1. Quantum Light: Quantumness of Correlations and their applications Natalia Korolkova, St Andrews, UK C. Croal, N. Quinn, L. Mista* University of St. Andrews, UK; *Palacky University, Olomouc, Czech Republic V. Chille, Ch. Peuntinger, Ch. Marquardt, G. Leuchs Max Planck Institute for the Science of Light, Erlangen, Germany - Experiments 14 March 2016, London

2. Quantum discord and Gaussian quantum discord Pure states: -entangled - separable Mixed states: -entangled (and discordant) -separable and have non-zero discord - separable, no discord Quantum discord - a more resilient form of quantum correlations

3. What can be quantum about separable states? Nonorthogonal separable states cannot be discriminated deterministically and exactly Measuring a local observable on a separable bipartite state can perturb the state The eigenvectors of a separable state can be entangled superpositions …. Review: The classical-quantum boundary for correlations: discord and related measures. K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, Rev. Mod. Phys. 84, 1655-1707 (2012) Gaussian discord: G. Adesso and A. Datta, Phys. Rev. Lett. 105, 030501 (2010) ;

4. Quantum discord: (quantum mutual information) - (one way classical correlation) H. Ollivier and W. H. Zurek, Phys. Rev. Lett. 88, 017901 (2001); L. Henderson and V. Vedral, J. Phys. A 34, 6899 (2001) Classically - equivalent definitions of mutual information: Shannon entropy: Conditional: Quantum – they are not equivalent; mutual information: von Neumann entropy:

5. Quantum conditional entropy related to upon POVM on B. Infimum: optimization to single out the least disturbing measurement on B - one way classical correlation Total info about A Quantum correlation: Info about A inferred via quantum measurement on B Total info about A Optimal measurements: Gaussian G. Adesso, A. Datta, PRL 105, 030501 P. Giorda, M. G. A. Paris, ibid, 020503 (2010) Gaussian Quantum discord

6. Gaussian states are those with a Gaussian Wigner function. - vector of quadratures; - covariance matrix. State is inseparable iff: Separability is determined by the PPT criterion: For N modes, mode j is separable iff: R. Simon, Phys. Rev. Lett. 84, 2726 (2000) (all second order moments of two modes)

7. Definition without entropies: A state is said to be discordant if and only if it cannot be fully determined without disturbing it with the aid of local measurements and classical communication: orthonormal basis Nonorthogonal separable states cannot be discriminated deterministically and exactly …. Discordant quantum states unavoidably exhibit quantum uncertainty on the measurement of any single local observable.

8. Non-classical correlations without entanglement allow for a computational speed-up in the DQC1 model of noisy quantum computation A. Datta et al. 2008-2011; Experiments: Experimental quantum computing without entanglement, Lanyon, Barbieri, Almeida, White, PRL 101, 200501 (2008) (photons); Laflamme group, Serra group, 2011 (NMR) Quantum computation with noisy quantum bits (DQC1, one-way) Locking of classical information into quantum states Metrology with mixed probes, Quantum illumination Quantum state merging and the “mother” protocol for communication Remote state preparation See also: Quantum discord as a resource in quantum communication, V. Madhok, A. Datta, International Journal of Modern Physics B, 27, 1245041, (2013) optimal ways to make use of noisy quantum states or channels for communication, metrology or establishing entanglement optimal ways to make use of noisy quantum states or channels for communication, metrology or establishing entanglement

9. “classical” definition of non-classicality in bi-partite system Gaussian states with non-zero quantum discord are often classical according to this definition Information-theoretical approach: can I prepare state by LOCC? Gaussian states with non-zero quantum discord are non-classical according to this definition A.Ferraro, M. G. Paris, Phys. Rev. Lett. 108, 260403 (2012) M. Piani, P. Horodecki, R. Horodecki, Phys. Rev. Lett. 100, 090502 (2008); M. Piani, M. Christandl, C. E. Mora, P. Horodecki, Phys. Rev. Lett. 102, 250503 (2009).

