LEOS:LEOS: QuantumQuantum EntanglementEntanglement WorkshopWorkshop

April 8, 2009

QuantumQuantum CommunicationCommunication TechnologyTechnology

Franco N. C. Wong Research Laboratory of Electronics Massachusetts Institute of Technology

Support: ONR, IARPA, ARO, DARPA Outline

ƒ Entanglement generation: from classical to quantum

ƒ Entanglement characterization

ƒ Efficient wavelength translation

ƒ Single-photon two-qubit quantum logic

ƒ Quantum key distribution

ƒ Secure communication via quantum illumination

ƒ Concluding remarks

2 Bits versus qubits: magic of superposition

ƒ Classical on-off system stores one bit – off state = 0, on state = 1 – system must be in state 0 or state 1

ƒ Quantum two-level system stores one qubit – photon example: H-polarization = |0〉, V-polarization = |1〉 – system can be in a superposition state: |ψ〉 = α|0〉 + β|1〉

V V D

H PBS H

3 Two qubits: more magic

ƒ Two entangled qubits

– |ψ〉 = (|01〉 -|10〉)/√2 = |H1V2 –V1H2〉/√2

V1

1 H path 1 |ψ〉 pat h 2 H2

V2

But, a 50-50 mixture of |H1V2〉 and |V1H2〉 gives the same results

4 Two qubits: some detective work

ƒ Let’s analyze it in the AD basis V

|ψ〉 = |H1V2 –V1H2〉/√2 A D H |ψ〉 = |D1A2 –A1D2〉/√2

AA11 H 11 DD ppaatthh 11 HWPHWP |H|1ψ〉V2〉 V ppaatt hh 22 DD22

AA22

So, a 50-50 mixture does not yield the same results

5 From classical to quantum

How to create entangled photons from two qubits?

|HV〉 → |H1V2 –V1H2〉

H H V path 1 V V H1V2 + V1H2 H

path 2

Entangled pair is generated at 50% success rate

6 Nonlinear optical frequency conversion

χ(2) interaction:

ω s ω (2) p Second-harmonic generation (ωs = ωi): χ

ωi

Biphoton generation

Spontaneous parametric down-conversion (SPDC):

ωs ωp χ(2)

ωi

7 Spontaneous parametric down-conversion (SPDC)

Biphoton generation

~10 10 ωs Output polarizations (2) χ Type I: E || E ω s i p ωi Type II: Es ⊥ Ei Very low efficiency

Energy conservation: ωp = ωs + ωi crystal grating period (PPLN, PPKTP) Phase matching condition ei∆kx: k k s i ∆k = kp –ks –ki + 2π/Λ = 0

–kp

8 Single-beam generation of entangled photons

PBS Output: |H'〉 |H'〉 -|V'〉 |V'〉 HWP ‰R s i s i signal analyzer plate is rotated ωp /2 ‰ UV pump KTP T idler PPKTP ω /2 p H/V A/D IF 50-50 HWP PBS

12000

10000

8000 Quantum-interference 6000 visibility measurements in H/V and A/D bases 4000

2000

PRA 69, 013807 (2004) Coincidence Counts (10-s interval) 0 0 45 90 135 180 225 270 315 360 θR (degrees) 9 Bidirectionally-pumped polarization-Sagnac source

Combine two identical sources

ƒ One photon in signal path and conjugate photon in idler path

ƒ Signal and idler do not interfere: can be nondegenerate

ƒ All photon pairs are good pairs: increased flux

10 Bidirectionally pumped polarization-Sagnac SPDC

Idler Signal

DM Phase-stable dual-λ Sagnac configuration PBS QWP S I 1 2 HWP Automatically achieve I1 spatial, spectral, S2 and temporal dual-λ UV indistinguishability HWP pump PPKTP (405 nm)

Kim et al., PRA 73, 012316 (2006); Laser Phys. 16, 1517 (2006)

