期刊
QUANTUM INFORMATION PROCESSING
卷 16, 期 11, 页码 -出版社
SPRINGER
DOI: 10.1007/s11128-017-1726-4
关键词
Quantum coherence; Hilbert-Schmidt distance; Qudit states; Gell-Mann matrices
资金
- Brazilian funding agency: Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq) [441875/2014-9, 303496/2014-2]
- Brazilian funding agency: Coordenacao de Desenvolvimento de Pessoal de Nivel Superior (CAPES) [6531/2014-08]
- Brazilian funding agency: Instituto Nacional de Ciencia e Tecnologia de Informacao Quantica (INCT-IQ) [2008/57856-6]
Using Bloch's parametrization for qudits (d-level quantum systems), we write the Hilbert-Schmidt distance (HSD) between two generic n-qudit states as an Euclidean distance between two vectors of observables mean values in R Pi ns=1ds2-1, where ds is the dimension for qudit s. Then, applying the generalized Gell-Mann's matrices to generate SU(ds), we use that result to obtain the Hilbert-Schmidt quantum coherence (HSC) of n-qudit systems. As examples, we consider in detail one-qubit, one-qutrit, two-qubit, and two copies of one-qubit states. In this last case, the possibility for controlling local and non-local coherences by tuning local populations is studied, and the contrasting behaviors of HSC, l(1)-norm coherence, and relative entropy of coherence in this regard are noticed. We also investigate the decoherent dynamics of these coherence functions under the action of qutrit dephasing and dissipation channels. At last, we analyze the non-monotonicity of HSD under tensor products and report the first instance of a consequence (for coherence quantification) of this kind of property of a quantum distance measure.
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