## Stable control of 10 dB two-mode squeezed vacuum states of light |

Optics Express, Vol. 21, Issue 9, pp. 11546-11553 (2013)

http://dx.doi.org/10.1364/OE.21.011546

Acrobat PDF (1140 KB)

### Abstract

Continuous variable entanglement is a fundamental resource for many quantum information tasks. Important protocols like superactivation of zero-capacity channels and finite-size quantum cryptography that provides security against most general attacks, require about 10 dB two-mode squeezing. Additionally, stable phase control mechanisms are necessary but are difficult to achieve because the total amount of optical loss to the entangled beams needs to be small. Here, we experimentally demonstrate a control scheme for two-mode squeezed vacuum states at the telecommunication wavelength of 1550 nm. Our states exhibited an Einstein-Podolsky-Rosen covariance product of 0.0309 ± 0.0002, where 1 is the critical value, and a Duan inseparability value of 0.360±0.001, where 4 is the critical value. The latter corresponds to 10.45 ± 0.01dB which reflects the average non-classical noise suppression of the two squeezed vacuum states used to generate the entanglement. With the results of this work demanding quantum information protocols will become feasible.

© 2013 OSA

## 1. Introduction

1. R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev.
Mod. Phys. **81**, 865–942 (2009) [CrossRef] .

2. D. Bouwmeester, J. Pan, K. Mattle, and M. Eibl, “Experimental quantum
teleportation,” Nature **390**, 575–579 (1997) [CrossRef] .

3. A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional Quantum
Teleportation,” Science **282**, 706–709 (1998) [CrossRef] [PubMed] .

4. C. H. Bennett and S. J. Wiesner, “Communication via One- and Two-Particle Operators on
Einstein-Podolsky-Rosen States,” Phys. Rev. Lett. **69**, 2881 (1992) [CrossRef] [PubMed] .

5. S. Braunstein and H. Kimble, “Dense coding for continuous
variables,” Phys. Rev. A **61**, 042302 (2000) [CrossRef] .

6. R. Schnabel, N. Mavalvala, D. E. McClelland, and P. K. Lam, “Quantum metrology for gravitational wave
astronomy,” Nat. Commun. **1**, 121 (2010) [CrossRef] [PubMed] .

9. C. Weedbrook, S. Pirandola, R. Garcia-Patron, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian Quantum Information,”
Rev. Mod. Phys. **84**, 621 (2012) [CrossRef] .

10. H. Briegel, W. Dür, J. Cirac, and P. Zoller, “Quantum repeaters: The role of imperfect local operations
in quantum communication,” Phys. Rev. Lett. **81**, 5932 (1998) [CrossRef] .

11. D. P. DiVincenzo, “Quantum Computation,”
Science **270**, 255 (1995) [CrossRef] .

12. J. Lodewyck, M. Bloch, R. Garcia-Patron, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. Cerf, R. Tualle-Brouri, S. McLaughlin, and P. Grangier, “Quantum key distribution over 25km with an all-fiber
continuous-variable system,” Phys. Rev. A **76**, 042305 (2007) [CrossRef] .

13. F. Furrer, T. Franz, M. Berta, A. Leverrier, V. Scholz, M. Tomamichel, and R. Werner, “Continuous Variable Quantum Key Distribution: Finite-Key
Analysis of Composable Security against Coherent Attacks,” Phys.
Rev. Lett. **109**, 100502 (2012) [CrossRef] [PubMed] .

^{8}. To achieve these requirements a stable control of the entanglement generation is necessary.

14. G. Smith and J. Yard, “Quantum communication with zero-capacity
channels,” Science **321**, 1812–5 (2008) [CrossRef] [PubMed] .

15. G. Smith, J. A. Smolin, and J. Yard, “Quantum communication with Gaussian channels of zero
quantum capacity,” Nat. Phot. **5**, 624–627 (2011) [CrossRef] .

16. Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for
continuous variables,” Phys. Rev. Lett. **68**, 3663–3666 (1992) [CrossRef] [PubMed] .

