Non-conventional receivers for coherent communication Francisco - PowerPoint PPT Presentation

Non-conventional receivers for coherent communication Francisco Elohim Becerra Department of Physics and Astronomy University of New Mexico, Albuquerque, NM, USA Munich Workshop on Information Theory of Optical Fiber (MIO 2018) December 6, 2018 Munich, Germany    … 01011 … ( m ) … 01011 … … 01011 … Receiver Transmitter

Measurements in Quantum Mechanics • Intrinsic noise of the system limits our ability to measure • How can we perform better measurements? Quantum resources! • Increase Sensitivity (Enhanced Quantum Measurements) • Quantum Metrology: (continuous) parameter estimation • Nonorthogonal State Discrimination: Distinguish states (from a finite known set) • Theoretical predictions in the 70’s • Experimental discrimination below the SQL (~0.2 dB) * Only 2 coherent states * K. Tsujino et al., PRL 106 , 250503 (2011).

Multiple Coherent States e   i Coherent state s    Im     Re  2 m  = M   = − 0 , 1 , 2 ,.., 1 m M M-ary Phase Shift Keying (PSK) M=2: Binary Phase Shift Keying (BPSK)   =  −  , Signal M=4: Quadrature Phase Shift Keying (QPSK)   =   −  −  , , , Signal i i

Multiple Coherent States e   i Coherent state s Coherent States are Nonorthogonal    Im  n  1    Overlap  Re  2 m  =  M 2   = − 0 , 1 , 2 ,.., 1 m M M-ary Phase Shift Keying (PSK) Discrimination Unavoidable Errors M=2: Binary Phase Shift Keying (BPSK)   =  −  , Signal Standard Quantum Limit (SQL) M=4: Quadrature Phase Shift Keying (QPSK) (Minimum Error by direct detection)   =   −  −  , , , Signal i i

Quantum Limit: Helstrom Bound BPSK QPSK      −  ,   −  −  , , , i i Error Probability -2 Error Probability 10 SQL SQL -4 10 Optimized Optimized Helstrom Discrimination Discrimination Bound -6 Helstrom 10 Strategies (Dolinar receiver 1 ) Strategies Bound 1 2 3 4 5 6 Average Photon Number Average Photon Number Demonstration of binary receiver beyond the SQL K. Tsujino et al., PRL 106 , 250503 (2011). 1 S. J. Dolinar, Research Laboratory of Electronics, MIT, Quarterly Progress Report No. 111 (1973).

Quantum Limit: Helstrom Boun QPSK     −  −  , , , i i -1 10 -2 10 Error Probability -3 10 SQL Optimized Discrimination Strategies -4 10 Helstrom Bound -5 10 5 10 15 20 Average Photon Number

Feed-Forward Receiver Design (M-ary Signals) Signal and LO with orthogonal polarizations    ( m ) LO  S S In Polarization SPD Test hypothesis  Displacement  −  SPD  (  ) D   =    0 0 ( ) vacuum   LO( ) +      −   −   LO S  V H (Local Oscillator)

Experimental concept (4-ary Signals)

Experimental Configuration (4-ary Signals)

Phase Preparation (50% duty cycle) Cal. Lock Cal. Lock Pulse Cycle Time (  s) Phase Preparation 633 Light Interference Pulses State and LO Region Interference Signal Calibration Displacement Calibration (Vis=99.7%)

Experimental Data Sample     −  −  , , , i i −  Prepared i Hypothesis Photon Feedback state Detection Period 0 1 1 π 1 2 3 π /2 0 3 3 π /2 0 4 3 π /2 0 5 3 π /2 1 6 π /2 1 7 3 π /2 0 8 −  3 π /2 0 9 i Decision 3 π /2 0 10 3 π /2

Experimental Error Probability     −  −  , , , i i DE=72% DE=72% Vis=99.7% Vis=99.7%

Experimental Error Probability     −  −  , , , i i DE=72% DE=72% Vis=99.7% Vis=99.7% BPSK ~0.2 dB

Experimental Error Probability     −  −  , , , i i DE=72% DE=72% Vis=99.7% Vis=99.7% 6 dB below SQL ~0.2 dB

PNR Quantum Receiver (Theory)     −  −  , , , i i

PNR Quantum Receiver (Experiment)     −  −  , , , i i

Optimized Displacement Receivers     −  −  , , , i i Optimized displacement * Muller, C. and Marquardt, C., New J. Phys. 17, 032003 (2015) A. R. Ferdinand, M. T. DiMario, F. E. Becerra, npj Quantum Information 3 , 43 (2017).

