# Quantifying entanglement of a two-qubit system via measurable and invariant moments of its partially transposed density matrix

@article{Bartkiewicz2015QuantifyingEO,
title={Quantifying entanglement of a two-qubit system via measurable and invariant moments of its partially transposed density matrix},
author={Karol Bartkiewicz and Jivr'i Beran and Karel Lemr and Michal Norek and Adam Miranowicz},
journal={Physical Review A},
year={2015},
volume={91},
pages={022323}
}
• Published 28 November 2014
• Physics
• Physical Review A
We describe a direct method to determine the negativity of an arbitrary two-qubit state in experiments. The method is derived by analyzing the relation between the purity, negativity, and a universal entanglement witness for two-qubit entanglement. We show how the negativity of a two-qubit state can be calculated from just three experimentally accessible moments of the partially transposed density matrix of a two-photon state. Moreover, we show that the negativity can be given as a function of…
18 Citations

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## References

SHOWING 1-10 OF 94 REFERENCES
Minimax optimization of entanglement witness operator for the quantification of three-qubit mixed-state entanglement
• Physics
• 2012
We develop a numerical approach for quantifying entanglement in mixed quantum states by convex-roof entanglement measures, based on the optimal entanglement witness operator and the minimax
Ordering two-qubit states with concurrence and negativity
• Physics
• 2004
We study the ordering of two-qubit states with respect to the degree of bipartite entanglement using the Wootters concurrence - a measure of the entanglement of formation - and the negativity - a
Method for universal detection of two-photon polarization entanglement
• Physics
• 2015
Detecting and quantifying quantum entanglement of a given unknown state poses problems that are fundamentally important for quantum information processing. Surprisingly, no direct (i.e., without
Two-qubit mixed states more entangled than pure states: Comparison of the relative entropy of entanglement for a given nonlocality
• Physics
• 2013
Amplitude damping changes entangled pure states into usually less-entangled mixed states. We show, however, that even local amplitude damping of one or two qubits can result in mixed states more
Comparison of the relative entropy of entanglement and negativity
• Physics
• 2008
It is well known that for two qubits the upper bounds of the relative entropy of entanglement (REE) for a given concurrence as well as the negativity for a given concurrence are reached by pure
Nonlocal Properties of Two-Qubit Gates and Mixed States, and the Optimization of Quantum Computations
It is proved that one of two mixed states can be transformed into the other by single-qubit operations if and only if these states have equal values of all 18 invariants, which provides a complete description of nonlocal properties.
Universal observable detecting all two-qubit entanglement and determinant based separability tests
• Physics
• 2008
We construct a single observable measurement of which mean value on four copies of an {\it unknown} two-qubit state is sufficient for unambiguous decision whether the state is separable or entangled.
Experimental determination of entanglement with a single measurement
• Physics
Nature
• 2006
A linear optics experiment is reported in which a pure-state entanglement measure is directly observed, namely concurrence, which is measured with a single, local measurement on just one of the photons.
Quantifying entanglement with witness operators
An infinite family of new entanglement quantifiers is introduced, having as its limits the best separable approximation measure and the generalized robustness, and provides sharper bounds to d_(min) and E_D than the negativity in most the states.