3. A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional Quantum
Teleportation,” Science **282**, 706–709 (1998) [CrossRef] [PubMed] .

17. T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum Enhancement of the Zero-Area Sagnac Interferometer
Topology for Gravitational Wave Detection,” Phys. Rev.
Lett. **104**, 251102 (2010) [CrossRef] [PubMed] .

18. M. Mehmet, S. Ast, T. Eberle, S. Steinlechner, H. Vahlbruch, and R. Schnabel, “Squeezed light at 1550 nm with a quantum noise reduction of
12.3 dB,” Opt. Exp. **19**, 25763–72 (2011) [CrossRef] .

*X*denotes the amplitude quadrature and

*P*denotes the phase quadrature. After superimposing both modes with relative phase

*φ*

_{ent}=

*π*/2 at a balanced beam splitter, the outputs are quadrature entangled. To verify the entanglement both modes are measured with homodyne detection, where the phases of the local oscillators,

*φ*and

_{A}*φ*, determine the measured quadrature. Such a scheme was implemented for instance in Refs. [3

_{B}3. A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional Quantum
Teleportation,” Science **282**, 706–709 (1998) [CrossRef] [PubMed] .

19. W. P. Bowen, R. Schnabel, and P. K. Lam, “Experimental Investigation of Criteria for Continuous
Variable Entanglement,” Phys. Rev. Lett. **90**, 043601 (2003) [CrossRef] [PubMed] .

22. S. Steinlechner, J. Bauchrowitz, T. Eberle, and R. Schnabel, “Strong Einstein-Podolsky-Rosen steering with unconditional
entangled states,” Phys. Rev. A **87**, 022104 (2013) [CrossRef] .

22. S. Steinlechner, J. Bauchrowitz, T. Eberle, and R. Schnabel, “Strong Einstein-Podolsky-Rosen steering with unconditional
entangled states,” Phys. Rev. A **87**, 022104 (2013) [CrossRef] .

*φ*

_{ent}was not controlled, but inherently stable for up to about 500 ms.

*φ*

_{ent},

*φ*and

_{A}*φ*to arbitrary values. For generating two-mode squeezed

_{B}*vacuum*states the control scheme involves only auxiliary beams with low power that are shot-noise limited at the measurement Fourier frequency. It also introduces only a small amount of optical loss, which is necessary for generating highly entangled states.

## 2. Experimental Setup

17. T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum Enhancement of the Zero-Area Sagnac Interferometer
Topology for Gravitational Wave Detection,” Phys. Rev.
Lett. **104**, 251102 (2010) [CrossRef] [PubMed] .

23. S. Ast, R. M. Nia, A. Schönbeck, N. Lastzka, J. Steinlechner, T. Eberle, M. Mehmet, S. Steinlechner, and R. Schnabel, “High-efficiency frequency doubling of continuous-wave laser
light,” Opt. Lett. **36**, 3467–9 (2011) [CrossRef] [PubMed] .

*μ*W after the 50 : 50 beam splitter) which was shot-noise limited at about 5 MHz. Phase modulation sidebands were imprinted to the control beam by an electro-optical modulator at 33.9 MHz for the first and 35.5 MHz for the second squeezed-light source. The beam reflected at the cavity was split from the input beam by a Faraday isolator (FI) and detected by a resonant photo detector. The photo current was demodulated at the sideband frequency into its I and Q components which served as error signals for the cavity length [24

24. E. D. Black, “An introduction to Pound-Drever-Hall laser frequency
stabilization,” Am. J. Phys. **69**, 79–87 (2001) [CrossRef] .

25. B. Hage, A. Franzen, J. DiGuglielmo, P. Marek, J. Fiurasek, and R. Schnabel, “On the distillation and purification of phase-diffused
squeezed states,” N. J. Phys. **9**, 227 (2007) [CrossRef] .