10. QQ: non-zero discord, not all the information about them can be locally retrieved; cannot prepare by LOCC; QC: zero A-discord, cannot be cloned locally (locally broadcasted) Information-theoretical approach: can I prepare state by LOCC? All these states are separable – but: CC QQ QC A.Ferraro, M. G. Paris, Phys. Rev. Lett. 108, 260403 (2012) M. Piani, P. Horodecki, R. Horodecki, Phys. Rev. Lett. 100, 090502 (2008); M. Piani, M. Christandl, C. E. Mora, P. Horodecki, Phys. Rev. Lett. 102, 250503 (2009).

11. Picture courtesy: Albert Einstein Institute, Hannover First generation: Silberhorn, Lam, Weiss, Koenig, Korolkova, Leuchs, PRL 86, 4267 (2001) Entanglement from squeezing Photon statistics of squeezed light – photon pairs - quantum correlations

12. A passive (non-entangling) operation on one classical part of a non-classically correlated separable state can create entanglement M.S. Kim et al., Phys. Rev. A 65, 032323 (2002). M. Brunelli et al., arXiv:1502.04996 (2015). So far: A beamsplitter produces entanglement if the input modes are squeezed

13. Entangling the whole by beam splitting a part separable entangled across no local squeezing! C. Croal, Ch. Peuntinger, V. Chille, Ch. Marquardt, G. Leuchs, N. Korolkova, L. Mišta: Entangling the whole by beam splitting a part, Phys. Rev. Lett. 115, 190501 (2015) Specific separability properties, can be tailored

14. State Preparation input mixed states

15. Entangling the whole by beam splitting a part Polarisation Squeezer EOM HWP QWP vacuum BS Coherent State EOM HWP QWP A B Correlated Displacements HWP PBS - - - Data Processing separable entangled across no local squeezing!

16. Specific separability properties Tailored quantum correlations as ingredient in communication protocols optimal ways to make use of noisy quantum states or channels for communication or establishing entanglement optimal ways to make use of noisy quantum states or channels for communication or establishing entanglement

17. Entanglement distribution by separable ancilla Sharing Entanglement without Sending It Viewpoint on our work: C. Silberhorn, Physics 6, 132

18. Correlated noise creates coherence This term correspond to CM of specially designed (classically correlated) noise

19. the lower symplect. eigenvalue A & B are entangled CV: Ch. Peuntinger et al., PRL 111, 230506 (2013); E. Vollmer et al., PRL 111, 230505 (2013) DV: A. Fedrizzi et al., PRL 111, 230504 (2013) highlighted C. Silberhorn, Physics 6, 132 (2013) Theory: CV: L. Mista and N. Korolkova Phys. Rev. A 77, 050302(R) (2008), ibid 80, 032310 (2009). DV: T. S. Cubitt, F. Verstraete, W. Dür, and J. I. Cirac, Phys. Rev. Lett. 91, 037902 (2003).

20. Duan‘s entanglement criterion C. Peuntinger et al., PRL 111, 230506 (2013) the lower symplectic eigenvalue A & B are entangled

21. “Normal” explanation: role of classical information Classical information lies in our knowledge about all the correlated displacement involved. Bob (or David for him) can recover through clever noise addition quantum resources initially present in the input quantum squeezed states.

22. Role of classical communication: we use our knowledge about initial pure product state to design correlated noise such that it cancels out Role of dissipation: dissipation to a common reservoir, not a product state any more (mode C viewed as “environmental mode”) Role of discord: need non-zero discord in order to obtain entanglement at final stage T.K. Chuan, J. Maillard, K. Modi, T. Paterek, M. Paternostro, M. Piani, Role of quantumness of correlations in entanglement distribution, (2012); A. Streltsov, H. Kampermann, D. Bruss, Quantum cost for sending entanglement, (2012) ; N. Quinn, C. Croal, N. Korolkova, J Russ Laser Research 36, 550 (2015); A. Datta, Studies on the Role of Entanglement in Mixed-state Quantum Computation, PhD th 2008. Entangling power of a BS: By passive operation on non-classically correlated state of ≥ 3 modes, modify its separability properties to facilitate entanglement activation/localization

