Quantum correlations by tailored dissipassion. Natalia Korolkova, St Andrews, UK R. Tatham, N. Quinn, L. Mišta

Transcription

1 Quantum correlations by tailored dissipassion Natalia Korolkova, St Andrews, UK R. Tatham, N. Quinn, L. Mišta

2 quantum correlations in separable mixed states entanglement "Quantum discord as resource for remote state preparation": B Dakic, Y-O Lipp, X Ma, M Ringbauer, S Kropatschek, S Barz, T Paterek, V Vedral, A Zeilinger, C Brukner, P Walther (Nature Physics 2012)

3 Classically - equivalent definitions of mutual information: Shannon entropy: Conditional: Quantum they are not equivalent; mutual information: von Neumann entropy: Quantum discord: (quantum mutual information) - (one way classical correlation)

4 quantum correlations in separable mixed states Dissipative systems, controlled dissipation, dissipative driving Early ideas: J. P. Poyatos, J. I. Cirac, P. Zoller, Phys. Rev. Lett. 77, 4728 (1996) Constructive use of nonlinear dissipation in ion traps (quantum state protection), Design of different couplings btw trapped ion and environment Cavity-loss-induced generation of entangled atoms, M. B. Plenio, S. F. Huelga, A. Beige, P. L. Knight, Phys. Rev. A 59, 2468 (1999)

5 Quantumness by dissipation (more recent examples) Interaction with a common environment can lead to the creation of an entangled state from an initial separable state F. Benatti and R. Floreanini, J. Phys. A: Math. Gen. 39, 2689 (2006); D. Mogilevtsev, T. Tyc, and N. Korolkova, Phys. Rev. A 79, (2009) Quantum computation, quantum state engineering, and quantum phase transitions driven by dissipation F. Verstraete, M. M. Wolf, and J. I. Cirac, Nature Physics 5, 633 (2009) Dissipatively driven entanglement of two macroscopic atomic ensembles C. A. Muschik, E. S. Polzik, and J. I. Cirac, Phys. Rev. A 83, (2011)

6 Quantifiers of non-classical correlations (quantum discord, etc): link the emergence of quantum correlations with changes in entropy in quantum systems coupled to the environment Quantum correlations as quantified by discord are about inducing quantumness by dissipation

7 Quantum discord: (quantum mutual information) - (one way classical correlation) Reasearch avenues: - operational interpretation? - fundamental nature of this resource?

8 Koashi-Winter inequality: Koashi, Winter, PRA 69, (2004) Monogamy of entanglement: a quantum system being entangled with another one limits its possible entanglement with a third system Interplay between entanglement and classical correlation. Perfect entanglement and perfect classical correlation are mutually exclusive

9 Emergence of quantum discord: simple example of two systems Local noisy channels, nonunital (!) e.g. dissipation. A C DV: Streltsov, Kampermann, Bruss, PRL 107, (2011); CV: Ciccarello, Giovannetti, PRA 85, (2012) Local non-unitary measurement. Streltsov, Kampermann, Bruss, PRL 2011 : Are there any noisy channels that might even increase the amount of quantum correlations? How does dissipation influence quantum correlations, and how are they affected by decoherence?

10 A mixed state is not a fundamental object, but a sign of our ignorance. Purification: every mixed state acting on finite dimensional Hilbert spaces can be viewed as the reduced state of some pure state. Ansatz: mixed quantum state + environment = pure quantum state

11 Local non-unitary measurement Discrete example after measurement on C: B A C with Purification: - GHZ state, max entangled Streltsov, Kampermann, Bruss, PRL 2011 : Are there any noisy channels that might even increase the amount of quantum correlations? How does dissipation influence quantum correlations, and how are they affected by decoherence?