*μ*W of the main laser beam were frequency shifted by 78 MHz for the first and by 82 MHz for the second squeezed-light source by means of an acousto-optical modulator (AOM). After passing a FI which prevented parasitic cavities, the beam was superimposed with the control beam at a 50 : 50 beam splitter forming a single sideband (SSB) at the respective frequency. One output port of the beam splitter was detected by a photo detector and demodulated at the SSB frequency to generate an error signal for the phase lock of the SSB to the control beam. Hence, the SSB became a phase reference for the squeezed quadrature angle. The squeezed light leaving the cavity through the coupling mirror was split from the pump beam by a dichroic beam splitter.

26. J. DiGuglielmo, A. Samblowski, B. Hage, C. Pineda, J. Eisert, and R. Schnabel, “Experimental Unconditional Preparation and Detection of a
Continuous Bound Entangled State of Light,” Phys. Rev.
Lett. **107**, 240503 (2011) [CrossRef] .

*A*and mode

*B*. To achieve two-mode squeezing according to Fig. 1, the phase

*φ*

_{ent}between the squeezed beams had to be controlled to

*π*/2. Therefore we tapped off a fraction of 1 % in one of the output beams of the beam splitter. The tap-off was superimposed at a balanced beam splitter with a local oscillator with a power of about 5 mW. The output beams were detected by two resonant photo detectors, PD

_{78}and PD

_{82}, and demodulated at 78 MHz and 82 MHz, respectively. The error signal generated by the 82 MHz demodulation was used to control the phase of the local oscillator, while the other was used to control

*φ*

_{ent}. By changing the phase of the electronic local oscillator used for the demodulation,

*φ*

_{ent}could be controlled to an arbitrary angle. Hence, besides the

*π*/2 phase shift used in this experiment,

*φ*

_{ent}can be locked to values more suitable in other experiments, e.g. for quantum dense metrology [8]. Generating the error signal for

*φ*

_{ent}in such a two-fold manner, increases the signal-to-noise ratio dramatically compared to the detection of the SSB-SSB beat or the beat of one of the single sidebands with the control beams. For the latter also a fraction of mode

*A*would be needed [26

26. J. DiGuglielmo, A. Samblowski, B. Hage, C. Pineda, J. Eisert, and R. Schnabel, “Experimental Unconditional Preparation and Detection of a
Continuous Bound Entangled State of Light,” Phys. Rev.
Lett. **107**, 240503 (2011) [CrossRef] .

*A*and mode

*B*, respectively, with a visibility of about 99.5 %. The outputs of the balanced beam splitter were detected by a pair of high quantum efficiency photo diodes. The photo current difference was demodulated at 82 MHz to generate an error signal for the local oscillator’s phase

*φ*and

_{A}*φ*, respectively. Here, the measured quadrature is defined by the phase of the electronic local oscillator used for the demodulation and hence, could be controlled to arbitrary values. An amplified output of the homodyne detector electronics was anti-alias filtered and sampled by a data acquisition card with two synchronized channels with a sampling frequency of 256 MHz. The samples were demodulated digitally at 8 MHz and lowpass filtered at 200 kHz. The electronic dark noise variance of the homodyne detector electronics was about 20 dB below the vacuum noise variances, measured with blocked signal ports.

_{B}## 3. Results

*φ*

_{ent}was controlled to

*π*/2. The vacuum noise reference was measured by blocking the signal ports of the homodyne detectors. By controlling

*φ*and

_{A}*φ*to the amplitude or phase quadrature we made a partial tomographic measurement [27

_{B}27. J. DiGuglielmo, B. Hage, A. Franzen, J. Fiurasek, and R. Schnabel, “Experimental characterization of Gaussian
quantum-communication channels,” Phys. Rev. A **76**, 012323 (2007) [CrossRef] .

^{6}data points, from which we reconstructed 12 out of 16 entries of the covariance matrix Here, the values given in brackets could not directly be measured as they correspond to non-commuting operators. In principle, these entries of the covariance matrix can be calculated from additional measurements at a linear combination of the amplitude and phase quadrature. Such measurements were first demonstrated in [27

27. J. DiGuglielmo, B. Hage, A. Franzen, J. Fiurasek, and R. Schnabel, “Experimental characterization of Gaussian
quantum-communication channels,” Phys. Rev. A **76**, 012323 (2007) [CrossRef] .