11 cw Sagnac source setup

12 Quantum interference visibilities (cw source)

700 no subtraction of background counts 600

500

400

300

Coincidences (/s/mW/nm) 200

100

0 0 50 100 150 200 250 300 350 400 450

Analyzer angle θ1 (degree) CHSH form of Bell’s inequality: V0 = 99.76% (quantum V45 = 99.45% limit = 2√2 ≈ 2.82843) Measured S = 2.825(Accidentals ± 0.015 (systematic) included) ± 0.0035 (statistical) Laser Phys. 16, 1517 (2006)

13 Quantum state tomography of cw source

Real part of density matrix Imaginary part of density matrix

0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0 0 -0.1 -0.1 -0.2 -0.2 -0.3 VV -0.3 VV -0.4 VH -0.4 VH -0.5 HV -0.5 HV HH HH HH HH HV HV VH VH VV VV

14 Spectral brightness comparison of bulk crystal sources

1316-nm PPKTP in Sagnac waveguide SPDC Kim ‘06 105 PPKTP in MZ 104 Fiorentino ’04

3 10 Single-pass PPKTP Kuklewicz ’04 102 Single BBO Double BBO Kurtsiefer ’01 Kwiat ’05 10

Double BBO 1 Kwiat ’99

10-1 Single BBO Kwiat ’95 10-2

Normalized flux (detected pairs/s/mW/nm)Normalized flux (detected 0.88 0.90 0.92 0.94 0.96 0.98 1 Quantum-interference visibility

15 Cavity-enhanced sum-frequency upconversion

cw 1064-nm pump Pump cavity: locked max power: 0.4 W to cavity PZT Input: 0.09 photon/ms servo Detection by 65%-efficient Si APD single-photon counter 4-cm PPLN 633-nm output

100%

100-dB 80% attenuator 1.55 μm laser

60% Single-photon upconversion 1548 nm (IR) → 631 nm (visible) 40% max. efficiency: 90% 20% Albota & Wong, Opt. Lett. 29, 1449 (2004)

0% Polarization-preserving upconversion Single-photon upconversion efficiency 0 5 10 15 20 25 JOSA-B 23, 918 (2006) Circulating pump power Pp (W)

16 Perfectly secure digital communication: the one-time pad

ƒ Alice has a plaintext message to send to Bob securely

ƒ She sends ciphertext = plaintext ⊕ random binary key …1101000… ⊕ …0100101… = …1001101…

ƒ Ciphertext is a completely random binary string impossible to recover plaintext from ciphertext without the key ƒ Bob decodes ciphertext ⊕ same binary key = Alice’s plaintext …1001101… ⊕ …0100101… = …1101000…

ƒ Security relies on single use of the secret key

ƒ Decoding relies on Alice and Bob having the same key

17 Quantum key distribution

ƒ Entangled photons provide randomness

Bob Alice PBS PBS

PBS Entangled- PBS photon 50/50 source 50/50 HWP HWP

ƒ Quantum mechanics allows detection of eavesdropping

Entanglement-based QKD: Ekert, PRL 67, 661 (1991)

18 Turning bugs into features: quantum cryptography

ƒ Bug: the state of an unknown qubit cannot be determined

ƒ Feature: eavesdropping on an unknown qubit is detectable

ƒ Alice and Bob randomly choose photon-polarization bases

horizontal/verticalor +45/-45 diagonal

for transmission (Alice) and reception (Bob)

ƒ Alice codes a random bit into her polarization choice

ƒ When Alice and Bob use the same basis… – their measurements provide a shared random key – eavesdropping (by Eve) can be detected through errors she creates

19 Single-photon two-qubit (SPTQ) quantum logic

ƒ Use polarization and momentum degrees of freedom of a single photon as two qubits – temporal overlap is guaranteed

ƒ Deterministic, linear-optical implementation of a universal gate set

ƒ Not scalable, but suitable for few-qubit processing tasks – hyperentanglement generation – physical simulations – entanglement distillation and purification