12 Initially: entanglement across any bipartition (GHZ) Now: any subsystem traced out no entanglement btw two remaining ones: B A C classical correlations btw those are maximal: Koashi-Winter: The entropy of marginal quantifies capacity of Alice s state to form correlations

13 Local non-unitary measurement on C Alice s and Bob s capacities to create correlations remain unchanged B A C Charlie s capacity to create correlations decrease upon the measurement on C:

14 After non-unitary measurement on C: classical correlations decrease capacity for Alice s correlations must be filled up Alice and Bob become entangled The discord between A and C arises as a side effect of this entanglement formation between the subsystem unaffected by the measurement and environment Tatham, Quinn, Korolkova, in preparation

15 Koashi-Winter inequality: - for pure tripartite system - min taken over all ensembles satisfying this Quantum Discord:

16 The discord between A and C arises as a side effect of the entanglement formation between the subsystem unaffected by the measurement and environment correlated entangled entangled B A C Quantum discord is not really a fundamental phenomenon but a side effect of all the changes in local entropy in a quantum system coupled to the environment

17 CV version, first experimental results: Theory: Ciccarello, Giovannetti, PRA 85, (2012) A C Madsen, Berni, Lassen, Andersen, Phys. Rev. Lett. 109, (2012)

18 But: started with a Gaussian mixture of coherent states = completely classical resources; Where does quantumness come from? Is there any quantumness? Does Gaussian discord give me a correct picture? Problems with quantum discord of Gaussian states?

19 Definition OK! Gaussian Discord Gaussian measurements optimal - one way classical correlation Total info about A Quantum correlation: Info about A inferred via quantum measurement on B Quantum conditional entropy related to upon POVM on B. Infimum: optimization to single out the least disturbing measurement on B Indirect confirmation that Gaussiam meas. optimal: Nonclassical correlations in continuous-variable non-gaussian Werner states, Mišta, Adesso, Korolkova, Phys. Rev. A 85,

20 Gaussian bi-partite states Naïve thinking: Gaussian states positive Wigner function most classical All non-product (but separable) bi-partite Gaussian states have a non-zero discord - quantum P. Giorda and M. G. A. Paris, Phys. Rev. Lett. 105, (2010); G. Adesso and A. Datta, Phys. Rev. Lett. 105, (2010) ; Quantum???

21 - classical definition of non-classicality Gaussian states with non-zero quantum discord are often classical according to this definition A. Ferraro, M. G. Paris, Phys. Rev. Lett. 108, (2012): Our results suggest that there are other quantum correlations in nature than those revealed by entanglement and quantum discord.

22 Information-theoretical concept of quantum/classical entanglement/separability according to Werner 1989 can be physically indistinguishable not all the information about them can be locally retrieved; Cannot prepare by LOCC. This phenomenon has no classical counterpart, quantumness of the correlations in separable state with positive discord

23 Quantumness in separable states: Nonorthogonal separable states cannot be discriminated exactly Measuring a local observable on a separable bipartite state can perturb the state The eigenvectors of a separable state can be entangled superpositions In general separable states have not a purely classical nature

24 Sometimes this quantumness has to be activated by some sort of post processing Non-orthogonal fill states but need to select individual states from the distribution Non-orthogonality quantumness has to be revealed

25 Here, we demonstrate that under certain measurement constraints, discord between bipartite systems can be consumed to encode information that can only be accessed by coherent quantum interactions. The inability to access this information by any other means allows us to use discord to directly quantify this quantum advantage. We experimentally encode information within the discordant correlations of two separable Gaussian states. The amount of extra information recovered by coherent interaction is quantified and directly linked with the discord consumed during encoding.. M. Gue et al (ANU + T. C. Ralph + Singapore), Nature Physics 8, 671 (2012)

26 We still do not have an adequate map for the quantum classical boader States with zero discord (CC-states) can exhibit quantum correlations acc. to phase-space criteria; Classical states acc. to P-function can have positive discord and cannot be prepared by LOCC

27 Simplest test-bench for Gaussian discord: two optical modes Do our arguments based on Koashi-Winter apply? Nature and usefulness of Gaussian discord in this scenario?

