We study the relation between hidden variables theories and quantum computation.We discuss an inconsistency between a hidden variables theory and controllability of quantum computation.To derive the inconsistency, we use the maximum value of the square of an expected value.We propose a solution of the problem by using new hidden variables theory.Also we discuss an inconsistency between hidden variables theories and the double-slit experiment as the most basic experiment in quantum mechanics.This experiment can be an easy detector to Pauli observable.We cannot accept hidden variables theories to simulate the double-slit experiment in a specific case.Hidden variables theories may not depicture quantum detector.This is a quantum measurement theoretical profound problem.We study the relation between hidden variables theories and quantum computation.We discuss an inconsistency between a hidden variables theory and controllability of quantum computation.To derive the inconsistency, we use the maximum value of the square of an expected value.We propose a solution of the problem by using new hidden variables theory.Also we discuss an inconsistency between hidden variables theories and the double-slit experiment as the most basic experiment in quantum mechanics.This experiment can be an easy detector to Pauli observable.We cannot accept hidden variables theories to simulate the double-slit experiment in a specific case.Hidden variables theories may not depicture quantum detector.This is a quantum measurement theoretical profound problem.

OALibJan 1, 20150 citations

Hidden Variables Revisited

J. M. Jauch, C. Piron

Reviews of Modern PhysicsJan 1, 196812 citations

The hypothesis of “hidden variables” as a unifying principle in physics.

Louis Vervoort

In the debate whether ‘hidden variables’ could exist underneath quantum probabilities, the ‘no hidden-variables’ position is at present favored. In this article I attempt to provide a more equilibrated verdict, by pointing towards the heuristic and explanatory power of the hidden-variables hypothesis, in particular in its deterministic form. I argue that this hypothesis can answer three foundational questions, whereas the opposing thesis (‘no hidden variables’) remains entirely silent for them. These questions are: 1) How to interpret probabilistic correlation ? (a question considered by Kolmogorov “one of the most important problems in the philosophy of the natural sciences”, and first analysed by Reichenbach); 2) How to interpret the Central Limit Theorem ?; and 3) Are there degrees of freedom that could unify quantum field theories and general relativity, and if so, can we (at least qualitatively) specify them ? It appears that only the hidden-variables hypothesis can provide coherent answers to these problems; answers which can be mathematically justified in the deterministic case. This suggests that the hidden-variables hypothesis should be considered a legitimate candidate as a guiding, unifying principle in the foundations of physics.In the debate whether ‘hidden variables’ could exist underneath quantum probabilities, the ‘no hidden-variables’ position is at present favored. In this article I attempt to provide a more equilibrated verdict, by pointing towards the heuristic and explanatory power of the hidden-variables hypothesis, in particular in its deterministic form. I argue that this hypothesis can answer three foundational questions, whereas the opposing thesis (‘no hidden variables’) remains entirely silent for them. These questions are: 1) How to interpret probabilistic correlation ? (a question considered by Kolmogorov “one of the most important problems in the philosophy of the natural sciences”, and first analysed by Reichenbach); 2) How to interpret the Central Limit Theorem ?; and 3) Are there degrees of freedom that could unify quantum field theories and general relativity, and if so, can we (at least qualitatively) specify them ? It appears that only the hidden-variables hypothesis can provide coherent answers to these problems; answers which can be mathematically justified in the deterministic case. This suggests that the hidden-variables hypothesis should be considered a legitimate candidate as a guiding, unifying principle in the foundations of physics.

Jan 3, 20200 citations

Quantum computing and hidden variables

Scott Aaronson

This paper initiates the study of hidden variables from a quantum computing perspective. For us, a hidden-variable theory is simply a way to convert a unitary matrix that maps one quantum state to another into a stochastic matrix that maps the initial probability distribution to the final one in some fixed basis. We list five axioms that we might want such a theory to satisfy and then investigate which of the axioms can be satisfied simultaneously. Toward this end, we propose a new hidden-variable theory based on network flows. In a second part of the paper, we show that if we could examine the entire history of a hidden variable, then we could efficiently solve problems that are believed to be intractable even for quantum computers. In particular, under any hidden-variable theory satisfying a reasonable axiom, we could solve the graph isomorphism problem in polynomial time, and could search an $N$ -item database using $O({N}^{1∕3})$ queries, as opposed to $O({N}^{1∕2})$ queries with Grover's search algorithm. On the other hand, the ${N}^{1∕3}$ bound is optimal, meaning that we could probably not solve $\mathrm{NP}$ -complete problems in polynomial time. We thus obtain the first good example of a model of computation that appears slightly more powerful than the quantum computing model.This paper initiates the study of hidden variables from a quantum computing perspective. For us, a hidden-variable theory is simply a way to convert a unitary matrix that maps one quantum state to another into a stochastic matrix that maps the initial probability distribution to the final one in some fixed basis. We list five axioms that we might want such a theory to satisfy and then investigate which of the axioms can be satisfied simultaneously. Toward this end, we propose a new hidden-variable theory based on network flows. In a second part of the paper, we show that if we could examine the entire history of a hidden variable, then we could efficiently solve problems that are believed to be intractable even for quantum computers. In particular, under any hidden-variable theory satisfying a reasonable axiom, we could solve the graph isomorphism problem in polynomial time, and could search an $N$-item database using $O({N}^{1∕3})$ queries, as opposed to $O({N}^{1∕2})$ queries with Grover's search algorithm. On the other hand, the ${N}^{1∕3}$ bound is optimal, meaning that we could probably not solve $\mathrm{NP}$-complete problems in polynomial time. We thus obtain the first good example of a model of computation that appears slightly more powerful than the quantum computing model.

arXiv:quant-ph/0408035Physical Review AMar 18, 200548 citations

N

-item database using

O({N}^{1∕3})

queries, as opposed to

O({N}^{1∕2})

queries with Grover's search algorithm. On the other hand, the

{N}^{1∕3}

bound is optimal, meaning that we could probably not solve

\mathrm{NP}

-complete problems in polynomial time. We thus obtain the first good example of a model of computation that appears slightly more powerful than the quantum computing model.