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The process is primarily motivated by the principle of implicit measurement.<ref>Nielsen, Michael; Chuang, Isaac. "Quantum Computation and Quantum Information"</ref>, which states that discarding a register during computation is physically equivalent to measuring it. Failure to uncompute garbage registers can have unintentional consequences. For example, if we take the state <math></math> <math>
\frac{1}{\sqrt 2}(|0\rangle|g_0\rangle + |1\rangle|g_1\rangle)
</math> where <math>g_0</math> and <math>g_1</math> are garbage registers. Then, if we do not apply any further operations to those registers, according to the principle of implicit measurement, the entangled state has been measured, resulting in a collapse to either <math>|0\rangle|g_0\rangle</math> or <math>|1\rangle|g_1\rangle</math> with probability <math>\frac{1}{2}</math>
==References==
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