State Discrimination: Probability of error 4-state discrimination (QPSK) Binary Phase-shift Keying (BPSK)      −    −  −  , , , , i i -1 10 𝑗𝛽 ۧ | -2 Error Probability 10 |- ۧ 𝛽 | ۧ 𝛽 Error Probability Error Probability ۧ |- 𝑗𝛽 -2 10 (QNL) (QNL) Dolinar -3 Heterodyne -4 10 Homodyne 10 receiver 1 Limit limit Helstrom -4 10 Bound 1 Single-shot Helstrom Optimized -6 Bound 1 10 Disc. Strategies -5 10 5 10 15 20 0 2 4 6 n Mean Photon Number n Mean Photon Number R. S. Kennedy, MIT Technical Report No. 110 (1972). C. Wittmann, et. al, Phys. Rev. Lett. 101 , 210501 (2008). M. Takeoka and M. Sasaki, Phys. Rev. A 78, 022320 (2008). K. Tsujino, et. al, Phys. Rev. Lett. 106 , 250503 (2011). 1 S. J. Dolinar, Research Lab. of Elec., MIT, Quart. Prog. Rep. No. 111 (1973). M. T. DiMario and F. E. Becerra, Phys. Rev. Lett. 121 , 023603 (2018)

Non-ideal visibility degrades performance Visibility ( ξ ) of Displacement characterizes noise and imperfections [1]: C. Wittmann, et. al, Phys. Rev. Lett. 101 , 210501 (2008). M. T. DiMario and F. E. Becerra, Phys. Rev. Lett. 121 , 023603 (2018) [2]: K. Tsujino, et. al, Phys. Rev. Lett. 106 , 250503 (2011).

Non-ideal visibility degrades performance Visibility ( ξ ) of Displacement characterizes noise and imperfections ۧ ۧ |𝛽 , | − 𝛽 Binary state discrimination On-Off Detection [1] [2] Ideal η Exp = 0.72 ξ Exp = 0.998 | α | 2 [1]: C. Wittmann, et. al, Phys. Rev. Lett. 101 , 210501 (2008). M. T. DiMario and F. E. Becerra, Phys. Rev. Lett. 121 , 023603 (2018) [2]: K. Tsujino, et. al, Phys. Rev. Lett. 106 , 250503 (2011).

Experimental Error Probability ۧ ۧ |𝛽 , | − 𝛽 Binary state discrimination On-Off Detection η Exp = 0.72 η Exp = 0.72 ξ Exp = 0.998 ξ Exp = 0.998 Dark count Prob. = 3.6x10 -3 After pulsing Prob.=1.1x10 -2 M. T. DiMario and F. E. Becerra, Phys. Rev. Lett. 121 , 023603 (2018)

PNR provides robustness to dark counts Phase (PSK) and Intensity OOK encoding Dark count probability of 10 -3 M. T. DiMario and F. E. Becerra, Phys. Rev. Lett. 121 , 023603 (2018)`

How To Surpass Homodyne M. T. DiMario and F. E. Becerra, Phys. Rev. Lett. 121 , 023603 (2018)`

References State Discrimination

Non on-Gauss ssian Rec Receivers for for mult ulti-state di discriminatio ion • Multiple state discrimination • Strategies surpassing the QNL • Photon-number resolution provides robustness • Optimized strategies 5  LO ( ) 4 i 3 • Surpassing the QNL at all powers 2 1 0 N … … 3 2 1 1 2 3 • Enhance information at low powers  4 1 5 5 4 3 2 9 8 7 6 10 <n> Feedback Period

Quantum Optics Lab Quantum Measurements: High-Capacity Atom-Photon Interfaces Nonconventional Detection     1 2 4 3 S 1 S 2 Atomic Entangled Entangled Quantum photons photons Memories Transmitter Receiver |  Bob |  Bob … |  Alice Alice Bob Eve NSF (CAREER) AFOSR (YIP)