Quantum measurement for optical and quantum communications Masahiro - - PowerPoint PPT Presentation

Quantum measurement for

• ptical and quantum communications

Masahiro Takeoka

National Institute of Information and Communications Technology (NICT) Communications Technology (NICT)

武岡 正裕 武岡 正裕 情報通信研究機構 情報通信研究機構

GCOE Symposium, Emerging Frontiers of Physics, 22 Feb 2011

Communication and quantum physics

Why quantum physics in communication?

EM waves (photons), electrons, etc…

Carriers are quantum mechanical particles

(p ), ,

Q t h i h ld b i l id d h Quantum mechanics should be seriously considered when quantum noise is a dominant noise in your carrier.

What is the ultimate minimum error limit? What is the ultimate minimum error limit?

e.g.) ideal laser light → quantum noise limited

What is the ultimate minimum error limit? What is the ultimate minimum error limit?

Quantization in optical communication

1 1

loss

Sender (laser) Receiver (measurement) (laser) ( ) Discriminate with small

Ideal laser light is

with small error?

Ideal laser light is in ‘coherent state’ Glauber (1963)

• min. uncertainty

Standard quantum limit (SQL)

SQL of signal discrimination

Error rate obtained by measuring the observable in which the signal information is embedded (intensity (number), quadrature, etc) e 1

SQL SQL

ex) Binary phase-shift keyed (BPSK) coherent communication （2値位相変調信号 コヒ レント通信） 10 10−3 ror rate ror rate

SQL SQL

（2値位相変調信号 コヒーレント通信） Homodyne detection BPSK signal 10 10 9 10 10−6 Bit er Bit er detection BPSK signal 10 10−9 2 2 4 4 6 6 8 8 10 10 Photon number/pulse Photon number/pulse

Measurement is more general

Positive Operator-Valued Measure (POVM)

t POVM:

Restricted by the postulate of quantum mechanics

• utcome

set of operators

Free from “physical quantity”!

Discrimination of binary coherent states

Binary Coherent States:

• C. W. Helstrom,
• C. W. Helstrom,
• Inform. Contr. 10, 254 (1967)
• Inform. Contr. 10, 254 (1967)

POVM BPSK coherent states Measurement states Quantum mechanical bound (Helstrom bound) Optimal POVM: → Projection onto the superpositions of coherent states

Quantum receivers

1

Homodyne limit Homodyne limit

(Coherent optical communication) (Coherent optical communication)

10 10−3

• r rate
• r rate

(Coherent optical communication) (Coherent optical communication)

Near optimal receiver Near optimal receiver

10 10−6 Bit erro Bit erro

• R. S. Kennedy, RLE, MIT, QPR,
• R. S. Kennedy, RLE, MIT, QPR,

Near optimal receiver Near optimal receiver （Kennedy receiver Kennedy receiver）

10 10−9

9

2 4 6 8 10 10

108, 219 (1973) 108, 219 (1973)

Coherent local oscillator Coherent local oscillator

No experiments have No experiments have beaten the homodyne limit! beaten the homodyne limit!

2 4 6 8 10 10 Photon number/pulse Photon number/pulse

Photon counter Photon counter Coherent local oscillator Coherent local oscillator

beaten the homodyne limit! beaten the homodyne limit!

Minimum error Minimum error (Helstrom bound) (Helstrom bound)

Optimal receiver Optimal receiver （Dolinar receiver Dolinar receiver）

Coherent local oscillator Coherent local oscillator Photon counter Photon counter Classical feedback Classical feedback (i fi it l f t!) (i fi it l f t!)

• S. J. Dolinar, RLE, MIT, QPR, 111, 115, (1973)
• S. J. Dolinar, RLE, MIT, QPR, 111, 115, (1973)

(infinitely fast!) (infinitely fast!)

