## Characterization of phase-averaged coherent states |

JOSA B, Vol. 30, Issue 10, pp. 2621-2627 (2013)

http://dx.doi.org/10.1364/JOSAB.30.002621

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### Abstract

We present the full characterization of phase-randomized or phase-averaged coherent states, a class of states exploited in communication channels and in decoy state-based quantum key distribution protocols. We report on the suitable formalism to analytically describe the main features of these states and on their experimental investigation, that results in agreement with theory. In particular, we consider a recently proposed non-Gaussianity measure based on the quantum fidelity, that we compare with previous ones, and we use the mutual information to investigate the amount of correlations one can produce by manipulating this class of states.

© 2013 Optical Society of America

**OCIS Codes**

(230.5160) Optical devices : Photodetectors

(270.0270) Quantum optics : Quantum optics

(270.5290) Quantum optics : Photon statistics

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: May 9, 2013

Revised Manuscript: July 25, 2013

Manuscript Accepted: August 12, 2013

Published: September 6, 2013

**Citation**

Alessia Allevi, Maria Bondani, Paulina Marian, Tudor A. Marian, and Stefano Olivares, "Characterization of phase-averaged coherent states," J. Opt. Soc. Am. B **30**, 2621-2627 (2013)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-30-10-2621

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### References

- H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94, 230504 (2005). [CrossRef]
- Y. Zhao, B. Qi, and H.-K. Lo, “Experimental quantum key distribution with active phase randomization,” Appl. Phys. Lett. 90, 044106 (2007). [CrossRef]
- H. Inamori, N. Lütkenhaus, and D. Mayers, “Unconditional security of practical quantum key distribution,” Eur. Phys. J. D 41, 599–627 (2007). [CrossRef]
- S. Olivares, “Quantum optics in the phase space,” Eur. Phys. J. Spec. Top. 203, 3–24 (2012). [CrossRef]
- M. Curty, T. Moroder, X. Ma, and N. Lütkenhaus, “Non-Poissonian statistics from Poissonian light sources with application to passive decoy state quantum key distribution,” Opt. Lett. 34, 3238–3240 (2009). [CrossRef]
- M. Bondani, A. Allevi, and A. Andreoni, “Light statistics by non-calibrated linear photodetectors,” Adv. Sci. Lett. 2, 463–468 (2009). [CrossRef]
- M. Bondani, A. Allevi, A. Agliati, and A. Andreoni, “Self-consistent characterization of light statistics,” J. Mod. Opt. 56, 226–231 (2009). [CrossRef]
- A. Andreoni and M. Bondani, “Photon statistics in the macroscopic realm measured without photon counters,” Phys. Rev. A 80, 013819 (2009). [CrossRef]
- A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions (McGraw-Hill, 1953), Vol. 1 & 2.
- G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed. (Cambridge University, 1944).
- K. E. Cahill and R. J. Glauber, “Ordered expansions in Bosons amplitude operators,” Phys. Rev. 177, 1857–1881 (1969). [CrossRef]
- K. E. Cahill and R. J. Glauber, “Density operators and quasiprobability distributions,” Phys. Rev. 177, 1882–1902 (1969). [CrossRef]
- V. Veitch, C. Ferrie, D. Gross, and J. Emerson, “Negative quasi-probability as a resource for quantum computation,” New J. Phys. 14, 113011 (2012). [CrossRef]
- V. Veitch, N. Wiebe, C. Ferrie, and J. Emerson, “Efficient simulation scheme for a class of quantum optics experiments with non-negative Wigner representation,” New J. Phys. 15, 013037 (2013). [CrossRef]
- A. Mari and J. Eisert, “Positive Wigner functions render classical simulation of quantum computation efficient,” Phys. Rev. Lett. 109, 230503 (2012). [CrossRef]
- M. Bondani, A. Allevi, and A. Andreoni, “Wigner function of pulsed fields by direct detection,” Opt. Lett. 34, 1444–1446 (2009). [CrossRef]
- S. Wallentowitz and W. Vogel, “Unbalanced homodyning for quantum state measurements,” Phys. Rev. A 53, 4528–4533 (1996). [CrossRef]
- K. Banaszek and K. Wódkiewicz, “Direct probing of quantum phase space by photon counting,” Phys. Rev. Lett. 76, 4344–4347 (1996). [CrossRef]
- A. Allevi, A. Andreoni, A. Bondani, G. Brida, M. Genovese, M. Gramegna, S. Olivares, M. G. A. Paris, P. Traina, and G. Zambra, “State reconstruction by on/off measurements,” Phys. Rev. A 80, 022114 (2009). [CrossRef]
- M. G. Genoni, M. G. A. Paris, and K. Banaszek, “Measure of the non-Gaussian character of a quantum state,” Phys. Rev. A 76, 042327 (2007). [CrossRef]
- M. G. Genoni, M. G. A. Paris, and K. Banaszek, “Quantifying the non-Gaussian character of a quantum state by quantum relative entropy,” Phys. Rev. A 78, 060303(R) (2008). [CrossRef]
- M. G. Genoni and M. G. A. Paris, “Quantifying non-Gaussianity for quantum information,” Phys. Rev. A 82, 052341 (2010). [CrossRef]
- I. Ghiu, P. Marian, and T. A. Marian, “Measures of non-Gaussianity for one-mode field states,” Phys. Scr. T153, 014028 (2013). [CrossRef]
- A. Uhlmann, “The ‘transition probability’ in the state space of a *-algebra,” Rep. Math. Phys. 9, 273–279 (1976). [CrossRef]
- A. Uhlmann, “Parallel transport and the ‘quantum holonomy’ along density operators,” Rep. Math. Phys. 24, 229–240 (1986). [CrossRef]
- A. Allevi, S. Olivares, and M. Bondani, “Manipulating the non-Gaussianity of phase-randomized coherent states,” Opt. Express 20, 24850–24855 (2012). [CrossRef]
- A. Allevi, S. Olivares, and M. Bondani, “Experimental quantification of non-Gaussianity of phase-randomized coherent states,” Int. J. Quantum Inform. 10, 1241006 (2012). [CrossRef]
- This results follows from the form of the joint photon statistics of the two outgoing modes that is factorized and reads p(n,m)=P(n;τ|β|2)P(m;(1−τ)|β|2), where P(n;N)=exp(−N)Nn(n!)−1 is the Poisson distribution.
- A. Allevi, M. Bondani, and A. Andreoni, “Photon-number correlations by photon-number resolving detectors,” Opt. Lett. 35, 1707–1709 (2010). [CrossRef]
- G. Zambra, A. Allevi, M. Bondani, A. Andreoni, and M. G. A. Paris, “Nontrivial photon statistics with low resolution-threshold photon counters,” Int. J. Quantum Inform. 5, 305–309 (2007). [CrossRef]

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