1 Multiphoton Entanglement Eli Megidish Quantum Optics Seminar,2010

2 Outline Multipartite Entanglement Multipartite detection QST & Entanglement Witness GHZ W states Cluster states – one way quantum computer

3 N=2: Multi partite entanglement Separable N=3: SeparableBiseparable Pure state is called genuine tripartite entangled if it is not fully separable nor biseparable : Pure state is called genuine biipartite entangled if it is not fully separable : In this talk,N>2, and will focus on GHZ,W states and cluster states.

4 Quantum state tomography n particles density matrix is given by:Any two level system density matrix: reconstruction of the density matrix by measurements. real parameters, one photon density matrix: are the pauli matrices. 1. BS. For two photon one has to measure: 2. PBS in H/V basis. 3. PBS in P/M basis. 4. PBS in R/L basis.

5 Measures of entanglement using density matrix: Fidelity- a measure of the state overlap: Peres- Horodecki criterion: Define the partial transpose: For a 2x2 or 2x3 system the density matrix If the the partial transpose has no negative eigenvalues than the state is separable!

6 Entanglement witness A witness operator detects genuine n-partite entanglement of a pure state B denotes the set of all biseparable states. signifies a multipartite entanglement. Bell state witness: We don’t construct the quantum state but we can detect genuine multipartite entanglement with ~N measurements. Therefore, by definition:

7 Greenberger Horne Zeilinger state Properties: When losing one particle we get a completely mixed state. Maximally entangled When we measure one particle in P/M basis we reduce the entanglement

8 GHZ sources Two random photons superimposed on a PBS are projected into a Bell state 164 But what if one photon is a part of a bell state But what if the other photon is also a part of a bell state In this way was created. 235

9 GHZ sources - Experiment Confirmation of the GHZ state is done using a measurement in the P/M basis. PDC in a double pass configuration:

10 Experiment six photons GHZ state 3 pairs of entangled photons are created using PDC: Fidelity=

11 GHZ Bell Theorem without inequalities 1.Individual and two photons measurement are random. 2.Given any two results of measurement on any two photons, we can predict with certainty the result of the corresponding measurement performed on the third photon. Symmetry: In every one of the yyx,yxy and xyy experiment, third photon measurement (circular and linear polarization) is predicted with certainty.

12 GHZ Bell Theorem without inequalities, Local realism Assume that each photon carries elements of reality for both x and y measurement that determine the specific individual measurement result: for P / M polarization for R / L polarization In order to explain the quantum predictions:

13 But what if we decided to measure XXX? Local realism: Independent on the measurement bases on the other photons. Possible results: Quantum Mech.: Possible results:

14 Results Exp: LHV: Quantum Mechanics: Quantum mach. is right 85% of the times!

15 W state “Less” entangled compared to GHZ state “Less” fragile to photon loss than GHZ state

16 Experiment Two indistinguishable pairs are created: We choose only of the times we get

17 Results- state characterization These probabilities are also obtained from Incoherent mixture Equally weighted mixture of bisparable states Bell state between modes b and c. To confirm the desired state we measure the correlation in the R/L bases.

18 Results- Entanglement properties Measurement basis Correlation function: is the probability for a threefold coincidence with the specific results and a specific phase settings. For w state:

19 Results- Entanglement properties

20 Correlations between photons in mode a and b, depending on the measurement result of photon in mode c. Two photon state tomography: Peres- Horodecki criterion: Bipartite entanglement Results- Robustness of Entanglement

21 Graph state A graph state is a multipartite entangled state that can be repressed by a graph. Qubit- vertex and there’s an edged between interacting (entangled) qubits. Given a graph the state vector for the corresponding graph is prepared as follows: 1.Prepare the qubits at each vertex in the pure state with the state vector 2.Apply the phase gate to all the vertices a,b in G. In the computational basis: Cluster states are a subset of the graph states that can be fitted into a cubic lattice. Two graphs are equivalent if under Stochastic Local Operation and Classical Communication (SLOCC) one transforms to the other.

