High-Capacity, Free-Space Quantum Key Distribution Based on Spatial and Polarization Encoding

Transcription

1 High-Capacity, Free-Space Quantum Key Distribution Based on Spatial and Polarization Encoding Robert W. Boyd The Institute of Optics and Department of Physics and Astronomy University of Rochester Alan E. Willner Department of Electrical Engineering University of Southern California Glenn A. Tyler the Optical Sciences Company Anaheim, California Presented at the ONR Quantum Information Science Review, Arlington Virginia, December 9,. (N4---6)

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3 The OAM-QKD Concept Laguerre-Gaussian Basis Angular Basis: linear combination of LG states (mutually unbiased with respect to LG)

4 Our Earlier OAM-QKD Implementation khz frame rate e use a seven-dimensional state space e transmit only 7 secure bits per second OAM Mirhosseini, Magaña-Loaiza, O Sullivan, Rodenburg, Malik, Lavery, Padgett, Gauthier, and Boyd, New J. Phys. 7, 3333 (). ANG

5 Next Step: gigabit-per-second OAM-based QKD system Alice VCSEL 7 sets BS BS VCSEL VCSEL Laser VCSEL OAM OAM OAM3 Mirror BS BS BS BS Launch telescope Mirror ANG ANG ANG3 7 sets VCSEL VCSEL Laser VCSEL Laser Free space transmission line Bob BS Mirror Receive telescope OAM sorter OAM channel ANG sorter ANG channel Detector array Detector array

6 Theoretical / Conceptual Issues What is best strategy? Assume that we have M OAM states (take M = 9) and assume initially that we will implement MUBs Do we include all 9 channels in the QKD protocol with N=9? Or do we implement 3 channels each with N=3? Or do we implement 9 channels each with of N=? Current Thinking: Data rate is largest for pure multiplexing (9 channels of N=) But security can be enhanced by including more states in the QKD protocol The best tradeoff probably depends on environmental issues such as atmospheric turbulence levels, and can be adjusted in real time. Further Issues: How do this tradeoff change if we implement more MUBs in our protocol? How do we perform security analysis for finite-length keys Collaborators: Anne Broadbent, Robert Fickler, and Kamil Bradler, U. Ottawa

7 Development of Static Holograms Hologram array Far-field diffraction patterns l = l = l = 4

8 We will simultaneously encode in polarization MUB MUB

9 High Capacity Free Space QKD Based on Spatial and Polarization Encoding: Fast Spatial Mode Encoding Alan E. Willner, Yongxiong Ren, Cong Liu Department of Electrical Engineering, University of Southern California, Los Angeles, CA 989-6

10 Plan and Accomplishment Plan n We will explore two potential approaches for high-speed (Gbit/s) spatial mode encoding ) N optical switch combined with multiple holograms ) N parallel VCSELs (with specially design data streams) combined with multiple holograms n We will determine an approach to demonstrate a Mbit/s Gbit/ s OAM-based QKD transmitter. We will explore potential limitations and their effects on system security. Accomplishment n Gbit/s OAM Encoding: Proof-of-concept experiment in a classical optical link n We experimentally demonstrated data encoding at Gbit/s using four possible OAM modes. The influence of mode spacing and time misalignment between modal channels on the switching crosstalk and bit-error-rates was investigated.

11 OAM Encoding-Based QKD System OAM and ANG Mode Encoding CW Light OAM & ANG Mode Selection { l, l, l 3, l 4, } OAM or ANG Encoded Light l l 3 l l 4 T T 3T t Single Photon Detector Array Data Stream OAM and ANG Mode Detection Lens Mode Sorter. ANG (angular mode basis) is composed of a linear combination of OAM modes OAM Modes Free Space Single Photon Detector Array. Mode Sorter ANG Modes q In theory, we have the following: # of bits info. photon = log q We need a fast spatial mode encoding scheme. # of possible states ( )

