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 ID: 536467
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Slide1
Quantum Light: Quantumness of Correlations and their applications
Natalia
Korolkova
,
St Andrews, UKC. Croal, N. Quinn, L. Mista*University of St. Andrews, UK;*Palacky University, Olomouc, Czech RepublicV. Chille, Ch. Peuntinger, Ch. Marquardt, G. LeuchsMax Planck Institute for the Science of Light, Erlangen, Germany - Experiments14 March 2016, LondonSlide2
Quantum discord and Gaussian quantum discordPure states:
entangled
- separableMixed
states: entangled (and discordant)
separable and have non-zero discord- separable, no discordQuantum discord - a more resilient form of quantum correlationsSlide3
What can be quantum about separable states?Nonorthogonal separable states cannot be
discriminated deterministically and exactlyMeasuring 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) ;Slide4
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:Slide5
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
a
bout A
Quantum correlation:
Info about A inferred via quantum measurement on B
Total info
a
bout A
Optimal measurements:
Gaussian
G.
Adesso
,
A.
Datta
,
PRL 105, 030501 P. Giorda, M. G. A. Paris, ibid, 020503(2010)
Gaussian Quantum discordSlide6
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)Slide7
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.Slide8
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 statesMetrology with mixed probes, Quantum illuminationQuantum state merging and the “mother” protocol for communicationRemote 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 entanglementSlide9
“classical” definition of non-classicality in bi-partite system
Gaussian states with non-zero quantum discord are often classicalaccording to this definition
Information-theoretical approach: can I prepare state by LOCC?
Gaussian states with non-zero quantum discord are non-classicalaccording to this definition
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).Slide10
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:CCQQQCFerraro, 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).Slide11
Picture courtesy: Albert Einstein Institute, Hannover
First generation:
Silberhorn, Lam, Weiss, Koenig, Korolkova, Leuchs, PRL 86, 4267 (2001)
Entanglement from squeezing
Photon statistics ofsqueezed light – photon pairs- quantum correlationsSlide12
A passive (non-entangling) operation on oneclassical part of a non-classically correlated separable statecan 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 squeezedSlide13
Entangling the whole by beam splitting a part
separable
e
ntangled across
n
o local
s
queezing!
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 tailoredSlide14
State
Preparation
i
nput mixed statesSlide15
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
e
ntangled across
n
o local
s
queezing!Slide16
Specific separability propertiesTailored quantum correlations as
ingredient in communication protocols
optimal ways to make use of noisy quantum states or channels for communication or establishing entanglementSlide17
Entanglement distribution by separable ancillaSharing Entanglement without Sending It
Viewpoint on our work:
C. Silberhorn, Physics 6, 132Slide18
Correlated noise creates coherence
This term correspond
to CM of specially
designed (classically
correlated) noise Slide19
the lower
symplect. eigenvalue
A & B are entangledCV: 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)
T
heory:
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). Slide20
Duan‘s entanglement criterion
C. Peuntinger et al.,
PRL
111, 230506 (2013
) the lower symplectic eigenvalueA & B are entangledSlide21
“Normal” explanation:
r
ole 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.Slide22
Role of classical communication:we use our knowledge about initial pure product state to design correlated noisesuch that it cancels out
Role of dissipation:d
issipation 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/localizationSlide23
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 ofentanglementSlide24
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 Slide25
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 partSlide26
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 ancillaSlide27
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 codingSlide28
Application – collaborative dense coding
Charlie controls the capacity of communicationWith protocol 1 – orange circles & ellipses;With protocol 2 – blue circle & ellipses
C.
Croal
, et al, Phys. Rev. Lett. 115, 190501 (2015)Slide29
Quantum Discord under local lossS. 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 correlationsemerge from separable(classically correlated) stateF. Ciccarello and V. Giovannetti, Phys. Rev. A 85, 022108 (2012)
continuous
variables:
e
xperiment:
L.S
. Madsen et al.,
Phys
. Rev.
Lett
. 109, 030402 (2012)Slide30
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)Slide31
Results: discord increase with lossSlide32
Underlying physics here:Nonorthogonal states cannot be discriminated exactly
a set of generic
non-orthogonal statesSlide33
Passive operation transmutes system-environment correlations into entanglement
interfere B with a
mode carrying displacements
such that the
noise partially cancels outalternatively: computationally on the raw data instead of physicallyclassical information about the displacements of the squeezed states
recover the entanglement
?!Slide34
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)Slide35
First experimental demonstrationof transformation of entanglementfrom class 1 to class 3 or class 4
Fully separableEntangled, but neither of the subsystems entangled with other two
One subsystem entangled with remaining two (e.g. A-BC)Entangled across two bipartitions (e.g. A-BC, B-AC)Fully entangled
entangled
f
ully 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) Slide36
www.st-andrews.ac.uk/~qoi
http://www.mpl.mpg.de/en/leuchs/research/qiv.html