5 research outputs found
Detection of entanglement with few local measurements
We introduce a general method for the experimental detection of entanglement
by performing only few local measurements, assuming some prior knowledge of the
density matrix. The idea is based on the minimal decomposition of witness
operators into a pseudo-mixture of local operators. We discuss an
experimentally relevant case of two qubits, and show an example how bound
entanglement can be detected with few local measurements.Comment: 5 pages + 1 figur
A measurable entanglement criterion for two qubits
We propose a directly measurable criterion for the entanglement of two
qubits. We compare the criterion with other criteria, and we find that for pure
states, and some mixed states, it coincides with the state's concurrency. The
measure can be obtained with a Bell state analyser and the ability to make
general local unitary transformations. However, the procedure fails to measure
the entanglement of a general mixed two-qubit state.Comment: 5 page
Entanglement of a Single Spin-1 Object: An Example of Ubiquitous Entanglement
Using a single spin-1 object as an example, we discuss a recent approach to
quantum entanglement. The key idea of the approach consists in presetting of
basic observables in the very definition of quantum system. Specification of
basic observables defines the dynamic symmetry of the system. Entangled states
of the system are then interpreted as states with maximal amount of uncertainty
of all basic observables. The approach gives purely physical picture of
entanglement. In particular, it separates principle physical properties of
entanglement from inessential. Within the model example under consideration, we
show relativity of entanglement with respect to dynamic symmetry and argue
existence of single-particle entanglement. A number of physical examples are
considered.Comment: 12 pages, 2 figure : title has been changed, paper is re-organized,
new section "Violation of Bell-type condition by single spin-1" is adde
Measurement of qubits
We describe in detail the theory underpinning the measurement of density matrices of a pair of quantum two-level systems (qubits). Our particular emphasis is on qubits realized by the two polarization degrees of freedom of a pair of entangled photons generated in a down-conversion experiment; however, the discussion applies in general, regardless of the actual physical realization. Two techniques are discussed, namely, a tomographic reconstruction (in which the density matrix is linearly related to a set of measured quantities) and a maximum likelihood technique which requires numerical optimization (but has the advantage of producing density matrices that are always non-negative definite). In addition, a detailed error analysis is presented, allowing errors in quantities derived from the density matrix, such as the entropy or entanglement of formation, to be estimated. Examples based on down-conversion experiments are used to illustrate our results