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

Quantum measurement for optical 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? Carriers are quantum mechanical particles EM waves (photons), electrons, etc… (p ), , Quantum mechanics should be seriously considered when Q t h i h ld b i l id d h quantum noise is a dominant noise in your carrier. e.g.) ideal laser light → quantum noise limited What is the ultimate minimum error limit? What is the ultimate minimum error limit? What is the ultimate minimum error limit? What is the ultimate minimum error limit?

Quantization in optical communication 0 1 0 1 loss Receiver Sender ( (measurement) ) (laser) (laser) Discriminate with small with small error? Ideal laser light is 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) ex) Binary phase-shift keyed (BPSK) 1 coherent communication （ 2 値位相変調信号 コヒーレント通信） （ 2 値位相変調信号 コヒ レント通信） ror rate ror rate e SQL SQL SQL SQL 10 − 3 10 Homodyne BPSK signal BPSK signal detection detection Bit er Bit er 10 − 6 10 10 − 9 10 9 10 10 0 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) Restricted by the postulate of quantum mechanics POVM: outcome t set of operators Free from “physical quantity”!

Discrimination of binary coherent states C. W. Helstrom, C. W. Helstrom, Binary Coherent States: Inform. Contr. 10, 254 (1967) Inform. Contr. 10, 254 (1967) BPSK POVM Measurement coherent states states Quantum mechanical bound (Helstrom bound) Optimal POVM: → Projection onto the superpositions of coherent states

Quantum receivers Homodyne limit Homodyne limit 1 (Coherent optical communication) (Coherent optical communication) (Coherent optical communication) (Coherent optical communication) or rate or rate 10 − 3 10 Near optimal receiver Near optimal receiver Near optimal receiver Near optimal receiver Bit erro Bit erro （ Kennedy receiver Kennedy receiver ） 10 − 6 10 R. S. Kennedy, RLE, MIT, QPR, R. S. Kennedy, RLE, MIT, QPR, 108, 219 (1973) 108, 219 (1973) No experiments have No experiments have Coherent local oscillator Coherent local oscillator 10 − 9 9 10 beaten the homodyne limit! beaten the homodyne limit! beaten the homodyne limit! beaten the homodyne limit! 0 0 2 2 4 4 6 6 8 8 10 10 10 10 Photon counter Photon counter Photon number/pulse Photon number/pulse Coherent local oscillator Coherent local oscillator Coherent local oscillator Coherent local oscillator Optimal receiver Optimal receiver Minimum error Minimum error Photon counter Photon counter (Helstrom bound) (Helstrom bound) （ Dolinar receiver Dolinar receiver ） Classical feedback Classical feedback (i fi it l f (i fi it l f (infinitely fast!) (infinitely fast!) t!) t!) S. J. Dolinar, RLE, MIT, QPR, 111, 115, (1973) S. J. Dolinar, RLE, MIT, QPR, 111, 115, (1973)

Trends of optical receiver sensitivity Trends of optical receiver sensitivity 10000 Space qualified & plan =10 -6 Ground test ETS-VI 1000 y@BER= OICETS tons/bit] SILEX 100 NeLS NeLS ensitivity [Phot C h Coherent TerraSAR-X Digital 10 coherent coherent Se Homodyne coherent PSK theoretical limit 1 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 or Classical Classical ( (electrical) (electrical) ( ) ) feedback feedback Coherent state Coherent state LO LO local oscillator local oscillator 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 Homodyne limit Homodyne limit 1 (Coherent optical communication) (Coherent optical communication) (Coherent optical communication) (Coherent optical communication) or rate or rate 10 − 3 10 Near optimal receiver Near optimal receiver Near optimal receiver Near optimal receiver Bit erro Bit erro （ Kennedy receiver Kennedy receiver ） 10 − 6 10 R. S. Kennedy, RLE, MIT, QPR, R. S. Kennedy, RLE, MIT, QPR, 108, 219 (1973) 108, 219 (1973) Coherent local oscillator Coherent local oscillator 10 − 9 9 10 0 0 2 2 4 4 6 6 8 8 10 10 10 10 Photon counter Photon counter Photon number/pulse Photon number/pulse Coherent local oscillator Coherent local oscillator Coherent local oscillator Coherent local oscillator Optimal receiver Optimal receiver Minimum error Minimum error Photon counter Photon counter (Helstrom bound) (Helstrom bound) （ Dolinar receiver Dolinar receiver ） Classical feedback Classical feedback (i fi it l f (i fi it l f (infinitely fast!) (infinitely fast!) t!) t!) S. J. Dolinar, RLE, MIT, QPR, 111, 115, (1973) S. J. Dolinar, RLE, MIT, QPR, 111, 115, (1973)

