Abstract

Computer operations that conserve energy do not, from an information viewpoint, increase entropy and therefore have no minimum energy cost associated with them. An information-conserving operation must be reversible in principle; reversible optical gates inevitably incur losses. The energy per calculation may have many meanings, as we show. The energy expended by a single photon in a conservative optical operation is negligible, much less than kT.

© 1990 Optical Society of America

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References

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1990 (1)

1989 (1)

1988 (1)

1986 (1)

1985 (4)

C. H. Bennett, R. Landauer, Sci. Am. 253(1), 48 (1985).
[CrossRef]

D. Deutsch, Proc. R. Soc. London Ser. A 400, 97 (1985).
[CrossRef]

A. Peres, Phys. Rev. A 32, 3266 (1985).
[CrossRef] [PubMed]

R. P. Feynman, Opt. News 11(2), 11 (1985);Found. Phys. 16, 507 (1986).
[CrossRef]

1984 (1)

W. H. Zurek, Phys. Rev. Lett. 53, 391 (1984).
[CrossRef]

1982 (4)

E. Fredkin, T. Toffoli, Int. J. Theor. Phys. 21, 219 (1982).
[CrossRef]

H. J. Bremermann, Int. J. Theor. Phys. 21, 299 (1982).
[CrossRef]

L. B. Levitin, Int. J. Theor. Phys. 21, 299 (1982).
[CrossRef]

K. K. Likharev, Int. J. Theor. Phys. 21, 311 (1982).
[CrossRef]

1966 (1)

J. Shamir, R. Fox, Phys. Lett. 23, 314 (1966).
[CrossRef]

1961 (1)

R. Landauer, IBM J. Res. Dev. 5, 183 (1961).
[CrossRef]

Bennett, C. H.

C. H. Bennett, R. Landauer, Sci. Am. 253(1), 48 (1985).
[CrossRef]

Bremermann, H. J.

H. J. Bremermann, Int. J. Theor. Phys. 21, 299 (1982).
[CrossRef]

Caulfield, H. J.

Deutsch, D.

D. Deutsch, Proc. R. Soc. London Ser. A 400, 97 (1985).
[CrossRef]

Feynman, R. P.

R. P. Feynman, Opt. News 11(2), 11 (1985);Found. Phys. 16, 507 (1986).
[CrossRef]

Fox, R.

J. Shamir, R. Fox, Phys. Lett. 23, 314 (1966).
[CrossRef]

Fredkin, E.

E. Fredkin, T. Toffoli, Int. J. Theor. Phys. 21, 219 (1982).
[CrossRef]

Johnson, K. M.

Landauer, R.

C. H. Bennett, R. Landauer, Sci. Am. 253(1), 48 (1985).
[CrossRef]

R. Landauer, IBM J. Res. Dev. 5, 183 (1961).
[CrossRef]

Levitin, L. B.

L. B. Levitin, Int. J. Theor. Phys. 21, 299 (1982).
[CrossRef]

Likharev, K. K.

K. K. Likharev, Int. J. Theor. Phys. 21, 311 (1982).
[CrossRef]

Miceli, W.

Peres, A.

A. Peres, Phys. Rev. A 32, 3266 (1985).
[CrossRef] [PubMed]

Seymor, R. J.

Shamir, J.

Surette, M. R.

Toffoli, T.

E. Fredkin, T. Toffoli, Int. J. Theor. Phys. 21, 219 (1982).
[CrossRef]

Zurek, W. H.

W. H. Zurek, Phys. Rev. Lett. 53, 391 (1984).
[CrossRef]

Appl. Opt. (3)

IBM J. Res. Dev. (1)

R. Landauer, IBM J. Res. Dev. 5, 183 (1961).
[CrossRef]

Int. J. Theor. Phys. (4)

E. Fredkin, T. Toffoli, Int. J. Theor. Phys. 21, 219 (1982).
[CrossRef]

H. J. Bremermann, Int. J. Theor. Phys. 21, 299 (1982).
[CrossRef]

L. B. Levitin, Int. J. Theor. Phys. 21, 299 (1982).
[CrossRef]

K. K. Likharev, Int. J. Theor. Phys. 21, 311 (1982).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. News (1)

R. P. Feynman, Opt. News 11(2), 11 (1985);Found. Phys. 16, 507 (1986).
[CrossRef]

Phys. Lett. (1)

J. Shamir, R. Fox, Phys. Lett. 23, 314 (1966).
[CrossRef]

Phys. Rev. A (1)

A. Peres, Phys. Rev. A 32, 3266 (1985).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

W. H. Zurek, Phys. Rev. Lett. 53, 391 (1984).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

D. Deutsch, Proc. R. Soc. London Ser. A 400, 97 (1985).
[CrossRef]

Sci. Am. (1)

C. H. Bennett, R. Landauer, Sci. Am. 253(1), 48 (1985).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

Conservative optical process with input channels coming from the left into a processor (B) and output channels going to the right.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

( A 1 + A 2 + + A n ) B ( A n + + A 2 + A 1 ) .
( A 1 + A 2 + + A k ) B 2 ( A 1 + + A k ) .
E ¯ r = N h ν / F ,
E ¯ p = E ¯ r / .
s = i s ( i ) , u = i u ( i ) ;
E ¯ p = E ¯ r u + s / P = P E ¯ r P u + s .
E ph = h v .
Δ E ph E ph = Δ v v 2 h v m c 2 < 10 34 ,
Δ E ¯ r = N h Δ v F < 10 21 E ¯ r ,

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