Corrections to “The Quantum Theory of Optical Communications” [Nov/Dec 09 1547-1569]

Corrections to “The Quantum Theory of Optical

Communications” [Nov/Dec 09 1547-1569]

The MIT Faculty has made this article openly available.

Please share

how this access benefits you. Your story matters.

Citation

Shapiro, J.H. “Corrections to “The Quantum Theory of Optical

Communications” [Nov/Dec 09 1547-1569].” Selected Topics in

Quantum Electronics, IEEE Journal of 16.3 (2010): 698. © Copyright

2010 IEEE

As Published

http://dx.doi.org/10.1109/JSTQE.2010.2048393

Publisher

Institute of Electrical and Electronics Engineers

Version

Final published version

Citable link

http://hdl.handle.net/1721.1/62230

Terms of Use

Article is made available in accordance with the publisher's

policy and may be subject to US copyright law. Please refer to the

publisher's site for terms of use.

698 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 16, NO. 3, MAY/JUNE 2010

Correspondence

Corrections to “The Quantum Theory of

Optical Communications”

Jeffrey H. Shapiro, Fellow, IEEE

We correct errors that were made in [1] and withdraw the Note

Added in Proof.

Below equation (152) it should say 2P /¯

hωp

≡ |κA

|



|∆k

| is the

downconverter’s photon-pair flux.

Equations (172) and (173) are incorrect. The correct results are as

follows:

E(θ

, θ

) =

−

cos[2(θA

− θ

)]

4P Tc

/¯

hω

+ 1

(172)

for P Tc

/¯

hω

> 0, and

S =

2

√

2

4P Tc

/¯

hω

+ 1

≈ 2

√

2

(173)

where the approximation employs P Tc

/¯

hω

 1.

Manuscript received March 30, 2010. Date of publication May 6, 2010; date of current version June 4, 2010.

The author is with the Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139 USA (e-mail: jhs@mit.edu).

Digital Object Identifier 10.1109/JSTQE.2010.2048393

Since the appearance of [1], we have found a fatal flaw in the

min-imum output entropy proofs from [2] and [3]. Those papers have now

been withdrawn, and so the Note Added in Proof in [1] is also being

withdrawn.

R

[1] J. H. Shapiro, “The quantum theory of optical communications,” IEEE J. Sel. Top. Quantum Electron., vol. 15, no. 6, pp. 1547–1569, Nov./Dec. 2009.

[2] S. Lloyd, V. Giovannetti, L. Maccone, N. J. Cerf, S. Guha, R. Garc´ıa-Patr´on, S. Mitter, S. Pirandola, M. B. Ruskai, J. H. Shapiro, and H. Yuan. (2010, Jan.). Proof of the bosonic minimum output entropy conjecture [Online]. Available: http://arxiv.org/abs/0906.2758v2

[3] S. Lloyd, V. Giovannetti, L. Maccone, S. Pirandola, and R. Garc´ıa-Patr´on. (2010, Jan.). Minimum output entropy of Gaussian channels [Online]. Available: http://arxiv.org/abs/0906.2762