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Displaced-photon counting for coherent optical communicatio Displaced-photon counting for coherent optical communicatio

Displaced-photon counting for coherent optical communicatio - PowerPoint Presentation

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Displaced-photon counting for coherent optical communicatio - PPT Presentation

Shuro Izumi Discrimination of phaseshif t keyed coherent states Super resolution with displacedphoton counting Phase estimation for coherent state Discrimination of phaseshif t keyed coherent states ID: 574573

displaced photon measurement counting photon displaced counting measurement state phase resolution super coherent states homodyne receiver detection optimal pnrd

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Slide1

Displaced-photon counting for coherent optical communication

Shuro IzumiSlide2

Discrimination of phase-shif

t keyed coherent states

Super resolution with

displaced-photon counting

Phase estimation for coherent stateSlide3

Discrimination of phase-shif

t keyed coherent states

Super resolution with

displaced-photon counting

Phase estimation for coherent stateSlide4

Optical communication

Encode the information on the optical states

Squeezed states

Entangled states

Photon number states

Super position states

Receiver

Sender

Laser

Detector

Optical state

Excellent properties

Decision

However..

Changed to mixed states by losses

Non-classical states are not optimal for signal carriers

Non-classical statesSlide5

Motivation

Discriminate

p

hase-shift

keyed coherent states

with

minimum error probability

Optical communication with coherent states

Remain pure state under loss condition✓ Easily generated compared with non-classical statesCoherent state is the best signal carrier under the losses because However

✓ It is impossible to discriminate coherent states without error because of their non-orthogonalitySlide6

Achievable minimum Error Probability

Standard Quantum Limit

…. Achievable Error probability by measurement of the observable which characterizes the states

Helstrom bound

…. Achievable Error probability for given states

How

to

realize

optimal measurement

?Overcome the SQL

and approach

the Helstrom bound

!!

C. W. Helstrom,

Quantum Detection and Estimation Theory

(Academic Press, New York, 1976).

0

1

0

1

Helstrom bound

SQL

Error

Phase-shift keyed

Homodyne measurement

Binary phase-shift keyed (BPSK)Slide7

on

off

Photon counter

Displacement

operation

Near-optimal receiver for BPSK signals Displaced-photon counting

R. S. Kennedy, Research Laboratory of Electronics, MIT, Technical Report No. 110, 1972

Local Oscillator

Beam splitter

Error

Helstrom bound

SQL (Homodyne measurement)

Displaced-photon countingSlide8

k

.

Tsujino

et al., Phys. Rev.

Lett

. 106, 250503(2011)Experimental demonstration of near-optimal receiver for BPSK signals

Detector

with high detection efficiency

Transition

edge

sensor (TES)→Detection efficiency : 95 % for 853nm

Photon counterClassical (electrical)

feedback

or

Optimal

receiver

for BPSK signals

Displaced-photon

counting

with

feedback

operation

(Dolinar receiver)

S

. J. Dolinar, Research Laboratory of Electronics, MIT, Quarterly Progress Report No. 111, 1973

R.

L. Cook,

et al.,

Nature 446, 774, (2007)

Displacement

optimization

Optimize the amount of Slide9

p

x

QPSK signals

p

x

Displaced-photon counting

Near-optimal

Displaced-photon

counting with feedback

Optimal

How

to

realize near

-

optimal

measurement for QPSK signals

?Slide10

R

. S. Bondurant,5 Opt.

Lett.

18

, 1896 (1993

)

Near-optimal receiver for QPSK signals

Photon counter

Classical

(electrical)feedback

p

x

Displaced-photon counting with feedback receiver

Helstrom

Heterodyne measurement (SQL)

Bondurant receiver

Infinitely fast feedback

More practical condition

finite feedback Slide11

x

p

on

off

Evaluation for finite feedforward steps

Change the displacement operation depending on previous results

S. Izumi et al., PRA.

86

, 042328

(2012)

M.

