# 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} }

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

Estimation of entanglement negativity of a two-qubit quantum system with two measurements

- PhysicsEPL (Europhysics Letters)
- 2018

Numerous work had been done to quantify the entanglement of a two-qubit quantum state, but it can be seen that previous works were based on joint measurements on two copies or more than two copies of…

Direct method for measuring and witnessing quantum entanglement of arbitrary two-qubit states through Hong-Ou-Mandel interference

- Physics
- 2017

We describe a direct method for experimental determination of the negativity of an arbitrary two-qubit state with 11 measurements performed on multiple copies of the two-qubit system. Our method is…

Two methods for measuring Bell nonlocality via local unitary invariants of two-qubit systems in Hong-Ou-Mandel interferometers

- Physics
- 2018

We describe a direct method to experimentally determine local two-qubit invariants by performing interferometric measurements on multiple copies of a given two-qubit state. We use this framework to…

Bell nonlocality and fully entangled fraction measured in an entanglement-swapping device without quantum state tomography

- Physics
- 2017

We demonstrate an efficient experimental procedure based on entanglement swapping to determine the Bell nonlocality measure of Horodecki et al. [Phys. Lett. A 200, 340 (1995)] and the fully-entangled…

Optimal observables to determine entanglement of a two qubit state

- Physics
- 2014

AbstractExperimental determination of entanglement is important not only to characterize the
state and use it in quantum information, but also in understanding complicated phenomena
such as phase…

Statistical mixtures of states can be more quantum than their superpositions: Comparison of nonclassicality measures for single-qubit states

- Physics
- 2015

A bosonic state is commonly considered nonclassical (or quantum) if its Glauber-Sudarshan $P$ function is not a classical probability density, which implies that only coherent states and their…

Quantifying geometric measure of entanglement by mean value of spin and spin correlations with application to physical systems

- Physics
- 2017

Abstract
We quantify the geometric measure of entanglement in terms of mean values of observables of entangled system. For pure states we find the relation of geometric measure of entanglement with…

Increasing relative nonclassicality quantified by standard entanglement potentials by dissipation and unbalanced beam splitting

- Physics
- 2015

If a single-mode nonclassical light is combined with the vacuum on a beam splitter, then the output state is entangled. As proposed in [Phys. Rev. Lett. 94, 173602 (2005)], by measuring this…

Nonclassicality quantified by standard entanglement potentials can be increased by dissipation and unbalanced beam splitting

- Physics
- 2015

If a single-mode nonclassical light is combined with the vacuum on a beam splitter, then the output state is entangled. As proposed in [Phys. Rev. Lett. 94, 173602 (2005)], by measuring the…

Experimental measurement of a nonlinear entanglement witness by hyperentangling two-qubit states

- PhysicsPhysical Review A
- 2018

We demonstrate that non-linear entanglement witnesses can be made particularly useful for entanglement detection in hyper-entangled or multilevel states. We test this idea experimentally on the…

## 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

- PhysicsQuantum Inf. Process.
- 2002

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

- PhysicsNature
- 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

- Computer Science
- 2005

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.