  We explore the collapse of "wavefunction" and the measurement of entanglement
in the superpositions of hyperspace vectors in classical physical
instantaneous-noise-based logic (INBL). We find both similarities with and
major differences from the related properties of quantum systems. Two search
algorithms utilizing the observed features are introduced. For the first one we
assume an unsorted names database set up by Alice that is a superposition
(unknown by Bob) of up to n=2^N strings; those we call names. Bob has access to
the superposition wave and to the 2N reference noises of the INBL system of N
noise bits. For Bob, to decide if a given name x is included in the
superposition, once the search has begun, it takes N switching operations
followed by a single measurement of the superposition wave. Thus the time and
hardware complexity of the search algorithm is O[log(n)] which indicates an
exponential speedup compared to Grover's quantum algorithm in a corresponding
setting. An extra advantage is that the error probability of the search is
zero. Moreover, the scheme can also check the existence of a fraction of a
string, or several separate string fractions embedded in an arbitrarily long,
arbitrary string. In the second algorithm, we expand the above scheme to a
phonebook with n names and s phone numbers. When the names and numbers have the
same bit resolution, once the search has begun, the time and hardware
complexity of this search algorithm is O[log(n)]. In the case of one-to-one
correspondence between names and phone numbers (n=s), the algorithm offers
inverse phonebook search too. The error probability of this search algorithm is
also zero.
