Measurements of General Quantum Correlations in Nuclear Magnetic Resonance Systems Eduardo Ribeiro deAzevedo

São Paulo Brazil

75 years 240 courses undergrad students ~200 Msc. and PHD programs UNIVERSITY OF SÃO PAULO - USP

UNIVERSITY OF SÃO PAULO AT SÃO CARLOS São Carlos City: people. 5 universities: 1 Federal University (UFSCAR). 1 State Univesity (USP). 3 Private Univesities. USP at São Carlos: 2 Campi, ~8.000 undergrad students

São Carlos Institute of Physics, USP, Brazil

Al OC 1 OC 6 - PPV ETL (ionomer) ITO DC V glass emitted light

NMR QIP in Brazil CBPF NMR group: Ivan Oliveira, Alberto Passos, Roberto Sarthour, Jair C. C Freitas (magnetism and magnetic materials) IFSC NMR group: Tito Bonagamba, Eduardo R. deAzevedo (Solid-State NMR, MRI) 2002 First experiments done in São Carlos using quadrupolar nuclei 2003 First thesis defence in NMR QIP (Fabio A. Bonk at IFSC) and (Juan Bulnes at CBPF) 2005 Publication of the Book Quantum Information Processing by Elsevier Gather with the quantum information theory group at UFABC – Lucas Celeri and Roberto Serra CBPF NMR spectrometer start to operate. Hiring of new researchers (Alexandre Souza-CBPF, Diogo Pinto IFSC, João Teles-UFSCAR, Ruben Auccaise - UEPG ) tend to strenght this researche area. 2012

PEOPLE INVOLVED Isabela Almeida Ruben Auccaise Alexandre Souza Ivan S. Oliveira Roberto Sarthour Tito Bonagamba ExperimentsTheory 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

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 Entanglemen t

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, Datta, A.; Shaji, A. and Caves. C. M. Physical Review Letters 100, p , Modi, K., Paterek, T., Son, W., Vedral, V. and Williamson M. Unified View of Quantum and Classical Correlations Physical Review Letters, v. 104, p , 2010.

A possible explanation for the speed up would be quantum correlations different for entanglement. How to detect them? General Quantum Correlations

Other types of correlations ? Quantum Computation Entanglemen t Merali, Z. Nature, v. 474, p. 24, Ollivier, H. & Zurek, W. H. Quantum discord: a measure of the quantumness of correlations.Phys. Rev. Lett. 88, (2001).

Classification of Quantum and Classical States All Correlated States Entangled States Separable States C CQ

Classification of Quantum and Classical Two-Qubit States All Correlated States Entangled States Separable States C CQ B ell diagonal states: Correlation Matrix:

Classification of Quantum and Classical States All Correlated States Entangled States Separable States C CQ B ell diagonal states: NMR sensitive part of the density matrix In this sense NMR seems to be the perfect tool for probing quantum correlations of separable states and their interaction with the environment;

–Entropic Discord*: disturbance made in a system when a measurement is applied. *Ollivier, H.; Zurek, W. Physical Review Letters, v. 88, n. 1, p , Quantum Discord S(ρ A ) S(ρ B ) S(ρAB)S(ρAB) Von Neumann Entropy

–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 , Quantum Discord S(ρ A ) S(ρ B ) S(ρAB)S(ρAB) Von Neumann Entropy

–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 , Quantum Discord S(ρ A ) S(ρ B ) S(ρAB)S(ρAB) Von Neumann Entropy

–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 , Quantum Discord S(ρ A ) S(ρ B ) S(ρAB)S(ρAB) Von Neumann Entropy

–For two-qubits Bell diagonal states*: *Luo, S. Quantum discord for two-qubit systems. Physical Review A, v. 7, n. 4, p , Quantum Discord

Probing Quantum Correlations What is required for probing discord and their degradation upon interaction with the environment? To prepare states with different amounts of QCs. 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 discord by NMR with Roberto Serra and Lucas Céleri ;

NMR system.NMR system. Sodium dodecyl sulfate in water forming a lyotropic liquid crystal – 23 Na NMR Anatoly K. Khitrin and B. M. Fung. The Journal of Chemical Physics, 112(16):6963–6965, Neeraj Sinha, T. S. Mahesh, K. V. Ramanathan, and Anil Kumar. The Journal of Chemical Physics, 114(10):4415–4420, /2 spins system Sample: Lyotropic Liquid Crystals -Sodium Dodecyl Sulfate (SDS) - Heavy Water (D 2 O) - Decanol (C 10 H 21 OH)