*φ*

_{ent}was precisely controlled to

*π*/2, as well as the phases of the homodyne detectors’ local oscillators were precisely controlled to the amplitude and phase quadratures, however, the covariances, which were not determined, should be close to 0 [22

22. S. Steinlechner, J. Bauchrowitz, T. Eberle, and R. Schnabel, “Strong Einstein-Podolsky-Rosen steering with unconditional
entangled states,” Phys. Rev. A **87**, 022104 (2013) [CrossRef] .

28. L. Duan, G. Giedke, J. Cirac, and P. Zoller, “Inseparability criterion for continuous variable
systems,” Phys. Rev. Lett. **84**, 2722–2725 (2000) [CrossRef] [PubMed] .

29. M. D. Reid, “Demonstration of the Einstein-Podolsky-Rosen paradox using
nondegenerate parametric amplification,” Phys. Rev. A **40**, 913 (1989) [CrossRef] [PubMed] .

^{6}data points into 10

^{4}chunks of 2 × 10

^{5}length. A Gaussian function was fitted to the histogram yielding 0.360 ± 0.001 for the Duan criterion and 0.0309 ± 0.0002 for the EPR-Reid criterion for the

*A*to

*B*direction. For the other direction similar results were obtained. In Ref. [22

**87**, 022104 (2013) [CrossRef] .

18. M. Mehmet, S. Ast, T. Eberle, S. Steinlechner, H. Vahlbruch, and R. Schnabel, “Squeezed light at 1550 nm with a quantum noise reduction of
12.3 dB,” Opt. Exp. **19**, 25763–72 (2011) [CrossRef] .

*X̂*+

_{A}*X̂*), and the variance of the difference of the phase quadrature operators, Var(

_{B}*P̂*−

_{A}*P̂*), versus time. Both variances were normalized to a joint measurement of vacuum states at the homodyne detectors,

_{B}**87**, 022104 (2013) [CrossRef] .

*φ*

_{ent}was not locked, the measurement time was only 200

*μ*s. The stability of our phase lock was not limited to the 10 s being presented in the figure. Indeed, we observed the stable production of our entangled states for more than 15 min. In principle, our active control loops allow an extension of the measurement time to arbitrary duration if the dynamic ranges of the used piezo actuators are large enough to compensate for thermal drifts.

## 4. Conclusion

^{7}samples (after sifting) is feasible with the present state [13

13. F. Furrer, T. Franz, M. Berta, A. Leverrier, V. Scholz, M. Tomamichel, and R. Werner, “Continuous Variable Quantum Key Distribution: Finite-Key
Analysis of Composable Security against Coherent Attacks,” Phys.
Rev. Lett. **109**, 100502 (2012) [CrossRef] [PubMed] .

30. M. Mehmet, T. Eberle, S. Steinlechner, H. Vahlbruch, and R. Schnabel, “Demonstration of a quantum-enhanced fiber Sagnac
interferometer,” Opt. Lett. **35**, 1665–1667 (2010) [CrossRef] [PubMed] .

## Acknowledgments

## References

1. | R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev.
Mod. Phys. |

2. | D. Bouwmeester, J. Pan, K. Mattle, and M. Eibl, “Experimental quantum
teleportation,” Nature |

3. | A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional Quantum
Teleportation,” Science |

4. | C. H. Bennett and S. J. Wiesner, “Communication via One- and Two-Particle Operators on
Einstein-Podolsky-Rosen States,” Phys. Rev. Lett. |

5. | S. Braunstein and H. Kimble, “Dense coding for continuous
variables,” Phys. Rev. A |

6. | R. Schnabel, N. Mavalvala, D. E. McClelland, and P. K. Lam, “Quantum metrology for gravitational wave
astronomy,” Nat. Commun. |

