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Geometry of quantum states: an introduction to quantum entanglement by Ingemar Bengtsson and Karol Zyczkowski
The goal of this book is to clarify the role of quantum entanglement in the study of convexity, colours and statistics and to show how this role has changed in the history of science.
Geometry of Quantum States
a ) p. 131 The discussion between eqs. (5.14) and (5.15) is incorrect (dA should be made as large as possible!). b ) p. 256 In the figure, the numbers 6) and 7) occur twice. c ) p. 292 At the end of…
ON MUTUALLY UNBIASED BASES
Mutually unbiased bases for quantum degrees of freedom are central to all theoretical investigations and practical exploitations of complementary properties. Much is known about mutually unbiased…
Truncations of random unitary matrices
We analyse properties of non-Hermitian matrices of size M constructed as square submatrices of unitary (orthogonal) random matrices of size N >M , distributed according to the Haar measure. In this…
A Concise Guide to Complex Hadamard Matrices
Basic properties of complex Hadamard matrices are reviewed and a catalogue of inequivalent cases known for the dimensions N = 2, 16, 12, 14 and 16 are presented.
Induced measures in the space of mixed quantum states
We analyse several product measures in the space of mixed quantum states. In particular, we study measures induced by the operation of partial tracing. The natural, rotationally invariant measure on…
Random unitary matrices
This work generates numerically random unitary matrices and shows that the statistical properties of their spectra and eigenvectors confer to the predictions of the random-matrix theory, for both CUE and COE.
Negativity of the Wigner function as an indicator of non-classicality
A measure of non-classicality of quantum states based on the volume of the negative part of the Wigner function is proposed. We analyse this quantity for Fock states, squeezed displaced Fock states…
Scalable noise estimation with random unitary operators
While the scalability of the stochastic protocol makes it most relevant in large Hilbert spaces (when quantum process tomography is infeasible), the method should be immediately useful for evaluating the degree of control that is achievable in any prototype quantum processing device.
Volume of the set of separable states
The question of how many entangled or, respectively, separable states there are in the set of all quantum states is considered. We propose a natural measure in the space of density matrices %…