12 High-speed Spatial Mode Encoding Scheme q High-speed (Gb/s) spatial mode encoding presents a critical challenge. q Programmable devices, such as SLMs and digital micromirrors, have limited modulation rates. Hologram Attenuated Laser N Optical Switch Physical RNG Mode Hologram Mode Hologram N N Combiner Coherent Pulses RNG: random number generator Mode 3 A high-speed N optical switch combined with multiple holograms could be potentially used to achieve Gbit/s data encoding

13 High-speed OAM Encoding Scheme High-speed N Optical Switch q A N GHz optical switch can be built by cascading multiple high-speed optical switches. q For example, seven optical switches would be need to built a 8 GHz optical switch OS Data # Data # OS OS Data # OS Data #3 OS Data #3 Data #3 OS OS Data #3 3 independent data streams in total Port # Port # Port #3 Port #4 Port # Port #6 Port #7 Port #8 Ø This approach can potentially achieve higher speed (such as >GHz) spatial encoding, but it is not efficiently scalable.

14 Scheme : Parallel VCSELs + Multiple Holograms Signal # SMF VCSEL Signal # VCSEL Signal #N VCSEL N Hologram Hologram Hologram N Attenuator Attenuator Attenuator N Beam Combiner Coherent Pulses OAM Generation q Multiple pairs of {VCSEL + hologram} could be used to generate multiple OAM or ANG modes. q Each VCSEL can be driven by an independent data signal with a data rate of ~ Mbit/s. q By designing the data patterns, we can ensure that only one VCSEL (i.e, only one OAM or ANG mode) is active within each symbol period.

15 Scheme : Parallel VCSELs + Multiple Holograms The design of data patterns for signals that are fed to VCSELs Signal # Signal # Signal # Signal #4 Hologram Hologram Hologram 3 Hologram 4 Only one signal is in each symbol period Ø Challenges: the design of data patterns for signal #-#N and the synchronization among all the VCSEL data channels. Ø We will explore the influence of using multiple different VCSELs as laser source on the system security and data rate.

16 Gbit/s OAM Encoding Proof-of-concept Experiment CW Laser nm EDFA 4 Optical Switch GHz Bandwidth 4 Optical Switch Data Stream 3 4 l= l= l l= l= l l= l= l 3 l= l= l 4 OAM Generation Beam Combiner Free-space Transmission Beam Separator l= l l= l= l l= l= l 3 l= l= l 4 l= OAM Detection Ch Ch Ch3 Ch4 Detection & Data Recovery Bit Streams (Switch driving signal) Mapping Relationship Branch OAM l Branch OAM l Branch 3 OAM l 3 Branch 4 OAM l 4 Active OAM modes q The 4 optical switch is built by cascading one switch with two switches, each of which has a -GHz switching bandwidth. q Given that four OAM states are used, bits can be encoded in a symbol period, Therefore, Gbit/s ( log 4) data rate is achieved. Op#cs Le)ers

17 Gbit/s OAM Encoding Experiment Setup Crosstalk for Different Mode Spacing Δ Δ= (l=, +, +, +3) Δ= (l=-3, -, +, +3) Δ=3 (l=-4, -, +, +4) Δ=4 (-6, -, +, +6) Mode Crosstalk Mode Crosstalk Mode Crosstalk Mode Crosstalk l = -. db l = db l = db l = db l = db l = - -. db l = db l = db l = db l = db l = db l = db l = db l = db l = db l = db q The system performance is affected by two kinds of crosstalk: switchinduced crosstalk and OAM intermodal crosstalk. q As mode spacing increases, OAM intermodal crosstalk decreases. Optics Letters

