al. PRL 98, (2007) HW b b a a b b a a b b a a b b a a V l r V r V l V l H r H r H l H 2

7 Quantum computation: one-way model

8 Measurement setup for single qubit rotation Passive scheme:

9 Measurement setup for single qubit rotation ctive scheme: Vallone et al. PRL 00, (2008)

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11 From HE 6 hyperentangled state to LC 6 linear cluster state HWP (45 ) HWP (0 ) Linear cluster state LC 6 realized by suitable waveplates in the output modes: CX 2 gate obtained by applying a 45 half waveplate to the internal modes CZ 65 gate obtained by applying a 0 half waveplate to the left modes LC 6 2 EE ab lr ab EE ab rl ab II ab lr ab II ab rl ab Ceccarelli et al. PRL 03, 6040 (2009)

12 State Fidelity: Entanglement Witness: Quantum nonlocality: (larger deviation from classical bounds) Persistency of entanglement: (tracing qubits 3 and 6, or and 4, the remaining four qubits are still entangled)

13 Measurement setup

14 Experimental realization of the CNOT gate Measure at the same time: - qubits 4, (E/I momentum) - qubits 3, 6 (r/l momentum) 4 2 Readout on qubits 2, 5 (polarization) Pattern Qubit (DOF) Laboratory basis 4 possible configurations:

15 Pattern & circuital representation (cases 2, 4): F = 0.88

16 Decoherence in 4-qubit HE Phased Dicke states Dicke state: totally symmetric quantum state defined in the computational basis { 0>, >} (robust against photon losses and projection measurements) Symmetric 4-qubit Dicke state with 2 excitations: Superposition of all permutations of 4-qubit product states with two logical s and two logical 0 s. 4-qubit phased Dicke state:

17 Q Phased Dicke States realized by implementing suitable unitary transformations to the x> state:

18 Introduce noise in the Dicke state by acting on the momentum DOF Decoherence studied by a new witness for multipartite entanglement detection: Pure state: W 2 3 D. russ et al. PRL 09

19 Experimental results E(): random robustness of entanglement Noise parameter. Chiuri et al. PRL (200)

20 Quantum Telecloning by HE Dicke states Combination of quantum teleportation and quantum cloning. Requires multipartite entanglement. Using HE Dicke states: perform the protocol by telecloning the quantum state associated to one Degree of Freedom instead of the photon. Qubits 2,3 belong to lice Qubits 4,5 belong to ob Qubit 3: ancilla TC : 4-qubit ent. state x 0 x x Input state: x TC x : initial state (to clone)

21 Quantum resource for Telecloning 2: TC M. Murao, et al., PR (999) llows fidelity F = 5/6 Qubit 3: is an ancillary qubit. y the protocol, only two qubits can receive an optimal copy of the initial state. not a Dicke state but we can generate ' TC TC XX 2 TC x HH rl lr VV rl 3 using the state produced by SPDC: ( )

22 Telecloning 3 Phase covariant Quantum Telecloning Input state: 2 ( i ) (2) 0 e D x x F = 5/6

23 Experimental setup

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26 General input state: 2 cos 2 0 x e i sin 2 x D (2) 4 234

27 Experimental setup

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29 Results

30 Generic qubit: F = 0.64

31 i i i i s s e L L E E e I I l r e r l V V e H H Next: 8-qubit hyperentanglement (using time-energy entanglement)

32 Conclusions 2-photon hyperentanglement in more DOFs allows multiqubit entangled states - less affected by decoherence - created at higher rep rate - 0 qubit HE states using other DOFs achievable (time-bin, OM, path ) Scalable systems are needed for multiqubit applications - SPDC is intrinsically probabilistic - incresing the number of DOFs implies an exponential requirement of resources Working with a limited number of DOFs (up to 4) is still more convenient than increasing the number of photons. Multiphoton multidof entangled states: solution in a medium term time scale

33 Perspectives Multi-qubit systems require to address single-qubit and two-qubit operations with high precision. Complex quantum optical schemes of increasing size realized in bulk optics suffers from severe limitations concerning stability, operation precision and physical size. New approach: dopt miniaturized optical waveguide devices in the quantum regime. On chip stable interferometers demonstrate complete phase stability, both of single path encoded qubits and of two-photon entangled states. Solutions: - Lithographic devices - Laser writing technique (F. Sciarrino s talk)

34 Giuseppe Vallone (Post-Doc, now at Università di Padova) ndrea Chiuri (PhD student) Thanks to: (FIR HYTEQ - Futuro in Ricerca) (EU QUSR Project)