Trends of optical receiver sensitivity

10000

Trends of optical receiver sensitivity

ETS-VI 1000 =10-6 Space qualified & plan Ground test SILEX OICETS NeLS 100 y@BER= tons/bit]

C h

TerraSAR-X Digital coherent NeLS 10 ensitivity [Phot

Coherent

coherent 1 Se

Homodyne coherent PSK theoretical limit

1990 1995 2000 2005 2010 2015 Launch year

8

Dolinar receiver (realtime adaptive feedback)

• S. J. Dolinar, RLE, MIT, QPR, 111, 115, (1973)
• S. J. Dolinar, RLE, MIT, QPR, 111, 115, (1973)

Photon counter Photon counter

• r

Classical Classical (electrical) (electrical) Coherent state Coherent state local oscillator local oscillator ( ) ( ) feedback feedback

LO LO

Electrical feedback has to be faster than the optical pulse width Helstrom bound is achieved in the limit of infinitely fast feedback y Proof-of-principle exp.

Cook, Martin & Geremia, Nature 446, 774 (2007)

Application to quantum info: arbitrary binary projection meas.

Takeoka, Sasaki & Lütkenhaus, Phys. Rev. Lett. 97, 040502 (2006)

However, sub-SQL for BPSK is … technically challenging （原理的には興味深いが高精度な実現は困難？

Quantum receivers

1

Homodyne limit Homodyne limit

(Coherent optical communication) (Coherent optical communication)

10 10−3

• r rate
• r rate

(Coherent optical communication) (Coherent optical communication)

Near optimal receiver Near optimal receiver

10 10−6 Bit erro Bit erro

• R. S. Kennedy, RLE, MIT, QPR,
• R. S. Kennedy, RLE, MIT, QPR,

Near optimal receiver Near optimal receiver （Kennedy receiver Kennedy receiver）

10 10−9

9

2 4 6 8 10 10

108, 219 (1973) 108, 219 (1973)

Coherent local oscillator Coherent local oscillator

2 4 6 8 10 10 Photon number/pulse Photon number/pulse

Photon counter Photon counter Coherent local oscillator Coherent local oscillator Minimum error Minimum error (Helstrom bound) (Helstrom bound)

Optimal receiver Optimal receiver （Dolinar receiver Dolinar receiver）

Coherent local oscillator Coherent local oscillator Photon counter Photon counter Classical feedback Classical feedback (i fi it l f t!) (i fi it l f t!)

• S. J. Dolinar, RLE, MIT, QPR, 111, 115, (1973)
• S. J. Dolinar, RLE, MIT, QPR, 111, 115, (1973)

(infinitely fast!) (infinitely fast!)

Extension of the Kennedy receiver

• n/off detector

Kennedy receiver Kennedy receiver

displacement

Takeoka and Sasaki, Phys. Rev. A 78, 022320 (2008)

• n/off detector
• n/off detector

p

（光子数の有無を識別。APD等）

New receivers New receivers

Optimal Displacement Optimal Displacement （光子数の有無を識別。APD等） displacement （変位演算子）

• n/off detector

p p p p

• ptimized γ

Optimal Squeezing + Optimal Squeezing + Displacement Displacement squeezing

LO

• n/off detector

squeezer

• ptimized ζ and β

pump

Approximate realization of the Helstrom meas.

Ideal POVM Ideal POVM

• n/off detector
• n/off detector

Average error probabilities

1 ty

K d K d

to beat

• babilit

Kennedy Kennedy D(γ γ )

the homodyne limit…

0.1 ror pro

Homodyne Homodyne (γ ) Detector

rage er

D(β β )+ )+S(ζ ζ ) QE > 90% DC < 10-2

0.01 Aver

Helstrom bound Helstrom bound (β ) (ζ ) Visibility ξ > 0 995

0.0 0.2 0.4 0.6 0.8 1.0 Average signal photon number

ξ > 0.995

g g p

Proof-of-principle experiment

• U. Erlangen

& NICT

Sig

visibility detection efficiency

*

Wittmann, et al., Phys. Rev. Lett. 101, 210501 (2008)

*Detection efficiency compensated

Superconducting Transition Edge Sensor (TES)

TES: calorimetric detection of photons

Fukuda et al., (AIST) Metrologia, 46, S288 (2009)

@850nm

Calorimetric detection of UV/optical/IR photons:

• Photon(s) absorbed by a heat capacity C connected to a thermal sink by a weak thermal link g.
• Temperature of the absorber is monitored by an ultra sensitive thermometer (superconducting to normal transition)
• Temperature of the absorber is monitored by an ultra-sensitive thermometer (superconducting-to-normal transition).
• Temperatures are ~100 mK to ensure low noise and high sensitivity.