18 Gbit/s OAM Encoding Experiment Results Waveforms at the switch output (a) Branch ① Waveforms at the RX for different Δ (b) Branch ① (c) ℓ=-3 (d) ℓ= (b) (a) Branch ② (c) ℓ=- (b) Branch② (d) ℓ=+ (b) (a3) Branch ③ (c3) ℓ=+ (d3) ℓ=+ (b3) (a4) Branch ④ (b3) Branch ③ (c4) ℓ=+3 (d4) ℓ=+3 (b4) (a) Combined waveform Time (Normalized by ps) (b4) Branch ④ (c) Combined waveform Eye Diagrams. (d) Combined waveform Time (Normalized by ps) q From the four switch output branches, the combined waveform verifies that light is routed to only one of the branches in each -ps period. q The waveforms when using mode set {-3, -, +, +3} exhibit better quality than those when using {, +, +, +3}, due to less OAM intermodal crosstalk. q By determining which mode is active in each symbol period, the encoded bit information can be recovered. Op#cs Le)ers

19 Gbit/s OAM Encoding Experiment Results BER Transmitted Power (measured at switch outputs) - - Average BER BER Mode Sp. = Mode Sp. = Mode Sp. = 3 Mode Sp. = Transmitted Power (dbm) q The Δ= case has worse BER performance due to larger OAM crosstalk. q The power penalty of Δ= case is estimated to be 3. db with respect to the Δ=3 case at the forward error correction limit of Op#cs Le)ers

20 34 S. Sunkist St. Anaheim, CA 986 Phone: (74) Fax: (74) High-Capacity, Free Space Quantum Key Distribution Based on Spatial and Polarization Encoding Atmospheric Considerations Kick Off Meeting Glenn A. Tyler Jeffrey L. Vaughn and Nicholas K. Steinhoff 9 December BC-4 - -

21 Turbulence Encountered in Navy Engagements Falls into Three Classic Categories Ordinary Turbulence Strong Turbulence (Experimental Data and Hand Analysis for tosc AMOS Upgrade) (ABL shot down three missiles) Deep Turbulence (Left: Anisoplanatism Right: Irradiance Coupling) ϑ ϑ 4 ϑ 8ϑ 6ϑ On-Axis s ϑ ϑ ϑ 4 ϑ ϑ 8 ϑ 8ϑ ϑ 6ϑ Diffraction Limited Point Source D B =.m D B =.m D B =.m Uncompensated Ordinary turbulence Encountered in Surveillance and Astronomy First order Rytov theory applies Hand analysis agrees very well with experiment Strong turbulence Encountered in relatively weak but long propagation paths First order Rytov Fails, scintillation saturates, onset of branch points Wave optics required and crossvalidated with analysis when appropriate Deep turbulence (Strong scintillation and Anisoplanatism) Encountered in tactical applications and horizontal path laser com Rytov number >, ϑ < λ/d, significant Anisoplanatism, atmospheric guiding Wave Optics crossvalidated with experiment required BC-4 - -

22 Identification of Atmospheric Disturbance Levels for Navy Lasercom Applications Air to Air Working Area for HV /7 and λ =. µm N f = Small Ship to Carrier Working Area for HV /7 and λ =. µm N f = Carrier to Air Working Area for HV /7 and λ =. µm N f = N f = N f = N f = D (m) N f = λ/θ Ordinary A Strong Turbulence High Scintillation sqrt( D D ) (m) N f = λ/θ λ/θ Reverse Ordinary A Strong Turbulence High Scintillation sqrt( D D ) (m) N f = λ/θ λ/θ Reverse Ordinary A Strong Turbulence High Scintillation Range (km) - - Three engagements are considered above; Air to Air (k), Small Ship (m) to Carrier (6m) and Carrier (6m) to Air (km) The colors indicate the turbulence level (Deep turbulence is below the black lines in the high scintillation region and shows where D = λ/ϑ ) To optimize the spatial bandwidth of the propagation link we would like to support a Fresnel number of five indicated by the green lines (the red and blue lines correspond to Fresnel numbers of two and ten, respectively) These lines end when the curvature of the earth blocks the beam The results illustrate the diameters required and the turbulence levels encountered for the three links of interest Air to Air is Ordinary Turbulence up to about km but requires meter class optics Small Ship to Carrier or Carrier to Small Ship requires 3 cm optics at ten kilometers and Deep Turbulence compensation Carrier to Air is ordinary turbulence and requires 3cm optics Range (km) Range (km) BC-4-3 -