28 A C B A C Add purifying mode and construct purification

29 Purification: add E, replace A with TMSV for AE: B A C Tatham, Quinn, Mista, Korolkova, in preparation

30 Using Koashi-Winter as in discrete case: correlated entangled entangled B A C Quantum discord emerges as a side effect of all the changes in local entropy in a quantum system coupled to the environment Confirmed by measurement results: see poster by V Chille & Ch Peuntinger

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35 Purification: add E, replace A with TMSV for AE: B A C Tatham, Quinn, Mista, Korolkova, in preparation

36 Max QD is larger for stronger modulation; mixed states can be more non-classical correlated Max increase of QD with dissipation: less modulation and phase shift entangled B entangled A C

37 Dissipation-induced coherence Quantum optics: correlations, coherence, correlation functions, ability to interfere. Quantum information: quantum entropy, entropy of entanglement. Quantum discord: correlations via changes in local entropy across dissipative system non-classical correlations, such as quantified by quantum discord, unite coherence with changes in entropy in quantum systems coupled to the environment link coherent and dissipative dynamics together link coherence and correlations to the entropy flow in a global system

38 Quantum resource in entanglement distribution: correlations induced by controlled dissipation Tailored dissipation as a tool: Controlled flow of (quantum) information between system and environment

39 Tailored dissipation as a tool: Designing nonlinear loss to overcome linear loss D. Mogilevtsev, A. Mikhalychev, V. S. Shchesnovich, N. Korolkova, submitted (2012)

40 Rate of nonlinear dissipation Rate of linear dissipation Initial state The Lindblad operator for engineered dissipation: pure target state The pure stationary state of this equation: cohereret one For possible to generate any desired state

41 The two-photon Fock state generation (a) Fidelity of the target two-photon Fock state generation for the designed loss with the Lindblad operator (b) The photon number distribution of the generated state for the maximal fidelity of the target two photon state generation A coherent initial state; target state: The Lindblad operator: (nonlinear dissipation)

42 Simple picture: Dissipation: jumps to the lower energy levels Rate (of transitions to the lower levels due to nonlinear dissipation ) << rate of linear loss Stationary state for nonlinear dissipation nonclassical state; Designing dissipation (form of the Lindblad operator) we determine the nonclassical target state Implementations: e.g. ion traps allow for dissipation engineering

43 Theoretical Quantum Information group N Korolkova, S Ivanov, (D Vasylyev), (D Milne), (R Tatham), N Quinn, C Croal; L. Mista - regular visitor from Olomouc

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46 Mutual information = total correlations btw A and B Classically - equivalent definitions of mutual information: Shannon entropy: Conditional: Quantum they are not equivalent; mutual information: von Neumann entropy: measurements!

47 - one way classical correlation Total info about A Quantum correlation: Info about A inferred via quantum measurement on B Quantum conditional entropy related to upon POVM on B. Infimum: optimization to single out the least disturbing measurement on B

48 Quantum discord: quantum mutual information one way classical correlation - classical - quantum, separable - entangled

49 quantum mutual information one way classical correlation QD = quantum mutual info - the classical mutual info of outcomes; QD = total correlations - classical correlations; + operational; conceptually easy; optimized over POVMs - hard to compute; asymmetric not unique DV: H. Ollivier and W. H. Zurek, Phys. Rev. Lett. 88, (2001); L. Henderson and V. Vedral, J. Phys. A 34, 6899 (2001) CV: G. Adesso and A. Datta, Phys. Rev. Lett. 105, (2010) P. Giorda and M. G. A. Paris, Phys. Rev. Lett. 105, (2010) L. Mista, R. Tatham, D. Girolami, N. Korolkova, G. Adesso, Phys. Rev. A. (2011)

50 quantum mutual information non-gaussian classical correlation MID = quantum mutual info - the classical mutual info of outcomes of local Fock-state detectors; + symmetric - no optimizations over local measurements often overestimates quantum correlations Measurement-induced disturbance (MID) S. Luo, Phys. Rev. A 77, (2008)

51 quantum mutual information maximal classical correlation extractable by local (Gaussian) processing AMID (Gaussian) = quantum mutual info - the maximal classical mutual info obtainable by (Gaussian) local measurements AMID optimized as discord and symmetric as MID L. Mista, R. Tatham, D. Girolami, N. Korolkova, G. Adesso, Phys. Rev. A (2011)