Extension of the Kennedy receiver Takeoka and Sasaki, Phys. Rev. A 78, 022320 (2008) Kennedy receiver Kennedy receiver on/off detector displacement p on/off detector on/off detector （光子数の有無を識別。 APD 等） （光子数の有無を識別。 APD 等） New receivers New receivers displacement （変位演算子） Optimal Displacement Optimal Displacement p p p p on/off detector LO optimized γ squeezing Optimal Squeezing + Optimal Squeezing + Displacement Displacement squeezer on/off detector pump optimized ζ and β

Approximate realization of the Helstrom meas. Ideal POVM Ideal POVM on/off detector on/off detector

Average error probabilities 1 to beat ty K K Kennedy Kennedy d d obabilit the homodyne limit… D ( γ ( γ ) γ ) ror pro Homodyne Homodyne 0.1 Detector rage er QE > 90% DC < 10 -2 D ( β ( β ) β )+ )+ S ( ζ ( ζ ) ζ ) Aver Visibility Helstrom bound Helstrom bound 0.01 ξ > 0.995 ξ > 0 995 0.0 0.2 0.4 0.6 0.8 1.0 Average signal photon number g g p

Proof-of-principle experiment U. Erlangen & NICT visibility detection efficiency Sig * *Detection efficiency compensated Wittmann, et al., Phys. Rev. Lett. 101, 210501 (2008)

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) AIST （産総研） （産総研） , Ti Ti- -TES @ TES @AIST , D. Fukuda et al., D. Fukuda et al., 1200 1200 848 nm λ 850 nm, 10 µ m TES n =1 Δ E FWHM 0.47 eV Photon detection probability 1000 960 ns τ etf with a free parameter QE η , with a free parameter QE η , n 0 n =0 QE 95 % QE 95 % 800 − ηµ m ( ηµ ) unts/bin e Total counts S total 10 6 µ = ( | ) P m n =2 η ! m 600 Cou P (n| µ )=S n /S total 400 n =3 200 S 0 n =4 µ = 1 . 5 S 1 DE=95% @848nm DE=95% @848nm n =5 S 2 S 3 0 3 -100 0 100 200 300 400 500 600 700 Pulse height Fukuda et al., Metrologia, 46, S288 (2009)

Experimental setup NICT & AIST State preparation Optimal displacement receiver D t Data PZT PZT Modulator 1 Fiber BS TES acquisition Optical Optical coherent states {|- α >, | α >} QRNG QRNG Local Local oscillator Modulator 2 BS Detection efficiency = 90% Amplitude Laser Modulator 0 Visibility = 98% Diode Dark count rate = 0.03/pulse Dark count rate 0.03/pulse (CW 853nm) (CW 853nm) Pulsation: 20ns 40kHz Pulsation: 20ns, 40kHz

BPSK signal: sub-SQL discrimination DE: 90% 0.25 DC: 0.003/pulse H Homodyne limit d li i rate Visibility: 98.6% (SQL) 0.20 error r 0.15 Tsujino et al., ODR submitted Bit e experiment 0.10 ODR theoretical ODR theoretical Preliminary result 0.05 (incl. imperfections) Tsujino et al., Opt. Express Opt. Express 0 1 0.1 1 1 0 2 0.2 0 4 0.4 0 6 0.6 18, 8107 (2010) Mean photon number

Future outlook: toward ultimate capacity limit ＜Conventional capacity limit (channel coding)＞ Encoder Sender Receiver Decoder channel channel Homodyne limit (SQL) Shannon limit（capacity） SQL + Shannon limit SQL + Shannon limit Quantum receiver scenario optimal POVM optimal POVM optimal POVM optimal POVM