Superconducting Transition Edge Sensor (TES)

1200

Ti Ti-

• TES @

TES @AIST AIST（産総研） （産総研）, , D. Fukuda et al.,

• D. Fukuda et al.,

1000 1200

n=0 n=1

λ 848 nm ΔEFWHM 0.47 eV τetf 960 ns QE 95 % Photon detection probability with a free parameter QE η, 850 nm, 10 µm TES

600 800

n 0 n=2

unts/bin

QE 95 %

Total counts Stotal 106

! ) ( ) | ( m e m P

m ηµ η

ηµ µ

−

=

with a free parameter QE η,

400

n=3

Cou

P(n|µ)=Sn/Stotal

5 . 1 = µ

200

n=5 n=4

S0 S1 S2 S3

DE=95% @848nm DE=95% @848nm

• 100

100 200 300 400 500 600 700

Pulse height

3

Fukuda et al., Metrologia, 46, S288 (2009)

Experimental setup

D t Optimal displacement receiver PZT State preparation NICT & AIST Data acquisition Modulator 1 PZT Fiber BS Optical TES Optical coherent states {|-α>, |α>} Local QRNG Local

• scillator

QRNG Modulator 2 BS Laser Diode Amplitude Modulator 0 Pulsation: 20ns 40kHz (CW 853nm)

Detection efficiency = 90% Visibility = 98% Dark count rate = 0.03/pulse

Pulsation: 20ns, 40kHz (CW 853nm)

Dark count rate 0.03/pulse

BPSK signal: sub-SQL discrimination

0.25

H d li i DE: 90%

0.20 rate

Homodyne limit (SQL) DC: 0.003/pulse Visibility: 98.6%

0.15 error r

ODR

Tsujino et al., submitted

0.10 Bit e

experiment ODR theoretical

0 1 1 0.05

0 4 0 2 0 6

ODR theoretical (incl. imperfections)

Tsujino et al.,

• Opt. Express

Preliminary result

0.1 1 Mean photon number

0.4 0.2 0.6

• Opt. Express

18, 8107 (2010)

Future outlook: toward ultimate capacity limit

＜Conventional capacity limit (channel coding)＞

Encoder

channel

Decoder Sender Receiver

channel

Homodyne limit (SQL) Shannon limit（capacity） Quantum receiver scenario SQL + Shannon limit SQL + Shannon limit

• ptimal POVM
• ptimal POVM
• ptimal POVM
• ptimal POVM

Ultimate capacity limit in optical communication

Signal (&noise) quantum mechanical Error correction (decoding) should be done before measurements Quantum channel coding （量子通信路符号化）

Encoder

channel

Quantum decoding Sender

+

Meas.

channel

g (Collective measurement)

Quantum channel coding Holevo, IEEE Trans. Inf. Theory 44, 269 (1998). Holevo, IEEE Trans. Inf. Theory 44, 269 (1998). Schumacher & Westmoreland Phys. Rev. A 56, 131 (1997). Schumacher & Westmoreland Phys. Rev. A 56, 131 (1997). Shannon + QM Giovannetti, et al., Phys. Rev. Lett. 92, 027902 (2004). Giovannetti, et al., Phys. Rev. Lett. 92, 027902 (2004). Capacity in lossy

• ptical channel

参照 量子情報通信 （オプトロニクス社, 2006）

Quantum decoding: QC with coherent states

Decode: 量子計算 Encode: Coherent states

U

… …

Quantum computing = control of coherent Quantum computing control of coherent state superposition (and entanglement)