Strong Modulated Pulase (SMP)*: *Fortunato, E.; Pravia, M.; Boulant, N.; Teklemariam, G.; Havel, T.; Cory, D. Design of modulating pulses to implement precise effective hamiltonians for quantum information processing. Journal of Chemical Physics, v. 116, n. 17, p. 7599, Nelder, J.A.; Mead, R. A simplex-method for function minimization. Computer Journal, v. 7, n. 4, p. 308, Tools for NMR QIP using quadrupolar Nuclei

Single hard pulse

Pure quadrupolar relaxation Redfield Equations +

Generalized Amplitude Damping Channel (GAD): –Longitudinal relaxation (T 1 ) Two Qubit System

–Global phase damping channel (GPD);

| time (ms) Monotonical Decay Different amount of classical and correations in each state

HOWEVER....

Decoherence Process in Bell-diagonal States: → Local Phase Damping Channel: *Maziero, J. and et al. Physical Review A, v. 80, p , Mutual Information Classical Correlation Entropic Discord Time (s) Sudden-Change Phenomena:

Decoherence Process in Bell-diagonal States: → Phase Damping Channel: *Maziero, J. and et al. Physical Review A, v. 80, p , Mutual Information Classical Correlation Entropic Discord Time (s) Sudden-Change Phenomena:

Decoherence Process in Bell-diagonal States: → Phase Damping Channel: *Maziero, J. and et al. Physical Review A, v. 80, p , Mutual Information Classical Correlation Entropic Discord Time (s) Sudden-Change Phenomena:

Decoherence Process in Bell-diagonal States: → Phase Damping Channel: *Maziero, J. and et al. Physical Review A, v. 80, p , Mutual Information Classical Correlation Entropic Discord Time (s) Sudden-Change Phenomena:

−2 spins 1/2: Two physical Qubits - NMR representation:

Generalized Amplitude Damping Channel: –Longitudinal relaxation (T 1 ) Energy exchange between system and environment Phase Damping Channel: -Transversal relaxation (T 2 ): Loss of coherence without loss of energy

Mutual information Classical correlation Quantum correlation Mutual information Classical correlation Quantum correlation

Hilbert-Schmidt distance between the state and the nearest classical state; C S ρ E D *Dakic, B.; Vedral, V.; Brukner, C. Necessary and sufficient condition for nonzero quantum discord. Physical Review Letters, v. 105, n. 19, p , Girolami, D.; Adesso, G. Observable measure of bipartite quantum correlations. Physical Review Letters, v. 108, n. 15, p , Modi, K. and et al. Unified view of quantum and classical correlations. Physical Review Letters, v. 104, n. 8, p , Geometric Discord Diogo sets a partneship with Gerardo Adesso

2 q-bits:

Para um sistema de 2 q-bits:

2 q-bits:

Direct Measurement Method: NMR Observables Zero and Double Quantum Coherences and anti-phase magnetizations Convert into a local measurement:

Direct Measurement Method: NMR Observables Convert into a local measurement: Zero and Double Quantum Coherences and anti-phase magnetizations

Θ j/i π/2π/2 23π/2π/2- π/2 3π/2- π/2π/2

–Negativity of Quantumness (Q N A )*: Minimum amount of entanglement created between the system and its measurement apparatus in a local measurement; Geometric measurement (trace norm); J. D. Montealegre, F. M. Paula, A. Saguia, and M. S. Sarandy, Phys. Rev. A 87, (2013). T. Nakano, M. Piani, and G. Adesso, Phys. Rev. A 88, (2013).

–Negativity of Quantumness (Q N A )*: Minimum amount of entanglement created between the system and its measurement apparatus in a local measurement; Geometric measurement (trace norm); Bell diagonal states: J. D. Montealegre, F. M. Paula, A. Saguia, and M. S. Sarandy, Phys. Rev. A 87, (2013). T. Nakano, M. Piani, and G. Adesso, Phys. Rev. A 88, (2013).

