# Noiseless phase amplification using noise - QNLO by hcj

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```									                             Who are we?

Quantum Information Group              Quantum Information Processing Group
Department of Physics            Max Planck Institute for the Science of Light
Technical University of Denmark (DTU)                Erlangen, Germany

Collaborators:
Lodahl et al (DTU Fotonik)
We develop technology for            Sørensen et al (NBI)
Quantum Computing                    Filip et al (Palacky Uni)
Quantum Communication                Takeoka, Sasaki et al (NICT)
Quantum Metrology                    Furusawa et al (Tokyo Uni)
Drummond, Corney (UQ)
Processing and metrology

U.L.A., G. Leuchs and C. Silberhorn, Laser and Photonics Reviews, 4, 337 (2010)
What is quantum information?
Coding information into a discrete variable:

N                                  cH H  cV V                    Lecture by Kumar

   cu un             2D Examples
  c0 0  c1 1                    Poster by Jain

n 0                                c LG  c LG                Lecture by Boyd

  c   c                 PhD talks (Tipsmark, Benichi)

  c   c                   Lectures by Childress
and Imamoglu

Coding information into a continuous variable:

Coherent state:       (x) = Gaussian
    ( x) x dx              Examples
Squeezed state:       (x) = Sqz. Gaussian

Single photon:        (x) = 1st order HG
 ( x)   x                           Lectures by Kippenberg, Hammerer, Polzik and Mølmer
What do we do?
Quantum information protocol
Quantum state generation                 • Quantum averaging (PRA, 82, 021801 (2010) )
• Squeezed state / Entangled state                                     V
1
V1  V2 
• Cat state                                                                 2
• Single photon state                                                  1 1 1 1 
   
V 2  V1 V2 
       

• Quantum erasure correcting code (Nat. Phot. 2010)

No code

With code

Quantum metrology/estimation
• Phase measurement                       • Quantum Key Distribution
• Super-resolution with coherent states   • Quantum Random number generation (Nat. Phot 2010)
• Binary coherent state discrimination
(PRL 104, 100505 (2010))

• Violating Bells inequality with a hybrid detection system
• Hybrid quantum repeater using cat states (arXiv: 1004.0083)
• Noiseless Quantum Amplification (Nat. Phys. 2010)
Goal

To reduce the phase noise of a coherent state through amplification
Deterministic amplification

Gain = G

Input-output relation:
aout  Gain  G 1v

Louisell, W.H I. Phys. Rev. 124 1646 (1961); Haus, H.A. and Mullen, J.A. Phys. Rev. 128 5 (1962); Caves, C.M. Phys. Rev. D 26 , 8 (1982).
Probabilistic amplification

Gain = G

Ralph, T.C. and Lund, A.B. QCMC Proc. of 9th Int. Conf. 155-160

Babichev et al. EPL (2003); Xiang et al. Nat. Ph. 4, 316 (2010); Ferreyrol et al. PRL 104, 123603 (2010);
(Zavatta et al. arXiv:1004.3399v1 [quant-ph]; Marek and Filip, PRA 81, 022302 (2010); Fiurasek PRA 80, 053822 2009)
Probabilistic amplification

N
aa++
M
aa M

Marek and Filip, PRA 81,
  0  1                         022302 (2010)

a   1  2 2


aa   0  2 1  2


Zavatta et al. arXiv:1004.3399; Fiurasek PRA 80, 053822 (2009)
Phase-Concentration Scheme
Our approach
Phase-Concentration Scheme
How does it really work?
Experimental Setup

- diode laser (809nm)   - electro-optical    - tap-off        - homodyne
- mode cleaning           modulators and a     measurement      tomography
- LO split-off            half-wave plate    - feed-forward
Wigner functions

|coh |2 = 0.186

Usuga, Muller, Wittmann, Marek, Filip, Marquardt, Leuchs and Andersen, Nature Physics (2010)
Phase variance

Usuga, Muller, Wittmann, Marek, Filip, Marquardt, Leuchs and Andersen, Nature Physics (2010)
Conclusion

Simple Setup

Reduced Variance
What is quantum information?

Single mode field                          [ a, a ]  1

ˆ aeikr it  a  eikr it 

ˆ
E i           e ˆ             ˆ                 x aa
2 0V                                             
p  i (a  a)

Degrees of freedom

Continuous:   x, p ,  , 
Discrete: Photon number, Polarization, Orbital Angular Momentum

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