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Measurements of General Quantum Correlations in Nuclear Magnetic Resonance Systems

Measurements of General Quantum Correlations in Nuclear Magnetic Resonance Systems

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## Measurements of General Quantum Correlations in Nuclear Magnetic Resonance Systems

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**Measurements of General Quantum Correlations in Nuclear**Magnetic Resonance Systems Eduardo Ribeiro deAzevedo**São Paulo**Brazil**UNIVERSITY OF SÃO PAULO - USP**• 75 years • 240 courses • 57.000 undergrad students • ~200 Msc. and PHD programs**UNIVERSITY OF SÃO PAULO AT SÃO CARLOS**São Carlos City: 250.000 people. 5 universities: 1 Federal University (UFSCAR). 1 StateUnivesity (USP). 3 PrivateUnivesities. USP at São Carlos: 2 Campi, ~8.000 undergradstudents**São Carlos Institute of Physics, USP, Brazil**www.ifsc.usp.br**DC V**Al ETL (ionomer) ITO glass OC1OC6 - PPV emitted light**NMR QIP in Brazil**CBPF NMR group: Ivan Oliveira, Alberto Passos, Roberto Sarthour, Jair C. C Freitas (magnetismandmagneticmaterials) IFSC NMR group: Tito Bonagamba, Eduardo R. deAzevedo (Solid-State NMR, MRI) 2002 2003 Firstexperimentsdone in São Carlos usingquadrupolarnuclei Firstthesisdefence in NMR QIP (Fabio A. Bonkat IFSC) and (Juan Bulnesat CBPF) 2005 Publicationofthe Book Quantum InformationProcessingbyElsevier 2007 Gatherwiththe quantum informationtheorygroupat UFABC – Lucas Celeriand Roberto Serra. 2009 2010 CBPF NMR spectrometer start to operate. Hiringofnewresearchers (Alexandre Souza-CBPF, Diogo Pinto IFSC, João Teles-UFSCAR, Ruben Auccaise - UEPG ) tend to strenghtthisresearchearea. 2012**PEOPLE INVOLVED**Experiments Theory Diogo S. Pinto Lucas Céleri Roberto Serra Jonas Maziero Felipe Fanchini David Girolami Gerardo Adesso F. M. Paula J. D. Montealegre A Saguia Marcelo Sarandy Isabela Almeida Ruben Auccaise Alexandre Souza Ivan S. Oliveira Roberto Sarthour Tito Bonagamba**NMR and the QIP**• NMR is also an excellent test bench for studies on open quantum systems: • efficient implementation and manipulation of the quantum states (excellent control of the unitary transformations coming from the radiofrequency pulses); • presence of real environments, which can be described by phase damping and generalized amplitude damping channels; • Experimental demonstration of QIP procedures, including quantum protocols, algorithms, quantum simulations etc.; • Development of many useful tools for QIP, including quantum protocols, algorithms, dynamic decoupling schemes, among others;**Quantum Computation**? Entanglement**In certain schemes of quantum computation where the quantum**bits are affected by noise, there seems to be a speed-up over classical scenarios even in the presence of negligibly small or vanishing entanglement. Knill, E.; Laflamme, R. Power of one bit of quantum information. Physical Review Letters, v. 81, n. 25, p. 5672, 1998. Datta, A.; Shaji, A. and Caves. C. M. Physical Review Letters 100, p.050502, 2008. Modi, K., Paterek, T., Son, W., Vedral, V. and WilliamsonM. Unified View of Quantum and Classical Correlations Physical Review Letters, v. 104, p.080501, 2010.**A possible explanation for the speed up would be quantum**correlations different for entanglement. General Quantum Correlations How to detect them?**Other types of correlations**Quantum Computation Ollivier, H. & Zurek, W. H. Quantum discord: a measure of the quantumness of correlations.Phys. Rev. Lett.88, 017901 (2001). ? Entanglement Merali, Z. Nature, v. 474, p. 24, 2011.**Classification of Quantum and Classical States**All Correlated States Separable States Entangled States CQ C**Classification of Quantum and Classical Two-Qubit States**• Bell diagonal states: All Correlated States Separable States Entangled States CQ C Correlation Matrix:**Classification of Quantum and Classical States**• Bell diagonal states: All Correlated States Separable States Entangled States CQ C In this sense NMR seems to be the perfect tool for probing quantum correlations of separable states and their interaction with the environment; NMR sensitivepartofthedensitymatrix**Quantum Discord**• Entropic Discord*: disturbance made in a system when a measurement is applied. *Ollivier, H.; Zurek, W. Physical Review Letters, v. 88, n. 1, p. 017901, 2002. S(ρA) S(ρAB) S(ρB) Von Neumann Entropy**Quantum Discord**• Entropic Discord*: disturbance made in a system when a measurement is applied. • Mutual