Restricted numerical range: a versatile tool in the theory of quantum information

Details Restricted numerical range: a versatile tool in the theory of quantum information Restricted numerical range: a versatile tool in the theory of quantum information

2009-05-22

arxiv.org/abs/0905.3646v2

J. Math. Phys. 51, 102204 (2010)

Physics

Quantum Physics

39 pages, 7 figures, Original preprint "Local numerical range: a versatile tool in the theory of quantum information" was broa

Scientific paper

10.1063/1.3496901

Numerical range of a Hermitian operator X is defined as the set of all possible expectation values of this observable among a normalized quantum state. We analyze a modification of this definition in which the expectation value is taken among a certain subset of the set of all quantum states. One considers for instance the set of real states, the set of product states, separable states, or the set of maximally entangled states. We show exemplary applications of these algebraic tools in the theory of quantum information: analysis of k-positive maps and entanglement witnesses, as well as study of the minimal output entropy of a quantum channel. Product numerical range of a unitary operator is used to solve the problem of local distinguishability of a family of two unitary gates.

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