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Bob hides a ball in one of four drawers. Alice is to locate it. Classically she has to open up to three drawers, quantally just one. The fundamental reason for this quantum speedup is not known. The usual representation of the quantum…
We explain the mechanism of the quantum speed-up - quantum algorithms requiring fewer computation steps than their classical equivalent - for a family of algorithms. Bob chooses a function and gives to Alice the black box that computes it.…
We investigate the reason for the quantum speedup -- quantum algorithms requiring fewer computation steps than their classical counterparts. We extend their representation to the process of setting the problem. The initial measurement…
In classical problem solving, there is of course correlation between the selection of the problem on the part of Bob (the problem setter) and that of the solution on the part of Alice (the problem solver). In quantum problem solving, this…
Bob chooses a function from a set of functions and gives Alice the black box that computes it. Alice is to find a characteristic of the function through function evaluations. In the quantum case, the number of function evaluations can be…
I provide an alternative way of seeing quantum computation. First, I describe an idealized classical problem solving machine that, thanks to a many body interaction, reversibly and nondeterministically produces the solution of the problem…
The usual representation of quantum algorithms, limited to the process of solving the problem, is physically incomplete. We complete it in three steps: (i) extending the representation to the process of setting the problem, (ii)…
Involving only the measurements of commuting observables - the problem-setting and the corresponding solution - quantum algorithms should be subject to classical logic. This would allow flanking their customary quantum description with a…
We consider the reversible processes between two one-to-one correlated measurement outcomes which underly both problem-solving and quantum nonlocality. In the former case the two outcomes are the setting and the solution of the problem, in…
In former work, we showed that a quantum algorithm is the sum over the histories of a classical algorithm that knows in advance 50% of the information about the solution of the problem - each history is a possible way of getting the…
In previous works, we showed that an optimal quantum algorithm can always be seen as a sum over classical histories in each of which the problem solver knows in advance one of the possible halves of the solution she will read in the future…
With reference to a search in a database of size N, Grover states: "What is the reason that one would expect that a quantum mechanical scheme could accomplish the search in O(square root of N) steps? It would be insightful to have a simple…
We consider devices with two inputs and two outputs, Alice and Bob each having access to one input and one output. To such a device we associate time-reverses by exchanging the roles of the inputs and the outputs. We find that there are…
Quantum resources may provide advantage over their classical counterparts. We say this as quantum advantage. Here we consider a single communication task to study different approaches of observing quantum advantage. We say this setting as a…
Quantum retrodiction is a time-symmetric approach to quantum mechanics with applications in a number of important problems. One of the major challenges to its more widespread applicability is the restriction of its symmetric formalism to…
In former work, we showed that a quantum algorithm requires the number of operations (oracle's queries) of a classical algorithm that knows in advance 50% of the information that specifies the solution of the problem. We gave a preliminary…
Suppose Alice wants to perform some computation that could be done quickly on a quantum computer, but she cannot do universal quantum computation. Bob can do universal quantum computation and claims he is willing to help, but Alice wants to…
Quantum algorithms require less operations than classical algorithms. The exact reason of this has not been pinpointed until now. Our explanation is that quantum algorithms know in advance 50% of the solution of the problem they will find…
We show that the sheer existence of a quantum computational speedup logically implies the mutually exclusive or of well-defined causal loops. In each of them, it is as if the problem-solver knew in advance one of the possible halves of the…
It can be argued that the ordinary description of the reversible quantum process between two one-to-one correlated measurement outcomes is incomplete because, by not specifying the direction of causality, it allows causal structures that…