Experimental implementation of near-optimal quantum measurements of - PowerPoint PPT Presentation

Experimental implementation of near-optimal quantum measurements of optical coherent states Masahiro Takeoka Christoffer Wittmann Kenji Tsujino Katiuscia N. Cassemiro *1 Masahide Sasaki Gerd Leuchs Ulrik L. Andersen *2 *1 Daiji Fukuda *2 Go Fujii *3 *3 Shuichiro Inoue *3 DEX-SMI Workshop on Quantum Statistical Inference, NII, 3 March 2009

Quantum optics: experimentally feasible approach to demonstrate quantum state discriminations polarization (& location) encoding in single-photon states Minimum error discrimination Huttner et al ., Phys. Rev. A 54, 3783 (1996) Unambiguous state discrimination Clarke et al ., Phys. Rev. A 63, 040305(R) (2001) Collective measurements Fujiwara et al ., Phys. Rev. Lett. 90, 167906 (2003) Pryde et al., Phys. Rev. Lett. 94, 220406 (2005) etc..... encoding in coherent states Programmable unambiguous state discriminator Bartuskova et al ., Phys. Rev. A 77, 034406 (2008) For applications?

Original motivation for the state discrimination C. W. Helstrom 1976

Quantum noise in optical coherent states Sender Receiver 1 0 0 1 0 0 Quantum Noise Non-orthogonality for

Trends of optical receiver sensitivity 10000 Space qualified & plan Sensitivity@BER=10 -6 Ground test D ETS-VI D M I 1000 [Photons/bit] OICETS SILEX 100 NeLS Coherent TerraSAR-X Digital Challenge to quantum limit 10 coherent Homodyne coherent PSK theoretical limit 1 1990 1995 2000 2005 2010 2015 Launch year 5

Discrimination of binary coherent states Binary Coherent States: POVM BPSK Measurement coherent states Min. error discrimination → Projection onto the superpositions of coherent states Minimum Error Probability:

Quantum receivers Homodyne limit Homodyne limit 1 1 (Coherent optical communication) (Coherent optical communication) Bit error rate Bit error rate − 3 10 − 3 10 Near optimal receiver Near optimal receiver （ Kennedy receiver ） （ Kennedy receiver ） − 6 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 − 9 10 − Coherent local oscillator 9 Coherent local oscillator 10 beaten the homodyne limit! beaten the homodyne limit! 0 2 4 6 8 10 0 2 4 6 8 10 Photon counter Photon counter Photon number/pulse Photon number/pulse Coherent local oscillator Coherent local oscillator Optimal receiver Optimal receiver Minimum error Minimum error Photon counter Photon counter (Helstrom Helstrom bound) bound) （ Dolinar ） ( （ receiver ） Dolinar receiver Classical feedback Classical feedback (infinitely fast!) (infinitely fast!) S. J. Dolinar Dolinar, RLE, MIT, QPR, 111, 115, (1973) , RLE, MIT, QPR, 111, 115, (1973) S. J.

Contents 1. Homodyne measurement The optimal strategy within Gaussian operations and classical communication 2. Practical near-optimal quantum receiver (Improvement of the Kennedy receiver) 2-1 Proposal and proof-of-principle experiment Toward beating the homodyne limit: 2-2 Device: superconducting photon detector (TES) 2-3 Theory: performance evaluation via the cut-off rate

Quantum receivers Homodyne limit (SNL) Homodyne limit (SNL) 1 1 (Coherent optical communication) (Coherent optical communication) Bit error rate Bit error rate − 3 10 − 3 10 Best strategy within Best strategy within Gaussian operations and Gaussian operations and classical communication classical communication − 6 10 − 6 10 (feedback) (feedback) − 9 10 − 9 10 Kennedy receiver Kennedy receiver 0 2 4 6 8 10 0 2 4 6 8 10 Photon number/pulse R. S. Kennedy, RLE, MIT, QPR, R. S. Kennedy, RLE, MIT, QPR, Photon number/pulse 108, 219 (1973) 108, 219 (1973) Minimum error Minimum error Dolinar receiver receiver Dolinar (Helstrom Helstrom bound) bound) ( S. J. Dolinar Dolinar, RLE, MIT, QPR, 111, 115, (1973) , RLE, MIT, QPR, 111, 115, (1973) S. J.

