# Quantum computing and hidden variables

@article{Aaronson2005QuantumCA, title={Quantum computing and hidden variables}, author={Scott Aaronson}, journal={Physical Review A}, year={2005}, volume={71}, pages={032325} }

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…

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## References

SHOWING 1-10 OF 80 REFERENCES

### Quantum Computing and Hidden Variables II: The Complexity of Sampling Histories

- Computer Science
- 2004

If the authors could examine the entire history of a hidden variable, then they could efficiently solve problems that are believed to be intractable even for quantum computers, and obtain the first good example of a model of computation that appears slightly more powerful than the quantum computing model.

### A SUGGESTED INTERPRETATION OF THE QUANTUM THEORY IN TERMS OF "HIDDEN" VARIABLES. II

- Physics
- 1952

In this paper, we shall show how the theory of measurements is to be understood from the point of view of a physical interpretation of the quantum theory in terms of hidden variables developed in a…

### Choice of Consistent Family, and Quantum Incompatibility

- Physics
- 1998

In consistent-history quantum theory, a description of the time development of a quantum system requires choosing a framework or consistent family, and then calculating probabilities for the…

### Quantum Mechanics in the Light of Quantum Cosmology

- Physics
- 1989

We sketch a quantum mechanical framework for the universe as a whole. Within that framework we propose a program for describing the ultimate origin in quantum cosmology of the quasiclassical domain…

### Quantum computation and quantum information

- PhysicsMathematical Structures in Computer Science
- 2007

This special issue of Mathematical Structures in Computer Science contains several contributions related to the modern field of Quantum Information and Quantum Computing. The first two papers deal…

### Modal interpretation of quantum mechanics, measurements, and macroscopic behavior.

- PhysicsPhysical review. A, Atomic, molecular, and optical physics
- 1994

The modal interpretation explained here construes the mathematical formalism of quantum mechanics in terms of physical properties (``be-ables,'' ``existents'') in such a way that the property…

### Book-Review - the Undivided Universe - an Ontological Interpretation of Quantum Theory

- Physics
- 1993

In the The Undivided Universe, David Bohn and Basil Hiley present a radically different approach to quantum theory. They develop an interpretation of quantum mechanics which gives a clear, intuitive…

### The Undivided Universe: An ontological interpretation of Quantum Theory

- Philosophy
- 1994

Systematic Theology by Louis BerkhofSaint Bonaventure (Stanford Encyclopedia of Philosophy)Bohmian Mechanics (Stanford Encyclopedia of Philosophy)Dogmatic Constitution on the Church (Lumen…

### Complexity, Entropy and the Physics of Information

- Education
- 1990

That's it, a book to wait for in this month. Even you have wanted for long time for releasing this book complexity entropy and the physics of information; you may not be able to get in some stress.…

### Lorentz-Invariance in Modal Interpretations

- Mathematics
- 1998

Modal interpretations are hidden-variables theories, specifying at each time a set of possible properties of a system (represented by projection operators) and a probability measure over that set. We…