Experiment…

Coherent state superposition：optical Schrödinger’s cat Schrödinger’s cat

• Superposition of macropscopic states
• Cat state in optical coherent states
• Cat state in optical coherent states

Statistical mixture

と の干渉縞

Photon subtraction generates Schrödinger cat-like states

Squeezed vacuum

Dakna Dakna et al., PRA 55, 3184, (1997) et al., PRA 55, 3184, (1997)

BS entangled Measurement in mode A changes the state in mode B! photon counting

m: 1, 3, 5, … m: 2, 4, 6, … Odd cat state: , , , Even cat state:

Experimental progress

Odd cat state:

• CNRS Ourjoumtsev et al., Science 312, 83 (2006).
• NBI

Neergaard-Nielsen et al., Phys. Rev. Lett. 97, 083604 (2006).

• NICT Wakui et al., Opt. Express, 15 3568 (2007).

E t t t Even cat state:

• CNRS Ourjoumtsev et al., Nature 448, 784 (2007).
• NICT Takahashi et al., Phys. Rev. Lett. 101, 233605 (2008).

Cat-state linear optics quantum computation

Ralph et al PRA 68 042319 (2003)

Theory:

Ralph, et al., PRA 68, 042319 (2003). Lund, et al., PRL 100, 030503 (2008).

Theory:

Synthesizing an arbitrary qubit in cat Synthesizing an arbitrary qubit in cat-

• basis?

basis?

Arbitrary superposition of optical cat

 Method: superposition of photon subtraction and no photon subtraction

 Implemented by displaced trigger beam  Can synthesize any cat state superposition

y y p p

1

• subtr. probab.

π phase

• r

Arbitrary superposition of optical cat

 Method: superposition of photon subtraction and no photon subtraction

 Implemented by displaced trigger beam  Can synthesize any cat state superposition

y y p p

1

• subtr. probab.

π phase

T k k d S ki Ph R A 75 064302 (2007) Takeoka and Sasaki, Phys. Rev. A 75, 064302 (2007).

Experiment with a squeezed vacuum

 Squeezed vacuum as input  Displacement by interfering with weak coherent state  Homodyne detection of output state conditioned on an APD click  Homodyne detection of output state conditioned on an APD click

 click from squeezing or displacement?

 Output: superposition of squeezed vacuum and squeezed photon – squeezed qubit!

Bloch sphere

27

Experimental results

• Varying the displacement beam intensity
• Comparing with superposition state

Comparing with superposition state with r = 0.38

• In an ideal, lossless scenario,

0.06 0.23 0.52 1.1 11 Wigner function fidelity map fidelity map

/ / / / /

ideal best

.63 / .66 .68 / .77 .75 / .81 .83 / .91 .94 / .95

Experimental results

phase-sweep longitude sweep longitude-sweep

Neergaard-Nielsen et al., Phys. Rev. Lett. 105, 053602 (2010).

Optics and Photonics News (December 2010): Optics in 2010 (Quantum Optics) p ( p )

movie http://www.opnmagazine-digital.com/ movie

Co-workers

Optical cat Optical cat state synthesis state synthesis

Hiroki Takahashi Hiroki Takahashi NICT (U. Sussex) NICT (U. Sussex) Kazuhiro Kazuhiro Hayasaka Hayasaka NICT NICT Jonas S. Jonas S. Neergaard Neergaard-

• Nielsen,

Nielsen, NICT NICT Makoto Takeuchi Makoto Takeuchi NICT NICT

Quantum receiver for coherent state Quantum receiver for coherent state discrimination discrimination discrimination discrimination

Go Go Fujii Fujii Nihon Univ. Nihon Univ. Masahide Sasaki Masahide Sasaki NICT GL NICT GL Shuichiro Shuichiro Inoue Inoue Nihon Univ. Nihon Univ. Daiji Daiji Fukuda Fukuda AIST AIST Kenji Kenji Tsujino Tsujino NICT (JST/SORST ) NICT (JST/SORST )

http://qict.nict.go.jp/eng/index.html NICT Quantum ICT group HP