22 Cluster state

23 Cluster state Single particle measurements on a cluster state: Measurement in the computational basis have the effect of disentangling the qubit from the cluster. Remove the vertex and its edges. Measurement in the basis: Pauli error in the case

24 Cluster state, How much entanglement is in there? - A state is maximally connected if any pair of qubits can be projected, with certainty into pure Bell state by local measurements on a subset of the other qubits. -The persistency of entanglement is the minimum number of local measurements such that, for all measurement outcomes, the state is completely disentangled Cluster states are maximally connected and has persistency

25 One way Quantum computer inputs outputs A new model (architecture) for quantum computer based on highly entangled state, cluster states. Computation is done using single qubit measurements. Classical feed forward make a Quantum One Way computer deterministic. Protocol: Prepare the cluster state needed. Encode the logic. Single qubit measurements along the cluster (feed forward) Read the processed qubits. Universal set includes: single qubit rotation and CNot/CPhase operation

26 One way Quantum computer – Building blocks 12 If we measured This is equivalent to the operation on the encoded qubit: Special case:The encoded qubit is teleported along the chain. If we measured classical feed forward in needed to correct the pauli errors.

MesurementReadout 3D -qubit rotation on the bloch sphere. Using single photon measurement in the appropriate basis: Classical feed forward make a Quantum One Way computer deterministic. One way Quantum computer – Building blocks

Measure particles 2,3 in the base If the outcomes are This is equivalent to the operation on the encoded qubits: Consider the cluster: These kind of operations generates entanglement. One way Quantum computer – Building blocks

29 Accounting for all possible 2 pair generated in PDC which are super imposed on a PBS: This state is equivalent to the four qubit linear cluster under the local unitary operation: One way Quantum computer – Experiment

30 The rotated photon is left on photon 4. Photon 4 was characterized using QST. Input state: Theory Exp Single qubit rotation was presented using three qubit linear cluster One way Quantum computer – Experiment

31 CPhase gate was presented using: The twp photon density matrix was reconstructed using QST Measure photons 2,3 in Theory Exp. One way Quantum computer – Experiment

32 We can simulate any network computation using the appropriate cluster and measurements ! So far the largest cluster state generated 6 (photons) 8 (ions). One way Quantum computer – Summary inputs outputs

33 “Measurement of qubits ”, James, PRA,64, (2001). “Experimental detection of multipartite entanglement using witness operator”, Bourennane, PRL, 92, , (2004). “Observation of three- photon Greenberger-Horne-Zeilinnger entanglement”, Bouwmeester, PRL, 82,1345, (1999) “Experimental test of quantum nonlocality in three photon Greenberger-Horne-Zeilinger entanglement”, – Pan Nature 403, (2000). “Experimental Demonstration of Four-Photon Entanglement and High-Fidelity Teleportation”,Pan, PRL, 86, 4435 (2001). “ Experimental entanglement of six photons in graph states”, Pan, nature, 3,91,(2007). “ Experimental realization of three qubit entangled W state”, Weinfurter, RPL,7,077901, (2004). “Entanglement in graph states and its applications” Briegel, arxive: quan “Persistent entanglement in arrays of interacting particles ”, Briegel, PRL, 86, 910(2001) “A one way quantum computer”, Briegel, PRL, 86, 5188, (2001). “Experimental one way quantum computer” Zeilinger, nature, 434, 169, (2005). References:

34

35 Summary Multipartite entanglement characteriation Multipartite entanglement properties. Bell theory without inequalities. One way quantum computer.

36 Experiment: Restricting for 4 fold coincidence:

37 Polarization baseMeasurement Operator

38 Two random polarized photon can be entangled using a Bell state projection: For the case that two photons emerge from 12

39 12

40 (a) Delay line Delay line

41 Delay line (b)

42 EPR

43

44

45

46