Geometry of quantum states: an introduction to quantum entanglement by Ingemar Bengtsson and Karol Zyczkowski

@article{Bengtsson2008GeometryOQ,
  title={Geometry of quantum states: an introduction to quantum entanglement by Ingemar Bengtsson and Karol Zyczkowski},
  author={Ingemar Bengtsson and Karol Życzkowski and Gerard J. Milburn},
  journal={Quantum Inf. Comput.},
  year={2008},
  volume={8},
  pages={860}
}
Preface 1. Convexity, colours and statistics 2. Geometry of probability distributions 3. Much ado about spheres 4. Complex projective spaces 5. Outline of quantum mechanics 6. Coherent states and group actions 7. The stellar representation 8. The space of density matrices 9. Purification of mixed quantum states 10. Quantum operations 11. Duality: maps versus states 12. Density matrices and entropies 13. Distinguishability measures 14. Monotone metrics and measures 15. Quantum entanglement… Expand
Quantum correlations and distinguishability of quantum states
A survey of various concepts in quantum information is given, with a main emphasis on the distinguishability of quantum states and quantum correlations. Covered topics include generalized and leastExpand
From quantum carpets to quantum suprematism?the probability representation of qudit states and hidden correlations
We develop the tomographic-probability picture where quantum states of qudits (spin-j systems, N-level atoms) are described by means of sets of fair classical probability distributions associatedExpand
Bipartite Quantum Entanglement
It was rather soon realized that quantum mechanics permitted the existence of states exhibiting statistical correlations that are unexplainable by classical probability theory (see chapter “ClassicalExpand
An elementary introduction to the geometry of quantum states with pictures
This is a review of the geometry of quantum states using elementary methods and pictures. Quantum states are represented by a convex body, often in high dimensions. In the case of [Formula: see text]Expand
Quantifying quantumness and the quest for Queens of Quantum
We introduce a measure of 'quantumness' for any quantum state in a finite-dimensional Hilbert space, based on the distance between the state and the convex set of classical states. The latter areExpand
Hermite Polynomial Representation of Qubit States in Quantum Suprematism Picture
We consider the Hermite polynomial representation (H-representation) of spin states for qubits and qudits in quantum suprematism picture, where the state geometry is illustrated by Triadas ofExpand
Typical Gaussian Quantum Information
We investigate different geometries and invariant measures on the space of mixed Gaussian quan- tum states. We show that when the global purity of the state is held fixed, these measures coincide andExpand
Properties of a geometric measure for quantum discord
We discuss some properties of the quantum discord based on the geometric measure advanced by Dakic, Vedral, and Brukner [Phys. Rev. Lett. 105, 190502 (2010)], with emphasis on Werner- and MEM-states.Expand
Peculiarities of quantum discord?s geometric measure
Some properties of the quantum discord based on the geometric measure advanced by Dakic et al (2010 Phys. Rev. Lett. 105 190502) are discussed here by recourse to a systematic survey of the two-qubitExpand
A Geometric View on Quantum Tensor Networks
Tensor network states and algorithms play a key role in understanding the structure of complex quantum systems and their entanglement properties. This report is devoted to the problem of theExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 831 REFERENCES
Random quantum operations
Abstract We define a natural ensemble of trace preserving, completely positive quantum maps and present algorithms to generate them at random. Spectral properties of the superoperator Φ associatedExpand
Parametrizing Quantum States and Channels
TLDR
This work describes one parametrization of quantum states and channels and several of its possible applications, including a simple characterization of pure states, an explicit formula for one additive entropic quantity, and an algorithm which finds one Kraus operator representation for a quantum operation without recourse to eigenvalue and eigenvector calculations. Expand
The Theory of Open Quantum Systems
PREFACE ACKNOWLEDGEMENTS PART 1: PROBABILITY IN CLASSICAL AND QUANTUM MECHANICS 1. Classical probability theory and stochastic processes 2. Quantum Probability PART 2: DENSITY MATRIX THEORY 3.Expand
Convex-roof extended negativity as an entanglement measure for bipartite quantum systems
We extend the concept of negativity, a good measure of entanglement for bipartite pure states, to mixed states by means of the convex-roof extension. We show that the measure does not increase underExpand
Quantum computation and quantum information
  • T. Paul
  • Mathematics, Computer Science
  • Mathematical 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 dealExpand
Orbits of quantum states and geometry of Bloch vectors for N-level systems
Physical constraints such as positivity endow the set of quantum states with a rich geometry if the system dimension is greater than 2. To shed some light on the complicated structure of the set ofExpand
Geometry of entangled states
Geometric properties of the set of quantum entangled states are investigated. We propose an explicit method to compute the dimension of local orbits for any mixed state of the general K3M problem andExpand
The Monge metric on the sphere and geometry of quantum states
Topological and geometrical properties of the set of mixed quantum states in the N-dimensional Hilbert space are analysed. Assuming that the corresponding classical dynamics takes place on the sphereExpand
Geometric quantum mechanics
Abstract The manifold of pure quantum states can be regarded as a complex projective space endowed with the unitary-invariant Fubini–Study metric. According to the principles of geometric quantumExpand
Entanglement of Formation of an Arbitrary State of Two Rebits
We consider entanglement for quantum states defined in vector spaces over the real numbers. Such real entanglement is different from entanglement in standard quantum mechanics over the complexExpand
...
1
2
3
4
5
...