Takeoka

et al., PRA.

71

, 022318

(2005)

N

→∞

Bondurant receiverSlide12

Displaced-photon counting

without feedforward

Helstrom

Heterodyne measurement (SQL)

Bondurant

N

=

N

=20

N

=10

N=5N=4

N=3Numerical evaluation

Improve the error probability with increasing the feedforward

steps

S. Izumi et al., PRA.

86

, 042328

(2012)Slide13

x

p

Displaced-photon counting

with Feedforward operation(Dolinar receiver )

Change the displacement operation depending on previous results

Photon-number resolving detector

*Symbol selection

Bayesian estimation

The signal which maximizes the posteriori probability

S. Izumi et al., PRA.

87

, 042328

(2013)Slide14

Heterodyne measurement (SQL)

Helstrom

bound

N

=10

N

=4

N

=3

On-off detector

Photon-number-resolving detector

N=5

Numerical evaluationImprove the error probability in small feedforward steps!!

S. Izumi et al., PRA. 87

, 042328

(2013)Slide15

Numerical evaluation with detector’s imperfection

Dark count

ν

:

counts/pulse

 

On-off detector

PNRD

Robust against dark count noiseS. Izumi et al., PRA. 87

, 042328 (2013)Slide16

Experimental realization of feedforward receiver for QPSK

NIST demonstrated the feedforward (feedback) receiver

F

. E.

Becerra et al.,

Nature Photon.

7

, 147 (

2013)

C. R. Muller et al., New J. Phys. 14

, 083009 (2012

)

F. E. Becerra et al., Nature Photon. 9, 48 (2015)

With on-off detector

With PNRD

Homodyne + Displaced-photon counting

Hybrid scheme from Max-Plank institute

Real time feedback with FPGA

Feedforward

operation

dependent

on

the result of homodyne measurementSlide17

Summary

We propose and numerically evaluated the receiver

for QPSK signals

Displaced-photon counting with PNRD based feedforward operation improve the performance for QPSK discriminationSlide18

Discrimination of phase-shif

t keyed coherent states

Super resolution with displaced-photon counting

Phase estimation for coherent stateSlide19

Phase sensing with displaced-photon counting

Better performance than homodyne measurement

Displaced-photon counting is near-optimal receiver for signal discrimination

Can

displaced-photon counting make improvements in phase sensing?

Super resolution

✓ Approach the Helstrom bound✓ Phase estimationSlide20

Super resolution and Sensitivity

Input state

Quantum measurement

Phase shift

Super sensitivity

N00N state

Coherent state

Nagata et al.,

Science

316

,

726 (2007)

Xiang et al., Nature Photonics

5

, 268 (2010)

Sensitivity

Resolution

Interference pattern

Coherent state

with particular quantum measurements

Super resolution

Narrower width

Non-classical states are not necessary

Y.

Gao et al

.,

J. Opt. Soc. Am. B.

27

, No.6 (2010)

E.

Distant et al

., Phys. Rev. Lett.

111

, 033603(2013)

K.

Jiang et al

.,

J. Appl. Phys.

114

, 193102(2013)

K. J.

Resch et al

.,

Phys. Rev. Lett.

98

, 223601

(2007)Slide21

Standard two-port intensity difference monitoring

Input state

Intensity difference monitoring

-Slide22

Super resolution with parity detection

Input state

Parity detection

Even

Odd

PNRD

Y.

Gao et al

.,

J. Opt. Soc. Am. B.

27

, No.6 (2010)

Super resolutionSlide23

Super resolution with homodyne measurement

E.

Distant et al

., Phys. Rev. Lett.

111

, 033603(2013)

Homodyne measurement

Super resolutionSlide24

Super resolution with homodyne measurement

Threshold

h

omodyne measurement POVM

Normalized

E.

Distant et al

., Phys. Rev. Lett.

