1.6: The Classical Bit
- Page ID
- 50155
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Because quantum measurement generally alters the object being measured, a quantum bit cannot be measured a second time. On the other hand, if a bit is represented by many objects with the same properties, then after a measurement enough objects can be left unchanged so that the same bit can be measured again.
In today’s electronic systems, a bit of information is carried by many objects, all prepared in the same way (or at least that is a convenient way to look at it). Thus in a semiconductor memory a single bit is represented by the presence or absence of perhaps 60,000 electrons (stored on a 10 fF capacitor charged to 1V). Similarly, a large number of photons are used in radio communication.
Because many objects are involved, measurements on them are not restricted to a simple yes or no, but instead can range over a continuum of values. Thus the voltage on a semiconductor logic element might be anywhere in a range from, say, 0V to 1V. The voltage might be interpreted to allow a margin of error, so that voltages between 0V and 0.2V would represent logical 0, and voltages between 0.8V and 1V a logical 1. The circuitry would not guarantee to interpret voltages between 0.2V and 0.8V properly. If the noise in a circuit is always smaller than 0.2V, and the output of every circuit gate is either 0V or 1V, then the voltages can always be interpreted as bits without error.
Circuits of this sort display what is known as “restoring logic” since small deviations in voltage from the ideal values of 0V and 1V are eliminated as the information is processed. The robustness of modern computers depends on the use of restoring logic
A classical bit is an abstraction in which the bit can be measured without perturbing it. As a result copies of a classical bit can be made. This model works well for circuits using restoring logic.
Because all physical systems ultimately obey quantum mechanics, the classical bit is always an approximation to reality. However, even with the most modern, smallest devices available, it is an excellent one. An interesting question is whether the classical bit approximation will continue to be useful as advances in semiconductor technology allow the size of components to be reduced. Ultimately, as we try to represent or control bits with a small number of atoms or photons, the limiting role of quantum mechanics will become important. It is difficult to predict exactly when this will happen, but some people believe it will be before the year 2015.