Quantum Games and Quantum Strategies
We investigate the quantization of non-zero sum games. For the particular case of the Prisoners' Dilemma we show that this game ceases to pose a dilemma if quantum strategies are allowed for. We also…
Multiparty entanglement in graph states
This work characterize and quantify the genuine multiparticle entanglement of such graph states in terms of the Schmidt measure, to which it provides upper and lower bounds in graph theoretical terms.
Quantum state tomography via compressed sensing.
- D. Gross, Yi-Kai Liu, S. Flammia, Stephen Becker, J. Eisert
- PhysicsPhysical Review Letters
- 18 September 2009
These methods are specialized for quantum states that are fairly pure, and they offer a significant performance improvement on large quantum systems, and are able to reconstruct an unknown density matrix of dimension d and rank r using O(rdlog²d) measurement settings, compared to standard methods that require d² settings.
Entanglement in Graph States and its Applications
- M. Hein, W. Dur, J. Eisert, R. Raussendorf, M. V. D. Nest, H. Briegel
- Computer Science, Physics
- 11 February 2006
This review gives a tutorial introduction into the theory of graph states, and discusses the basic notions and properties of these states, including aspects of non-locality, bi-partite and multi- partite entanglement and its classification in terms of the Schmidt measure.
Colloquium: Area laws for the entanglement entropy
Physical interactions in quantum many-body systems are typically local: Individual constituents interact mainly with their few nearest neighbors. This locality of interactions is inherited by a decay…
Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
This work reviews selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics and elucidate the role played by key concepts, such as Lieb-Robinson bounds, entanglement growth, typicality arguments, quantum maximum entropy principles and the generalised Gibbs ensembles.
Most quantum States are too entangled to be useful as computational resources.
It is shown that quantum states can be too entangled to be useful for the purpose of computation, in that high values of the geometric measure of entanglement preclude states from offering a universal quantum computational speedup.
Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators
This paper shows how to certify the accuracy of a low-rank estimate using direct fidelity estimation, and describes a method for compressed quantum process tomography that works for processes with small Kraus rank and requires only Pauli eigenstate preparations and Pauli measurements.
Evenly distributed unitaries: On the structure of unitary designs
We clarify the mathematical structure underlying unitary t-designs. These are sets of unitary matrices, evenly distributed in the sense that the average of any tth order polynomial over the design…
Optimal local implementation of nonlocal quantum gates
It is shown that one bit of classical communication in eachdirection is both necessary and sufficient for the nonlocal implementation of the quantum CNOT, while in general two bits in each direction is required for the implementation of a general two-bit quantum gate.