The quantum correlation between the selection of the problem and that of the solution sheds light on the mechanism of the quantum speed up

Abstract

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 correlation becomes quantum. This means that Alice contributes to selecting 50% of the information that specifies the problem. As the solution is a function of the problem, this gives to Alice advanced knowledge of 50% of the information that specifies the solution. Both the quadratic and exponential speed ups are explained by the fact that quantum algorithms start from this advanced knowledge.

Earlier version submitted to QIP 2011. Further clarified section 1, "Outline of the argument", submitted to Phys Rev A, 16 pages

References in corpus (3)

• Most quantum states are too entangled to be useful as computational resources
• Quantum algorithms know in advance 50% of the solution they will find in the future
• The 50% advanced information rule of the quantum algorithms

Cited by in corpus (8)

• Implementation of classical communication in a quantum world
• Completing the physical representation of quantum algorithms provides a quantitative explanation of their computational speedup
• A relational time-symmetric framework for analyzing the quantum computational speedup
• Highlighting the mechanism of the quantum speedup by time-symmetric and relational quantum mechanics
• Unobservable causal loops as a way to explain both the quantum computational speedup and quantum nonlocality
• Back to the seminal Deutsch algorithm
• Completing the physical representation of quantum algorithms provides a retrocausal explanation of their speedup
• An exact relation between number of black box computations required to solve an oracle problem quantumly and quantum retrocausality