–Negativity of Quantumness (Q N A )*: Minimum amount of entanglement created between the system and its measurement apparatus in a local measurement; Geometric measurement (trace norm); Bell diagonal states: J. D. Montealegre, F. M. Paula, A. Saguia, and M. S. Sarandy, Phys. Rev. A 87, (2013). T. Nakano, M. Piani, and G. Adesso, Phys. Rev. A 88, (2013).

Freezing phenomenon: –Initial state condition*: –Eg.: c 1 = 1, c 2 = -0.2, c 3 = 0.2 (λ 0 = 0, λ 1 = 0, λ 2 = 0.6, λ 3 = 0.4) *You, B.; Cen, L-X. Physical Review A, v. 86, p , 2012.

Freezing phenomenon: –Initial state condition*: –Eg.: c 1 = 1, c 2 = -0.2, c 3 = 0.2 (λ 0 = 0, λ 1 = 0, λ 2 = 0.6, λ 3 = 0.4) *You, B.; Cen, L-X. Physical Review A, v. 86, p , Time (s) 2 D G DGDG

Generalized Amplitude Damping Channel:

2 qubits system represented by 2 coupled spins ½: –Sample: 100 mg of 13 C-labeled CHCl 3 dissolved in 0.7 mL CDCl 3 –Spectrometer: –Initial State: H – 500 MHz, T 1 = 9 s, T 2 = 1.2 s C – 125 MHz, T 1 = 25 s, T 2 = 0.18 s Acoplamento J – Hz Varian Premium Shielded – 11 T Fidelity = 0.993

2 qubits system represented by 2 coupled spins ½: –Sample: 100 mg of 13 C-labeled CHCl 3 dissolved in 0.7 mL CDCl 3 –Spectrometer: –Initial State: H – 500 MHz, T 1 = 9 s, T 2 = 1.2 s C – 125 MHz, T 1 = 25 s, T 2 = 0.18 s Acoplamento J – Hz Varian Premium Shielded – 11 T

–1º State: Fidelity = –2º State: Fidelity = 0.993

Geometric Discord: Time (s) Direct Measurement Tomography Theoretical

Negativity of Quantumness: Time (s) (Theoretical)

(a) Discord (b) Geometric Discord (c) Trace Distance (d) Bures Distance Preliminary Results Aaronson, B.; Lo Franco, R.; Adesso, G. Physical Review A, v. 88, p , Freezing Universality

Relaxation Process Phase Damping (PD) Generalized Amplitude Damping (GAD) Decoherence Channels:

Phase Damping Channel: -Transversal relaxation (T 2 ): Loss of coherence without loss of energy Two Qubit System *Souza, A.M. and et al. Quantum Information Computation, v. 10, p. 653, 2010.

Phase Damping Channel: -Transversal relaxation (T 2 ): -Global Phase Damping (spin 3/2 system)*: Loss of coherence without loss of energy *Souza, A.M. and et al. Quantum Information Computation, v. 10, p. 653, Two Qubit System

Phase Damping Channel: -Transversal relaxation (T 2 ): -Global Phase Damping (spin 3/2 system)*: Loss of coherence without loss of energy *Souza, A.M. and et al. Quantum Information Computation, v. 10, p. 653, Two Qubit System

Phase Damping Channel: -Transversal relaxation (T 2 ): -Global Phase Damping (spin 3/2 system)*: Loss of coherence without loss of energy *Souza, A.M. and et al. Quantum Information Computation, v. 10, p. 653, Two Qubit System

Emergence of the Pointer Basis: S E A Measurement Decoherence Collapse of A in some classical state which is not altered by decoherence! Pointer Basis The pointer basis emerges when classical correlation between S and A becomes constant!* J. D. Montealegre, F. M. Paula, A. Saguia, and M. S. Sarandy, Phys. Rev. A 87, (2013). Time (s)

Phase Damping Channel: –2 spins ½ system

Generalized Amplitude Damping Channel: –3/2 spins system –Sample: Lyotropic Liquid Crystals Sodium Dodecyl Sulfate (SDS) Heavy Water (D 2 O) Decanol (C 10 H 21 OH) –Spectrometer: Varian Inova – 8 T Na – 92 MHz ν Q = 10.4 kHz

Differences between representing two qubit systems with two spins 1/2 coupled and one spin 3/2. Effects of phase damping and generalized amplitude damping channels. Experimental observation of Sudden-change, Freezing, Double Sudden-Change phenomena and the emergence of Pointer Basis. Conclusion

Acknowledgments