Wigner Distribution Malfunction John Philpott, Malvin C. Teich, and Bahaa E. A. Saleh Citation: Physics Today 43, 11, 123 (1990); View online: https://doi.org/10.1063/1.2810781 View Table of Contents: http://physicstoday.scitation.org/toc/pto/43/11 Published by the American Institute of Physics LETTERS erally adduced in favor of "unwinding versial to their respective advocates. to-one and do not discard any infor- the program": Unavoidable energy Eginhart Biedermann uses this as an mation. Goto and his colleagues dissipation occurs only where infor- opportunity to return to a different claim that this is not essential. In a mation is discarded, that is, when and earlier debate already published fashion typical of critics of reversible resetting the output register (or the in Nature. The earlier debate con- computation, Biedermann analyzes measuring apparatus) to the stan- cerned a much more fundamental and the energy requirements of his own dardized state; "after a long computa- conceptual question: What is the notion of minimally dissipative com- tion the final state of a reversible minimal energy dissipation require- putation. Once again he tells us that computer has many more balls [the ment imposed on computation by the static friction is essential, but does not information-bearing particles in the laws of physics? Biedermann takes tell us what is wrong with Likharev's Fredkin-Toffoli billiard-ball model] issue with Charles Bennett's notion scheme, which clearly avoids static whose state depends on the computa- of reversible computation, first pub- friction. 3 tion" ; and after unwinding the pro- lished in 1973. Bennett demonstrated In his final paragraph, Biedermann gram, the input register can be "un- that computation can be carried out suggests that the exponents of rever- copied," without dissipation, against a with an energy dissipation per step sible computation have been carried copy of the input information pre- that can be reduced to any desired along by uncritical enthusiasm. Ac- served there for just this purpose. extent, if we are willing to compute tually, reversible computation is a However, if the second argument sufficiently slowly. This concept has somewhat counterintuitive notion on were correct (even though every re- been confirmed and elaborated by a first exposure, as demonstrated by versible computing step is a 1:1 imag- great many subsequent investigators Biedermann's repeated objections. ing process!) this computation would with different backgrounds and view- Feynman, at a 1981 workshop, was reduce entropy (or generate neg- points, including the late Richard the only one I have ever seen who Feynman.1 Bennett's work has been entropy), evidently by taking heat 2 caught on immediately. My own his- from the environment. The computer labeled "epoch-making." I do not tory was very different. When I first would get colder the longer it ran. believe that reversible computation heard from Bennett about his evolv- During unwinding, this negentropy requires a detailed defense against all ing ideas, in 1971, I was totally certainly would get lost again. But of Biedermann's critique, and cite skeptical. After all, this was a major below three recent items to lead to the with Landauer's dissipationless copy- 3 departure from my own earlier publi- ing process we can do much better citation trail. cations. It took me six months to by providing a resetting store at I do suggest that the reader of become convinced. It is now, how- the output (with all bits in the 0 Biedermann's critique keep two items ever, almost two decades and many position). Copying this "information" in mind. First of all, reversible com- papers later, and it should no longer into the output register after compu- putation as viewed by Bennett and by be that difficult! tation is completed involves precisely me is not totally without dissipation, the same, presumedly dissipationless as was claimed for one of the propos- References copying steps Landauer described in als that my Opinion item analyzed. reference 3. Evidently, his copying 1. R. P. Feynman, Int. J. Theor. Phys. 21, Additionally, Biedermann states that 467 (1982). process makes it possible to discard for computation with a roughly pre- information without dissipating ener- 2. J. A. Wheeler, W. H. Zurek, eds., Quan- dictable execution time, a limited tum Theory and Measurement, Prince- gy. (Unwinding the program then is total energy expenditure, say, lOOkT, just a waste of time and energy, and ton U. P., Princeton, N. J. (1983). is required. I do not consider the 3. C. H. Bennett, IBM J. Res. Dev. 32, 16 there is no need for extra hardware to exact energy expenditure significant; store all the input information.) (1988). R. Landauer, in Proc. 3rd Int. the key point is that the expenditure Symp. Foundations of Quantum Me- In conclusion, the question arises of is not proportional to the number of