information: *Ollivier, H.; Zurek, W. Physical Review Letters, v. 88, n. 1, p. 017901, 2002. S(ρA) S(ρAB) S(ρB) Von Neumann Entropy**Quantum Discord**• Entropic Discord*: disturbance made in a system when a measurement is applied. • Mutual information: • Classical Correlation: *Ollivier, H.; Zurek, W. Physical Review Letters, v. 88, n. 1, p. 017901, 2002. S(ρA) S(ρAB) S(ρB) Von Neumann Entropy**Quantum Discord**• Entropic Discord*: disturbance made in a system when a measurement is applied. • Mutual information: • Classical Correlation: • Quantum Discord: *Ollivier, H.; Zurek, W. Physical Review Letters, v. 88, n. 1, p. 017901, 2002. S(ρA) S(ρAB) S(ρB) Von Neumann Entropy**Quantum Discord**• For two-qubitsBell diagonal states*: *Luo, S. Quantum discord for two-qubit systems. Physical Review A, v. 7, n. 4, p. 042303, 2008.**Probing Quantum Correlations**What is required for probing discord and their degradation upon interaction with the environment? • To prepare states withdifferentamountsofQCs . • To perform a reliable read-out of the final states. • To have a good description and characterization of the system relaxation. • NMR has all that!!!!**Diogo sets a partnership do study quantum discordby NMR**with Roberto Serra and Lucas Céleri ;**Sodium dodecylsulfate in water forming a lyotropic liquid**crystal – 23Na NMR • 3/2 spins system • Sample: Lyotropic Liquid Crystals -Sodium Dodecyl Sulfate (SDS) - Heavy Water (D2O) - Decanol (C10H21OH) • NMR system. Anatoly K. Khitrin and B. M. Fung. The Journal of Chemical Physics, 112(16):6963–6965, 2000. NeerajSinha, T. S. Mahesh, K. V. Ramanathan, and Anil Kumar. The Journal of Chemical Physics, 114(10):4415–4420, 2001.**Tools for NMR QIP using quadrupolar Nuclei**• StrongModulatedPulase (SMP)*: *Fortunato, E.; Pravia, M.; Boulant, N.; Teklemariam, G.; Havel, T.; Cory, D. Design ofmodulating pulses toimplement precise effectivehamiltonians for quantum informationprocessing. JournalofChemicalPhysics, v. 116, n. 17, p. 7599, 2002. Nelder, J.A.; Mead, R. A simplex-method for functionminimization. Computer Journal, v. 7, n. 4, p. 308, 1965.**Purequadrupolar**relaxation RedfieldEquations +**Generalized Amplitude DampingChannel (GAD):**• Longitudinal relaxation (T1) TwoQubit System**Monotonical**Decay | Differentamountofclassicalandcorreations in eachstate time (ms)**Sudden-ChangePhenomena:**• Decoherence Process in Bell-diagonal States: • Local Phase Damping Channel: MutualInformation ClassicalCorrelation EntropicDiscord Time (s) *Maziero, J. and et al. Physical Review A, v. 80, p. 044102, 2009.**Sudden-ChangePhenomena:**• Decoherence Process in Bell-diagonal States: • Phase Damping Channel: MutualInformation ClassicalCorrelation EntropicDiscord Time (s) Time (s) *Maziero, J. and et al. Physical Review A, v. 80, p. 044102, 2009.**Sudden-ChangePhenomena:**• Decoherence Process in Bell-diagonal States: • Phase Damping Channel: MutualInformation ClassicalCorrelation EntropicDiscord Time (s) Time (s) Time (s) *Maziero, J. and et al. Physical Review A, v. 80, p. 044102, 2009.**Sudden-ChangePhenomena:**• Decoherence Process in Bell-diagonal States: • Phase Damping Channel: MutualInformation ClassicalCorrelation EntropicDiscord Time (s) Time (s) Time (s) *Maziero, J. and et al. Physical Review A, v. 80, p. 044102, 2009.**TwophysicalQubits - NMR representation:**• 2 spins 1/2:**Lossofcoherencewithoutlossofenergy**Energyexchangebetween system andenvironment • Generalized Amplitude DampingChannel: • Longitudinal relaxation (T1) • PhaseDampingChannel: • Transversal relaxation (T2):**Mutualinformation**Mutualinformation Classicalcorrelation Classicalcorrelation Quantum correlation Quantum correlation**Geometric Discord**Hilbert-Schmidt distancebetweenthestateandthenearestclassicalstate; E ρ S D C Diogo sets a partneshipwith Gerardo Adesso *Dakic, B.; Vedral, V.; Brukner, C. Necessary and sufficient condition for nonzero quantum discord. Physical Review Letters, v. 105, n. 19, p. 190502, 2010. Girolami, D.; Adesso, G. Observablemeasureofbipartite quantum correlations. Physical Review Letters, v. 108, n. 15, p. 150403, 2012.Modi, K. and et al.Unified view of quantum and classical correlations. Physical Review Letters, v. 104, n. 8, p. 080501, 2010.**DirectMeasurementMethod:**NMR Observables Zero and Double Quantum Coherences andanti-phasemagnetizations Convertintoa local measurement:**DirectMeasurementMethod:**NMR Observables Zero and Double Quantum Coherences andanti-phasemagnetizations Convertintoa local measurement: