QUANTUM KOLMOGOROV COMPLEXITY AND ITS APPLICATIONS
By C. Mora, Hans J. Briegel, Barbara Kraus. 2006
42 citations recorded by the source corpus.
Kolmogorov complexity is a measure of the information contained in a binary string. We investigate here the notion of quantum Kolmogorov complexity, a measure of the information required to describe a quantum state. We show that for any definition of quantum Kolmogorov complexity measuring the number of classical bits required to describe a pure quantum state, there exists a pure n-qubit state which requires exponentially many bits of description. This is shown by relating the classical communication complexity to the quantum Kolmogorov complexity. Furthermore, we give some examples of how quantum Kolmogorov complexity can be applied to prove results in different fields, such as quantum computation and thermodynamics, and we generalize it to the case of mixed quantum states.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Computational Theory and Mathematics
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In Artificial Intelligence
- B. Schoelkopf
- Rafael Chaves
- Dominik Janzing
- Bernhard Schölkopf
- Jan Peters
- Kun Zhang
- David Lopez-Paz
- Joris M. Mooij
In Atomic and Molecular Physics, and Optics
In Computational Theory and Mathematics
- B. Schoelkopf
- Rafael Chaves
- Dominik Janzing
- Bernhard Schölkopf
- Kun Zhang
- Jan Peters
- Jilles Vreeken
- Kailash Budhathoki
Citations in the corpus
- Algorithmic independence of initial condition and dynamical law in thermodynamics and causal inference (2015, methodology): “Moreover, quantum thermodynamics [33] should rather rely on quantum Kolmogorov complexity [34].”