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Tensor of coherences parameterization of multiqubit density operators for entanglement characterization
 

Summary: Tensor of coherences parameterization of multiqubit density operators for
entanglement characterization
Claudio Alta ni
SISSA-ISAS
International School for Advanced Studies
via Beirut 2-4, 34014 Trieste, Italy 
For multiqubit densities, the tensor of coherences (or Stokes tensor) is a real parameterization
obtained by the juxtaposition of the aĆne Bloch vectors of each qubit. While it maintains the
tensorial structure of the underlying space, it highlights the pattern of correlations, both classical
and quantum, between the subsystems and, due to the aĆne parameterization, it contains in its
components all reduced densities of all orders. The main purpose of our use of this formalism is to
deal with entanglement. For example, the detection of bipartite entanglement is straightforward,
as it is the synthesis of densities having positive partial transposes between desired qubits. In
addition, nding explicit mixtures for families of separable states becomes a feasible issue for few
qubit symmetric densities (we compute it for Werner states) and, more important, it provides some
insight on the possible origin of entanglement for such densities.
PACS numbers: 03.67.Mn, 03.67.-a, 03.65.Ud
I. INTRODUCTION
The main purpose of this work is to discuss a parameterization of a multiqubit (pure or mixed) density operator and
to show its usefulness in dealing with classical and quantum correlations. The principle behind the parameterization

  

Source: Altafini, Claudio - Functional Analysis Sector, Scuola Internazionale Superiore di Studi Avanzati (SISSA)

 

Collections: Engineering; Mathematics