Gaussian operations and classical communication (GOCC) Gaussian Gaussian operation operation Classical communication If is a Gaussian state, any classical communication does not help the protocol! (for any trace decreasing Gaussian CP map, one can construct a corresponding trace preserving GCP map) Eisert, et al, PRL 89, 137903 (2002) Fiurasek, PRL 89, 137904 (2002) Giedke and Cirac, PRA 66, 032316 (2002)

Gaussian operations and classical communication (GOCC) In our problem, and are Gaussian. However, the receiver does not know which signal is coming.. Measurement via GOCC non-Gaussian state! Does classical communication increase the distinguishability?

without CC Discrimination via Gaussian measurement without CC. Gaussian measurement Optimal measurement under Bayesian strategy… Homodyne measurement with (independent on ) Average error probability

Classical communication (conditional dynamics) ( N-M )-mode conditional state Input G-meas. Gaussian Classical communication does not (without CC) unitary increase the distinguishability M -mode operation Ancillae G-measurements ? (without CC) : measurement outcome Homodyne measurement : pure Gaussian states measurement-dependent measurement-dependent

Minimum error discrimination of binary coherent states under Gaussian operation and classical communication is achieved by a simple homodyne detection Limit of Gaussian operations Homodyne limit Takeoka and Sasaki, Phys. Rev. A 78, 022320 (2008) For multiple coherent states? multi-partite signals? Classical-quantum capacity with restricted (GOCC) measurement?

Contents 1. Homodyne measurement The optimal strategy within Gaussian operations and classical communication 2. Practical near-optimal quantum receiver (Improvement of the Kennedy receiver) 2-1 Proposal and proof-of-principle experiment Toward beating the homodyne limit: 2-2 Device: superconducting photon detector (TES) 2-3 Theory: performance evaluation via the cut-off rate

Kennedy receiver Kennedy, RLE, MIT, QPR 108, 219 (1973) Displacement operation Photon Transmittance: T~1 detection 1 1 Kennedy receiver Kennedy receiver BS Bit error rate Bit error rate − 3 10 − 3 10 Local Homodyne limit Homodyne limit oscillator 10 − − 6 6 10 − 9 10 − 9 10 0 0 2 2 4 4 6 6 8 8 10 10 On/off discrim. detection error Photon number/pulse Photon number/pulse

Practical imperfections quantum efficiency, dark counts Interference visibility Photon detection Input signals T → 1 0 photons 0 0 0 0 non-zero 1 1 1 1 photons BS Local oscillator

Visibility Average error probability Log 10 P e Homodyne 0 Kennedy ( ξ =0.99) Kennedy ( ξ =0.9999) Kennedy ( ξ =0.999999) Kennedy ( ξ =0.99999999) -2 Kennedy ( ξ =0.9999999999) -4 n < 1 -6 -8 0 2 4 6 8 10 Average photon number

Kennedy receiver at extremely weak signals 1 Average error probability Homodyne limit Homodyne limit Kennedy receiver Kennedy receiver 0.1 (ideal) (ideal) Helstrom bound 0.01 0.0 0.2 0.4 0.6 0.8 1.0 Average signal photon number

Generalizing of the Kennedy receiver Kennedy receiver Kennedy receiver displacement on/off detector Optimal Displacement Optimal Displacement optimized γ on/off detector Squeezing + Displacement Squeezing + Displacement (Gaussian unitary operation) (Gaussian unitary operation) squeezer on/off detector Takeoka and Sasaki, optimized ζ and β Phys. Rev. A 78, 022320 (2008)

Average error probabilities 1 Average error probability Kennedy Kennedy γ ) ( γ D ( ) D Homodyne Homodyne 0.1 β )+ ζ ) ( β ( ζ D ( )+ S S ( ) D 0.01 Helstrom bound bound Helstrom 0.0 0.2 0.4 0.6 0.8 1.0 Average signal photon number

Proof-of-principle experiment Wittmann, et al., Phys. Rev. Lett. 101, 210501 (2008) Optimal Displacement Optimal Displacement Receiver Receiver on/off detector AO Sig

Average error probability (experimental) * * *Detection efficiency compensated “Proof Proof- -of of- -principle principle” ” demonstration succeeded! demonstration succeeded! “ Wittmann, et al., Phys. Rev. Lett. 101, 210501 (2008)

Contents 1. Homodyne measurement The optimal strategy within Gaussian operations and classical communication 2. Practical near-optimal quantum receiver (Improvement of the Kennedy receiver) 2-1 Proposal and proof-of-principle experiment Toward beating the homodyne limit: 2-2 Device: superconducting photon detector (TES) 2-3 Theory: performance evaluation via the cut-off rate

Detector requirements to beat the homodyne limit… 1 Kennedy Kennedy Homodyne limit Homodyne limit BER Detector 0.1 QE > 90% Helstrom Helstrom DC < 10 -3 bound bound 0.01 Opt. disp. receiver Opt. disp. receiver Visibility 0.0 0.2 0.4 0.6 0.8 1.0 ξ > 0.995 Average photon number Advanced detectors?

Transition Edge Sensor (TES) TES: calorimetric detection of photons Fukuda et al., (2009) @AIST @850nm

Contents 1. Homodyne measurement The optimal strategy within Gaussian operations and classical communication 2. Practical near-optimal quantum receiver (Improvement of the Kennedy receiver) 2-1 Proposal and proof-of-principle experiment Toward beating the homodyne limit: 2-2 Device: superconducting photon detector (TES) 2-3 Theory: performance evaluation via the cut-off rate