20 Polarization-CNOT gate

H: V: PBS

Input

6000

5000 Dove prism: 45º orientation 4000 3000

2000 Coincidences/s HR 1000 HL 0 VR Output state VL VL VR HL PRL 93, 070502 (2004) HR Input state

CNOT truth table 21 P-CNOT entangling gate

H + V HR + VL ⊗ R P-CNOT 2 2

Verification of entanglement θ θ Ψ3 = ()cosθA H + sin A V ⊗ (R + L ) 2

Ψ4 = ()cos A H + sinθ A V ⊗ ()R − L 2

22 P-CNOT entanglement results θ entanglement results θ Ψ3 = ()cosθA H + sin A V ⊗ (R + L ) 2 |Ψ3〉 Visibility = (91.7 ± 1.6)%

Ψ4 = ()cos A H + sinθ A V ⊗ ()R − L 2 |Ψ4〉 Visibility = (90.8 ± 0.8)%

6

|Ψ3〉 |Ψ4〉

4 coincidences / s 2 3 10

0 0 45 90 135 180 225 270 315 Analysis angle θ (deg.) A

23 The Fuchs-Peres-Brandt (FPB) Probe ƒ The most powerful individual BB84 attack (no error correction)

Eve Alice Bob

Probe qubit

Shapiro & Wong, PRA 73, 012315 (2006) Fuchs & Peres, PRA 53, 2036 (1996); Brandt, PRA 71, 042312 (2005) 24 Physical simulation of entangling-probe BB84 attack

PRA 75, 042327 (2007) 25 Quantum illumination

Can entanglement be used in noisy, lossy environment?

Quantum illumination: a new paradigm of quantum measurements – Original idea: Seth Lloyd, Science 321, 1463 (2008) – Gaussian states: Tan et al., PRL 101, 253601 (2008) – Receiver design: Guha, arXiv:0902.2932 [quant-ph]

signal Entangled Target source

idler return signal + noise Receiver

26 A two-way secure communication protocol Alice-to-Bob-to-Alice transmission with passive eavesdropper Eve

Alice Bob

Eve

Alice Bob

27 Error probabilities for optimum quantum receivers

ƒ If Eve ONLY measures Alice’s transmission, she gets no information:

ƒ If Eve ONLY measures Bob’s transmission, she gets no information:

ƒ If Eve measures BOTH Alice and Bob’s transmissions, she gets some information:

ƒ BUT Alice gets more reliable information:

J.H. Shapiro, arXiv:0903.3150 [quant-ph]

28 QI suboptimal receiver: optical parametric amplifier

signal SPDC multimode BPSK source tap

idler Eve

tap low-gain OPA noise + injection direct detection Bob

Alice Guha, arXiv:0902.2932 [quant-ph]

29 Comparison of error probability bounds

Lossy, noisy, low-brightness scenario:

30 Comparison of error probability bounds

Necessity of low brightness and high noise:

Alice

Eve

31 An example

ƒ Lossy, noisy, low-brightness operation:

ƒ M = 2 x 106 temporal modes

ƒ Error probability bounds Alice:

Eve:

32 Quantum-illumination secure communication

ƒ Depends on phase-sensitive cross correlation – phase coherence must be maintained via a tracking system

ƒ Require authentication to preclude a man-in-the-middle attack – monitor the physical integrity of Alice-to-Bob

ƒ Loss versus data rate tradeoff

33 Summary

ƒ Entanglement is fun, mysterious, magical – it’s all about superposition, interference, distinguishability – easy to generate for certain types of entanglement

ƒ Useful in many applications – quantum key distribution, quantum communications, quantum computing, quantum sensing

ƒ Single-photon two-qubit quantum logic – physical simulation of quantum algorithms

ƒ Quantum-illumination secure communication – can operate under high loss and high noise regime – -3 dB suboptimal receiver design is known – more work on security and proof-of-principle experiment

34