23. Entanglement distribution by separable ancilla entangled separable C remains separable throughout A and B entangled two-mode biseparable state, bound entanglement Ch. Peuntinger, V. Chille, L. Mišta, N. Korolkova, M. Förtsch, J. Korger, Ch. Marquardt, G. Leuchs, PRL 111, 230506 (2013) - experiment entangling BS – conceptually as in previous case localization of entanglement

24. Experiment C. Croal, Ch. Peuntinger, V. Chille, Ch. Marquardt, G. Leuchs, N. Korolkova, L. Mišta: Entangling the whole by beam splitting a part, Phys. Rev. Lett. 115, 190501 (2015) entangled

25. Protocol 1: Results Mode A is entangled with modes BC and mode C is entangled with modes AB - simplectic eigenvalues Entangling the whole by beam splitting a part

26. Protocol 2: Results Mode A is entangled with modes BC but the rest of the modes are separable - simplectic eigenvalues Essential step in entanglement distribution by separable ancilla

27. Dense coding allows to transmit information more efficiently than classically possible. In CV, this was done using a two-mode entangled state, where in the limit of infinite photon number the capacity was double the coherent state capacity. It has since been demonstrated for three modes using a CV GHZ state. Measurement of the third mode controls capacity of the scheme. S. L. Braunstein and H. J. Kimble, Phys. Rev. Lett. 61, 042302 (2000). J. Jing et al. Phys. Rev. Lett. 90, 167903 (2003). Dense coding: Application of protocol 1 – collaborative dense coding

28. Application – collaborative dense coding Charlie controls the capacity of communication With protocol 1 – orange circles & ellipses; With protocol 2 – blue circle & ellipses C. Croal, et al, Phys. Rev. Lett. 115, 190501 (2015)

29. Quantum Discord under local loss S. Campbell et al., Phys. Rev. A 84, 052316 (2011) A. Streltsov et al., Phys. Rev. Lett. 107, 170502 (2011) F. Ciccarello and V. Giovannetti, Phys. Rev. A 85, 010102 (2012) discrete variables: Quantum correlations emerge from separable (classically correlated) state F. Ciccarello and V. Giovannetti, Phys. Rev. A 85, 022108 (2012) continuous variables: experiment: L.S. Madsen et al., Phys. Rev. Lett. 109, 030402 (2012)

30. Discord dynamics in open system: scheme V. Chille, N. Quinn, C. Peuntinger, C. Croal, L. Mišta, Jr., Ch. Marquardt, G. Leuchs, N. Korolkova, Phys. Rev. A 91, 050301(R) (2015)

31. Results: discord increase with loss

32. Underlying physics here: Nonorthogonal states cannot be discriminated exactly Underlying physics here: Nonorthogonal states cannot be discriminated exactly a set of generic non-orthogonal states

33. Passive operation transmutes system-environment correlations into entanglement interfere B with a mode carrying displacements such that the noise partially cancels out alternatively: computationally on the raw data instead of physically classical information about the displacements of the squeezed states  recover the entanglement?!

34. violation of Duan’s separability criterion (product form)  entanglement across the A-(BC) splitting before the BS  proves entanglement:  B shares quantum correlations with (AC)  B realizes a true quantum communication between the locations of modes A and C, which cannot be replaced by LOCC Same element as in protocols 1 & 2 showing entangling power of BS: V. Chille, N. Quinn, C. Peuntinger, C. Croal, L. Mišta, Jr., Ch. Marquardt, G. Leuchs, N. Korolkova, Phys. Rev. A 91, 050301(R) (2015)

35. First experimental demonstration of transformation of entanglement from class 1 to class 3 or class 4 1.Fully separable 2.Entangled, but neither of the subsystems entangled with other two 3.One subsystem entangled with remaining two (e.g. A-BC) 4.Entangled across two bipartitions (e.g. A-BC, B-AC) 5.Fully entangled entangled fully separable (one-mode biseparable state) Up the hierarchy ladder of entanglement classes: G. Giedke, B. Krauss, M. Lewenstein, J. I. Cirac, Phys. Rev. A 64, 052303 (2001)

36. www.st-andrews.ac.uk/~qoi http://www.mpl.mpg.de/en/leuchs/research/qiv.html