7. | W. Wasilewski, K. Jensen, H. Krauter, J. J. Renema, M. V. Balabas, and E. S. Polzik, “Quantum Noise Limited and Entanglement-Assisted
Magnetometry,” Phys. Rev. Lett. |

8. | S. Steinlechner, J. Bauchrowitz, M. Meinders, H. Müller-Ebhardt, K. Danzmann, and R. Schnabel, “Quantum-Dense Metrology,” arXiv 1211.3570 (2012). |

9. | C. Weedbrook, S. Pirandola, R. Garcia-Patron, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian Quantum Information,”
Rev. Mod. Phys. |

10. | H. Briegel, W. Dür, J. Cirac, and P. Zoller, “Quantum repeaters: The role of imperfect local operations
in quantum communication,” Phys. Rev. Lett. |

11. | D. P. DiVincenzo, “Quantum Computation,”
Science |

12. | J. Lodewyck, M. Bloch, R. Garcia-Patron, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. Cerf, R. Tualle-Brouri, S. McLaughlin, and P. Grangier, “Quantum key distribution over 25km with an all-fiber
continuous-variable system,” Phys. Rev. A |

13. | F. Furrer, T. Franz, M. Berta, A. Leverrier, V. Scholz, M. Tomamichel, and R. Werner, “Continuous Variable Quantum Key Distribution: Finite-Key
Analysis of Composable Security against Coherent Attacks,” Phys.
Rev. Lett. |

14. | G. Smith and J. Yard, “Quantum communication with zero-capacity
channels,” Science |

15. | G. Smith, J. A. Smolin, and J. Yard, “Quantum communication with Gaussian channels of zero
quantum capacity,” Nat. Phot. |

16. | Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for
continuous variables,” Phys. Rev. Lett. |

17. | T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum Enhancement of the Zero-Area Sagnac Interferometer
Topology for Gravitational Wave Detection,” Phys. Rev.
Lett. |

18. | M. Mehmet, S. Ast, T. Eberle, S. Steinlechner, H. Vahlbruch, and R. Schnabel, “Squeezed light at 1550 nm with a quantum noise reduction of
12.3 dB,” Opt. Exp. |

19. | W. P. Bowen, R. Schnabel, and P. K. Lam, “Experimental Investigation of Criteria for Continuous
Variable Entanglement,” Phys. Rev. Lett. |

20. | N. Takei, N. Lee, D. Moriyama, J. S. Neergaard-Nielsen, and A. Furusawa, “Time-gated Einstein-Podolsky-Rosen
correlation,” Phys. Rev. A |

21. | B. Hage, J. Janousek, S. Armstrong, T. Symul, J. Bernu, H. M. Chrzanowski, P. K. Lam, and H.-A. Bachor, “Demonstrating various quantum effects with two entangled
laser beams,” Eur. Phys. J. D |

22. | S. Steinlechner, J. Bauchrowitz, T. Eberle, and R. Schnabel, “Strong Einstein-Podolsky-Rosen steering with unconditional
entangled states,” Phys. Rev. A |

23. | S. Ast, R. M. Nia, A. Schönbeck, N. Lastzka, J. Steinlechner, T. Eberle, M. Mehmet, S. Steinlechner, and R. Schnabel, “High-efficiency frequency doubling of continuous-wave laser
light,” Opt. Lett. |

24. | E. D. Black, “An introduction to Pound-Drever-Hall laser frequency
stabilization,” Am. J. Phys. |

25. | B. Hage, A. Franzen, J. DiGuglielmo, P. Marek, J. Fiurasek, and R. Schnabel, “On the distillation and purification of phase-diffused
squeezed states,” N. J. Phys. |

26. | J. DiGuglielmo, A. Samblowski, B. Hage, C. Pineda, J. Eisert, and R. Schnabel, “Experimental Unconditional Preparation and Detection of a
Continuous Bound Entangled State of Light,” Phys. Rev.
Lett. |

