Entanglement in four qubit states: Polynomial invariant of degree 2, genuine multipartite concurrence and one-tangle

Jafarizadeh, M. A.; Yahyavi, M.; Karimi, N.; Heshmati, A.

doi:10.1016/j.physleta.2018.11.037

Cited by 7 publications

(3 citation statements)

References 23 publications

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“…The direct measurement of concurrence in a two-qubit pure state has been detailed in [21], employing a practical protocol adaptable to a two-cavity setup in microwave 3D cavity QED and in trapped ion systems. Additionally, a defined entanglement measure for even-N qubits quantum states is presented in [22], denoted as the polynomial invariant of degree 2 (PID-2). In [23], a comprehensive protocol for measuring PID-2 in any arbitrary even-N qubit pure state is outlined, utilizing quantum circuits to gauge the entanglement.…”

Section: Introductionmentioning

confidence: 99%

Implementation and measurement of quantum entanglement using IBM quantum platforms

Karimi,

Navid Elyasi,

Yahyavi

2024

Phys. Scr.

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The ease of simulating quantum physics using numerical tools is attributed to the linearity of quantum physics algebra.Conversely, as the size of quantum systems grows, the demand for classical resources in simulation escalates exponentially.Consequently, ensuring sufficient accuracy is crucial for optimizing simulation tool performance. Quantum entanglement,a pivotal phenomenon in quantum information underpinning various communication protocols, quantum algorithms, andcryptography, is profoundly influenced by system size, leading to an exponential increase in the required classical resources asthe quantum system scales up. In this context, IBM’s quantum platforms stand as essential simulation tools for achieving highlyaccurate measurements of entanglement. This article leverages the Qiskit package to delve into the exploration of one suchmeasurement aspect of entanglement, namely, concurrence, within pure two-qubit quantum systems.

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Section: Introductionmentioning

confidence: 99%

Implementation and measurement of quantum entanglement using IBM quantum platforms

Karimi,

Navid Elyasi,

Yahyavi

2024

Phys. Scr.

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“…Later 3-tangle was generalized for multipartite cases [17,18]. The approach was then extended to the class of mixed states [19,20]. Tangle is useful to other aspects of quantum information as well.…”

Section: Introductionmentioning

confidence: 99%

Quantifying parallelism of vectors is the quantification of distributedn-party entanglement

Banerjee¹,

Panigrahi²

2020

J. Phys. A: Math. Theor.

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The three way distributive entanglement is shown to be related to the parallelism of vectors. Using a measurement based approach we form a set of 2-dimensional vectors, representing the post measurement states of one of the parties. These vectors originate at the same point and have an angular distance between them. The area spanned by a pair of such vectors is a measure of the entanglement of formation. This leads to a geometrical manifestation of the 3-tangle in 2-dimensions, from an inequality in area which generalizes for n-qubits to reveal that the n-tangle also has a planar structure. Quantifying the genuine n-party entanglement in every 1|(n − 1) bi-partition, we show that the genuine n-way entanglement does not manifest in n-tangle. A new quantity geometrically similar to 3-tangle is then introduced that represent the genuine n-way entanglement. Extending our formalism to 3-qutrits, we show that the non locality without entanglement arises from a condition under which the post measurement state vectors of a separable state show parallelism. A connection to non trivial sum uncertainty relation analogous to Maccone and Pati uncertainty relation (Maccone and Pati 2014 Phys. Rev. Lett. 113 260401) is then shown using decomposition of post measurement state vectors along parallel and perpendicular direction of the pre-measurement state vectors.

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“…presented three schemes for directly measuring the concurrence of two-photon polarization-entangled pure and mixed states. In the case of measurability of the entanglement measures for the quantum systems with more than two-qubit, in 19 we obtained the measurability of the polynomial invariant of degree 2 for even- N qubit pure states 20 . Given these papers and the importance of the measurability of the entanglement measures, has led us to investigate the measurability of one of the entanglement measures, so called, D-Concurrence in paper.…”

Section: Introductionmentioning

confidence: 99%

Measurability of D-concurrence

Karimi

Heshmati

Yahyavi

et al. 2019

Sci Rep

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An effective approach to quantify entanglement of any bipartite systems is D-concurrence, which is important in quantum information science. In this paper, we present a direct method for experimental determination of the D-concurrence of an arbitrary bipartite pure state. To do this, we show that measurement of the D-concurrence of bipartite pure state can be conversed into the measurement performed on some observables so called generalized Gell-Mann operators. We first introduce the concept of D-concurrence for a bipartite system. Then we explain the method of measuring this entanglement measure for the pure state. Finally, for clarify of the subject, we give an example consisting of two parties A and B with dimensions 3.

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Entanglement in four qubit states: Polynomial invariant of degree 2, genuine multipartite concurrence and one-tangle

Cited by 7 publications

References 23 publications

Implementation and measurement of quantum entanglement using IBM quantum platforms

Implementation and measurement of quantum entanglement using IBM quantum platforms

Quantifying parallelism of vectors is the quantification of distributedn-party entanglement

Measurability of D-concurrence

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