111

, 033603(2013)

Count probability with the phase shift

a=0.1

a=1.0

a=2.0

a=0.1

a=1.0

a=2.0

Trade off

between sensitivity

(variance

)

and resolutionSlide25

Evaluatio

n of sensitivity

E.

Distant et al

., Phys. Rev. Lett.

111

, 033603(2013)Slide26

Super resolution with displaced-photon counting

Photon counter

Displacement

operation

Does displaced-photon counting show the super resolutio

n

?

General phase detection scheme

Mach-Zehnder

phase detection scheme

Count probability with the phase shift Slide27

Super resolution with displaced-photon counting

Homodyne measurement (with normalization)

Parity detection (same input power to the phase shifter)

Displaced-photon counting

Super resolution

Width

Width :

Width :

Width :Slide28

Evaluation of resolution and sensitivity

a=0.1

Displaced-photon counting

a=1.0

Parity detection

Resolution

Sensitivity

a=0.1

Displaced-photon counting

a=1.0

Parity detection

Shot noise limit

Displaced-photon counting shows better performance

Displaced-photon counting also shows super resolutionSlide29

Summary

Displaced-photon counting shows both super resolution and good sensitivity

Super

resolution

can be observed with coherent state and quantum measurement

→parity detection, homodyne measurement

a=0.1

Displaced-photon counting

a=1.0

Parity detection

Shot noise limitSlide30

Discrimination of phase-shif

t keyed coherent states

Super resolution with displaced-photon counting

Phase estimation for coherent stateSlide31

Phase estimation

Quantum measurement

Estimator

Input state

Phase shift

Optimal input state

Optimal measurement

Optimize for

good

estimation

Figure of merit

Variance of the estimator Slide32

Cramer-Rao bound

Cramer-Rao bound

The variance of estimator must be larger than inverse of

Fisher information

.

For M states ,

B.R.Frieden

, “Science from

Fisher Information” ,

CAMBRIDGE UNI.PRESS(2004)Slide33

Fisher information (FI)

Quantum FI

Classical FI

depends only on input state.

depends on input state

 

and measurement.

Possible to derive the minimum variance for given state

S.L.Braunstein and

C.M.Caves,

PRL, 72, 3439 (1994)

Possible to derive the minimum variance for given state and measurement

How

much

information

state

has

How

much

information

we can extract from the state by measurementSlide34

Fisher information for coherent state

Phase shift

Quantum FI

Quantum measurement

Homodyne measurement

Heterodyne measurement

Classical FI

S.Olivares

et, al.,

J.Phys.B

, Mol. Opt.

Phys

, 42(2009)

Homodyne

HeterodyneSlide35

Fisher information for coherent state with displaced-photon counting (PNRD)

PNRD

Displaced-PNRD

Fisher information for discrete variableSlide36

Displaced-photon

counting decrease

slowly

Fisher information

Homodyne decrease r

apidlySlide37

Experimental

setup ~Preliminary experiment

99:1 BS

LO

probe

PNRD

PZT

Transition edge sensor (TES)

Photon-number resolving up to 8-photon

Detection efficiency 92%

Fukuda et al., (AIST)

Metrologia

,

46

,

S288 (2009)

Laser

1550 nmSlide38

Experimental

condition

Probe amplitude

Displacement amplitude

Detection efficiency

Visibility Slide39

Experimental

results ~Preliminary experiment

Heterodyne

Displaced-PNRD Experiment

Displaced-PNRD Theory

Homodyne

Displaced-PNRD Theory with imperfections

# of measurement

Expectation value

# of measurement

Variance

Expectation value

VarianceSlide40

Summary

D

isplaced-photon counting gives higher fisher information

than homodyne measurement

around Θ=0

Is it possible to use this result for phase sensing?

✓ We demonstrated preliminary experiment →We experimentally show that displaced-photon counting gives better performance in particular condition

→Adjustment of the experimental setup more carefully is required