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Paper 1

Entanglement of approximate quantum strategies in XOR games

Dimiter Ostrev, Thomas Vidick

Year

2016

Journal

arXiv preprint

DOI

arXiv:1609.01652

arXiv

1609.01652

We show that for any $\varepsilon>0$ there is an XOR game $G=G(\varepsilon)$ with $Θ(\varepsilon^{-1/5})$ inputs for one player and $Θ(\varepsilon^{-2/5})$ inputs for the other player such that $Ω(\varepsilon^{-1/5})$ ebits are required for any strategy achieving bias that is at least a multiplicative factor $(1-\varepsilon)$ from optimal. This gives an exponential improvement in both the number of inputs or outputs and the noise tolerance of any previously-known self-test for highly entangled states. Up to the exponent $-1/5$ the scaling of our bound with $\varepsilon$ is tight: for any XOR game there is an $\varepsilon$-optimal strategy using $\lceil \varepsilon^{-1} \rceil$ ebits, irrespective of the number of questions in the game.

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Paper 2

Genuine Multipartite Entanglement in the $3$-Photon Decay of Positronium

B. C. Hiesmayr, P. Moskal

Year

2017

Journal

arXiv preprint

DOI

arXiv:1706.06505

arXiv

1706.06505

The electron-positron annihilation into two photons is a standard technology in medicine to observe e.g. metabolic processes in human bodies. A new tomograph will provide the possibility to observe not only direct $e^+ e^-$ annihilations but also the $3$ photons from the decay of ortho-positronium atoms formed in the body. We show in this contribution that the three-photon state with respect to polarisation degrees of freedom depends on the angles between the photons and exhibits various specific entanglement features. In particular genuine multipartite entanglement, a type of entanglement involving all degrees of freedoms, is subsistent if the positronium was in a definite spin eigenstate. Remarkably, when all spin eigenstates are mixed equally, entanglement --and even stronger genuine multipartite entanglement-- survives. Due to a "\textit{symmetrization}" process, however, $Dicke$-type of entanglement remains whereas $GHZ$-type of entanglement vanishes. The survival of particular entanglement properties in the mixing scenario may make it possible to extract quantum information in form of distinct entanglement features, e.g., from metabolic processes in human bodies.

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