chanics, S. Kobayashi, H. Ezawa, Y. whether "reversible computation" is elementary logic functions carried Murayama, S. Nomura, eds., Phys. Soc. another of those "many episodes" out during a long computation. But Jpn., Tokyo (1990), p. 407. C. M. Caves, Landauer so correctly describes in his why should we even require a compu- W. G. Unruh, W. H. Zurek, Phys. Rev. Opinion column, where "the advo- tation to be characterized by a "pre- Lett. 65, 1387 (1990). cates are ... carried away by their dictable passage time"? Even for 4. K. K. Likharev, S. V. Rylov, V. K. Se- enthusiasm" and the skeptic will not today's practical computers, which menov, IEEE Trans. Magn. 21, 947 be "invited to the conferences, which have a well-defined execution time (1985). the proponents ... dominate." In all per step, the number of successive 5. E. Goto, N. Yoshida, K. F. Loe, W. Hioe, generality, the skeptics are simply logic steps required to carry out a in Proc. 3rd Int. Symp. Foundations of program is, in general, not predict- Quantum Mechanics, S. Kobayashi, H. those who take the trouble to think a Ezawa, Y. Murayama, S. Nomura, eds., few steps further than the enthusi- able. Finally, Biedermann ignores the fact that some reversible comput- Phys. Soc. Jpn., Tokyo (1990), p. 412. asts, who try to ignore everything Note also my rebuttal recorded as part that does not fit into their (friction- er proposals, such as that of Konstan- of the discussion following the paper. less) dreams. tin Likharev using Josephson junc- tion circuits,4 are clocked just as ROLF LANDAUER actual current computers are. IBM Thomas J. Watson Research Center References 10/90 Yorktown Heights, New York 1. R. Landauer, Nature 335, 779 (1988). The occasional published dissent 2. E. Biedermann, Nature 340, 681 (1989). that, like Biedermann's, still consid- 3. R. Landauer, Nature 340, 681 (1989). ers reversible computation to be ex- Wigner Distribution EGINHART BIEDERMANN cessively optimistic is balanced on the 2/90 Boblingen, West Germany other side by the proposal of Eiichi Malfunction Goto and his colleagues asserting that I am writing to point out some minor LANDAUER REPLIES: My Opinion col- the special precautions invoked in mathematical inconsistencies in the reversible computation are not need- umn provided a conservative assess- 5 otherwise interesting and informa- ment of some logic technology propos- ed. Reversible computation uses log- tive article on squeezed and anti- als and undoubtedly appears contro- ic functions at every step that are one- bunched light by Malvin C. Teich and PHYSICS TODAY NOVEMBER, 1990 1 2 3 Bahaa E. A. Saleh (June, page 26). tion principle and the probability So did Doc Draper. The coherent state localized at <x> interpretation of quantum mechan- It is also unfortunate that Reid and <p> is properly described by the ics. If one writes the wavefunction of apparently does not recognize how (normalized) wavefunction a single spinless particle in polar useful some engineering achieve- coordinates p and cp, an arbitrary ments initially developed for defense exp(2i<p>;t) normalizable function f(p) is an eigen- have been for society at large. Me- Xexp[-(x-<x» 2 ] function with angular momentum chanical heart valves, silicon carbide When this wavefunction is inserted zero, while fip) exp(im<p) has angu- ceramics, Mylar, flameproof epoxy into the Wigner phase-space distribu- lar momentum fim. If one considers paint, cordless tools, graphite compos- tion function, denned as a linear superposition of the two ite materials, self-contained breath- wavefunctions, the corresponding ing apparatus, freeze-dried food, mi- W(x,p) = probability density is given by crowave technology, nuclear power, 2\f(p)\~ [1 + cosbrup)]. As probabili- pacemakers, helicopters, electric ana- — \ip' (x + —y) if>(x - —y) exp(2i/jy) Ay ties should be single-valued, the quan- log computers and nuclear medicine IT j 2 2 tization of angular momentum fol- are just some examples. the result given by Teich and Saleh is lows without invoking the single- Ironically, Reid feels the Greek obtained, namely valued-ness of the wavefunction as mathematician, physicist and inven- 2 the starting point. This argument tor Archimedes would be a much W(x,p) = (21 n) exp[ - 2(x - <*» ] holds in two as well in higher spatial worthier person for the academy to Xexp[-2(p-<p» 2 ] dimensions. The reasoning given for name a prize after. I say "ironically" the quantization of angular momen- It is easily shown that the above because while Archimedes made orig- tum in integer units for "normal" inal contributions in geometry and definition of W(x,p) properly yields (non-fractional-statistic) particles J^(A:)|2 when integrated with respect mathematics and founded the fields of 2 shows that the description of anyons statics, hydrostatics and mathemat- top, and |<p(jD)| when integrated with has to involve a superselection rule respect to x.