27. | J. DiGuglielmo, B. Hage, A. Franzen, J. Fiurasek, and R. Schnabel, “Experimental characterization of Gaussian
quantum-communication channels,” Phys. Rev. A |

28. | L. Duan, G. Giedke, J. Cirac, and P. Zoller, “Inseparability criterion for continuous variable
systems,” Phys. Rev. Lett. |

29. | M. D. Reid, “Demonstration of the Einstein-Podolsky-Rosen paradox using
nondegenerate parametric amplification,” Phys. Rev. A |

30. | M. Mehmet, T. Eberle, S. Steinlechner, H. Vahlbruch, and R. Schnabel, “Demonstration of a quantum-enhanced fiber Sagnac
interferometer,” Opt. Lett. |

**OCIS Codes**

(270.6570) Quantum optics : Squeezed states

(270.5565) Quantum optics : Quantum communications

(270.5568) Quantum optics : Quantum cryptography

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: March 5, 2013

Revised Manuscript: April 13, 2013

Manuscript Accepted: April 13, 2013

Published: May 3, 2013

**Citation**

Tobias Eberle, Vitus Händchen, and Roman Schnabel, "Stable control of 10 dB two-mode squeezed vacuum states of light," Opt. Express **21**, 11546-11553 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-9-11546

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### References

- R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys.81, 865–942 (2009). [CrossRef]
- D. Bouwmeester, J. Pan, K. Mattle, and M. Eibl, “Experimental quantum teleportation,” Nature390, 575–579 (1997). [CrossRef]
- A. Furusawa, J. L. Sorensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, “Unconditional Quantum Teleportation,” Science282, 706–709 (1998). [CrossRef] [PubMed]
- C. H. Bennett and S. J. Wiesner, “Communication via One- and Two-Particle Operators on Einstein-Podolsky-Rosen States,” Phys. Rev. Lett.69, 2881 (1992). [CrossRef] [PubMed]
- S. Braunstein and H. Kimble, “Dense coding for continuous variables,” Phys. Rev. A61, 042302 (2000). [CrossRef]
- R. Schnabel, N. Mavalvala, D. E. McClelland, and P. K. Lam, “Quantum metrology for gravitational wave astronomy,” Nat. Commun.1, 121 (2010). [CrossRef] [PubMed]
- W. Wasilewski, K. Jensen, H. Krauter, J. J. Renema, M. V. Balabas, and E. S. Polzik, “Quantum Noise Limited and Entanglement-Assisted Magnetometry,” Phys. Rev. Lett.104, 133601 (2010). [CrossRef] [PubMed]
- S. Steinlechner, J. Bauchrowitz, M. Meinders, H. Müller-Ebhardt, K. Danzmann, and R. Schnabel, “Quantum-Dense Metrology,” arXiv 1211.3570 (2012).
- C. Weedbrook, S. Pirandola, R. Garcia-Patron, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian Quantum Information,” Rev. Mod. Phys.84, 621 (2012). [CrossRef]
- H. Briegel, W. Dür, J. Cirac, and P. Zoller, “Quantum repeaters: The role of imperfect local operations in quantum communication,” Phys. Rev. Lett.81, 5932 (1998). [CrossRef]
- D. P. DiVincenzo, “Quantum Computation,” Science270, 255 (1995). [CrossRef]
- J. Lodewyck, M. Bloch, R. Garcia-Patron, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. Cerf, R. Tualle-Brouri, S. McLaughlin, and P. Grangier, “Quantum key distribution over 25km with an all-fiber continuous-variable system,” Phys. Rev. A76, 042305 (2007). [CrossRef]
- F. Furrer, T. Franz, M. Berta, A. Leverrier, V. Scholz, M. Tomamichel, and R. Werner, “Continuous Variable Quantum Key Distribution: Finite-Key Analysis of Composable Security against Coherent Attacks,” Phys. Rev. Lett.109, 100502 (2012). [CrossRef] [PubMed]
