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Title slide. PQE 2003. Quantum information with photons and atoms: from tomography to error correction. C. W. Ellenor, M. Mohseni, S.H. Myrskog, J.K. Fox, J. S. Lundeen, K. J. Resch, M. W. Mitchell, and Aephraim M. Steinberg - PowerPoint PPT Presentation

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<ul><li><p>Quantum information with photons and atoms: from tomography to error correctionC. W. Ellenor, M. Mohseni, S.H. Myrskog, J.K. Fox, J. S. Lundeen, K. J. Resch, M. W. Mitchell, and Aephraim M. SteinbergDept. of Physics, University of TorontoTitle slide</p></li><li><p>U of T quantum optics &amp; laser cooling group:PDF:Morgan Mitchell Optics: Kevin Resch ( Wien)Jeff LundeenChris Ellenor ( Korea)Masoud MohseniReza Mir( Lidar) Atom Traps: Stefan MyrskogJalani FoxAna JofreMirco SierckeSalvatore MaoneSamansa Maneshi TBA: Rob Adamson</p><p>Theory friends: Daniel Lidar, Janos Bergou, John Sipe, Paul Brumer, Howard WisemanAcknowledgments</p></li><li><p>OUTLINE Introduction:Photons and atoms are promising for QI.Need for real-world process characterisationand tailored error correction.No time to say more.</p><p> Quantum process tomography on entangled photon pairs- E.g., quality control for Bell-state filters.- Input data for tailored Quantum Error Correction.</p><p> An experimental application of decoherence-freesubspaces in a quantum computation.</p><p> Quantum state (and process?) tomography on center-of-mass states of atoms in optical lattices.</p><p> Coming attractions</p></li><li><p>Density matrices and superoperators</p></li><li><p>HWPHWPHWPHWPQWPQWPQWPQWPPBSPBSArgon Ion LaserDetector BDetector ATwo-photon Process TomographyTwo waveplates per photonfor state preparationTwo waveplates per photon for state analysisSPDC source</p></li><li><p>Hong-Ou-Mandel Interference&gt; 85% visibility for HH and VV polarizationsHOM acts as a filter for the Bell state:</p><p> = (HV-VH)/2Goal: Use Quantum Process Tomography to find the superoperator which takes in outCharacterize the action (and imperfections) of the Bell-State filter.</p></li><li><p>Measuring the superoperator}Output DM InputHHHVVVVH}}}etc.16 analyzer settings16 input statesCoincidencences</p></li><li><p>Measuring the superoperatorInput Output DMHHHVVVVHetc.SuperoperatorInputOutput</p></li><li><p>Measuring the superoperatorInput Output DMHHHVVVVHetc.InputOutputSuperoperator</p></li><li><p>Testing the superoperatorLL = input statePredictedNphotons = 297 14</p></li><li><p>Testing the superoperatorLL = input statePredictedObservedNphotons = 297 14Nphotons = 314</p></li><li><p>So, How's Our Singlet State Filter?</p></li><li><p>Model of real-world beamsplitter45 unpolarized 50/50 dielectric beamsplitter at 702 nm (CVI Laser)birefringent element+singlet-state filter+birefringent elementSinglet filterAR coatingmulti-layer dielectric</p></li><li><p>PredictedBest Fit:1 = 0.76 2 = 0.80 Model beamsplitter predicitonsSinglet filter</p></li><li><p>ObservedPredictedComparison to measured SuperopPredicted</p></li><li><p>HHxxHy We use a four-rail representation of our two physical qubits and encode the logical states 00, 01, 10 and 11 by a photon traveling down one of four optical rails numbered 1, 2, 3 and 4, respectively. 1234Photon number basis1st qubit2nd qubitComputational basisOracleAAPerforming a quantum computation in a decoherence-free subspaceThe Deutsch-Jozsa algorithm:</p></li><li><p>Modified Deutsch-Jozsa Quantum Circuityf(x)HxxHyH Error model and decoherence-free subspacesConsider a source of dephasing which acts symmetricallyon states 01 and 10 (rails 2 and 3)</p></li><li><p>341212423Experimental SetupOracleOptional swap for choice of encodingPreparationMirrorWaveplatePhase ShifterPBSDetectorABCD3/44/3DJ experimental setup3</p></li><li><p>CBCCCBBBDFS EncodingOriginal encodingDJ without noise -- raw 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