23 High Dimensional MUB States Are Analytically Determined In Quantum Communications applications it is desirable to utilize Mutually Unbiased Bases (MUBs) The basis vectors are denoted as m> where m takes on N values Each MUB state set has N vectors which in turn are written in terms of the N basis vectors The p TH set of MUB States are given by n, p = N m= A pnm m They satisfy the following relations q, m n, p = δ nm δ pq, + A δ N p pq A p For N an odd prime there are N+ MUBs and the expansion coefficients A pnm are given by* A pnm δnm, for p = ; πi ( pn nm) N e, otherwise. N = + Note that p=n results in the Fourier kernel As a consequence the MUB states have important properties Within each basis the states are orthogonal If the wrong basis is used no information is obtained since all probabilities are equal We typically use the basis vectors (p=) and the Fourier (p=n) The basis states have minimum energy loss and are similar to OAM *I.D. Ivonovic, Geometrical Description of Quantum State Determination, Journal of Physics A: Mathematical and General, (98) = I N BC-4-4 -

24 Preconditioned MUB States Based upon Minimum Energy Loss OAM States Address Propagation Issues Transmit Receive Matrix (N f =, N=) exhibits desired character at receiver Desired Conventional Preconditioned The preconditioned result includes propagation loses and only differs from desired by a loss factor For high dimensions and low Fresnel numbers (N f =, N=) the preconditioned MUB states look quite similar except for the fundamental basis Transmitted Preconditioned MUB States.. Received MUB States. For low Fresnel Numbers the transmitted and received fields are quite different The basis vectors are unaffected because they are already a minimum energy loss state BC-4 - -

25 Ordinary and Strong Turbulence Engagements Are Amenable to AO Enhancement Ordinary Turbulence (Ground to Space, σ l =.) Strong Turbulence (Long Horizontal Path, σ l =.39) Desired Compensated Uncompensated Desired Both engagements utilize HV7 turbulence with a wavelength of λ =. µm For Ground to Space: L = km represents a LEO propagation at zenith, D R = cm and D T = 3. m so we have N f =.3 For Long Horizontal Path: L=km, altitude = m at xmit site and 6m at receive site, D R = D T = 4 cm for N f = Compensated Uncompensated BC

26 A Variety of Techniques Have Been Developed for JTO Deep Turbulence Engagements Compensation techniques for this level of turbulence include multiple DMs, Branch Cut reconstructors, one or more laser guide stars and a variety of iteration approaches Gradient Descent Tomography utilizes two DMs and does not require a wavefront sensor These and other approaches will be used to address Qcom in Navy Engagements BC-4-7 -

27 Preconditioned MUB States in Deep Turbulence Amplitude and Phase of Minimum Energy Loss Basis for Deep Turbulence (a) Pertains to N f = and (b) Pertains to N f = Preconditioned MUB States for Deep Turbulence (a) Pertains to N f = and (b) Pertains to N f = MUB MUB MUB MUB 3 MUB MUB MUB MUB 3 amplitude phase ε =.6 ε =.673 ε 3 = (J / /m) (rad) (J / /m) (rad) (J / /m) (rad) ε =.746 ε =.83 ε 3 =.877 x -4 x -4 x (J / (J / /m) /m) (J / /m) (rad) (rad) (rad) j= j= j=3 (J / /m) (J / /m) (J / /m) (J / /m) (J / /m) (J / /m) (J / /m) (J / /m) (J / /m) (J / /m) (J / /m) (J / /m) (J / /m) (J / /m) (J / /m) (J / /m) (J / /m) (J / /m) (J / /m) (J / /m) (J / /m) (J / /m) (J / /m) (J / /m) (a) (b) (a) (b) In this work it is assumed that the atmosphere is probed to assess its volume characteristics The elementary minimum energy loss basis states are found by solving the appropriate Eigen equations These state have high efficiencies The preconditioned MUB states exploit the scintillation filament structure BC-4-8 -