- G. Smith and J. Yard, “Quantum communication with zero-capacity channels,” Science321, 1812–5 (2008). [CrossRef] [PubMed]
- G. Smith, J. A. Smolin, and J. Yard, “Quantum communication with Gaussian channels of zero quantum capacity,” Nat. Phot.5, 624–627 (2011). [CrossRef]
- Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, “Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett.68, 3663–3666 (1992). [CrossRef] [PubMed]
- T. Eberle, S. Steinlechner, J. Bauchrowitz, V. Händchen, H. Vahlbruch, M. Mehmet, H. Müller-Ebhardt, and R. Schnabel, “Quantum Enhancement of the Zero-Area Sagnac Interferometer Topology for Gravitational Wave Detection,” Phys. Rev. Lett.104, 251102 (2010). [CrossRef] [PubMed]
- M. Mehmet, S. Ast, T. Eberle, S. Steinlechner, H. Vahlbruch, and R. Schnabel, “Squeezed light at 1550 nm with a quantum noise reduction of 12.3 dB,” Opt. Exp.19, 25763–72 (2011). [CrossRef]
- W. P. Bowen, R. Schnabel, and P. K. Lam, “Experimental Investigation of Criteria for Continuous Variable Entanglement,” Phys. Rev. Lett.90, 043601 (2003). [CrossRef] [PubMed]
- N. Takei, N. Lee, D. Moriyama, J. S. Neergaard-Nielsen, and A. Furusawa, “Time-gated Einstein-Podolsky-Rosen correlation,” Phys. Rev. A74, 060101(R) (2006). [CrossRef]
- B. Hage, J. Janousek, S. Armstrong, T. Symul, J. Bernu, H. M. Chrzanowski, P. K. Lam, and H.-A. Bachor, “Demonstrating various quantum effects with two entangled laser beams,” Eur. Phys. J. D63, 457–461 (2011). [CrossRef]
- S. Steinlechner, J. Bauchrowitz, T. Eberle, and R. Schnabel, “Strong Einstein-Podolsky-Rosen steering with unconditional entangled states,” Phys. Rev. A87, 022104 (2013). [CrossRef]
- S. Ast, R. M. Nia, A. Schönbeck, N. Lastzka, J. Steinlechner, T. Eberle, M. Mehmet, S. Steinlechner, and R. Schnabel, “High-efficiency frequency doubling of continuous-wave laser light,” Opt. Lett.36, 3467–9 (2011). [CrossRef] [PubMed]
- E. D. Black, “An introduction to Pound-Drever-Hall laser frequency stabilization,” Am. J. Phys.69, 79–87 (2001). [CrossRef]
- B. Hage, A. Franzen, J. DiGuglielmo, P. Marek, J. Fiurasek, and R. Schnabel, “On the distillation and purification of phase-diffused squeezed states,” N. J. Phys.9, 227 (2007). [CrossRef]
- J. DiGuglielmo, A. Samblowski, B. Hage, C. Pineda, J. Eisert, and R. Schnabel, “Experimental Unconditional Preparation and Detection of a Continuous Bound Entangled State of Light,” Phys. Rev. Lett.107, 240503 (2011). [CrossRef]
- J. DiGuglielmo, B. Hage, A. Franzen, J. Fiurasek, and R. Schnabel, “Experimental characterization of Gaussian quantum-communication channels,” Phys. Rev. A76, 012323 (2007). [CrossRef]
- L. Duan, G. Giedke, J. Cirac, and P. Zoller, “Inseparability criterion for continuous variable systems,” Phys. Rev. Lett.84, 2722–2725 (2000). [CrossRef] [PubMed]
- M. D. Reid, “Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification,” Phys. Rev. A40, 913 (1989). [CrossRef] [PubMed]
- M. Mehmet, T. Eberle, S. Steinlechner, H. Vahlbruch, and R. Schnabel, “Demonstration of a quantum-enhanced fiber Sagnac interferometer,” Opt. Lett.35, 1665–1667 (2010). [CrossRef] [PubMed]

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