Vahid Jannesary | Searcharxiv

arXiv2024

A class of entanglement witnesses and a realignment-like criterion

We present a multi-parameter family of positive maps between spaces of differing dimensions. This framework facilitates the construction of Entanglement Witnesses (EWs) specifically designed for systems living in $d_1 \times d_2$ dimensions. A sufficient condition for positivity is presented. Interestingly, it is shown that all EWs constructed this way are equivalent to a single realignment-like criterion which for $d_1 \neq d_2$ is in general stronger than the original realignment criterion. We illustrate effectiveness of this criterion considering examples of Positive Partial Transpose (PPT) entangled states in $3 \times 3$ and $3 \times 4$ dimensions.

quant-ph↗

arXiv2021

GHZ states as near-optimal states for reference frame alignment

Let two coordinate systems, in possession of Alice and Bob, be related to each other by an unknown rotation $R\in SO(3)$. Alice is to send identical states $|ψ_0\ra$ to Bob who will make measurements on the received state and will determine the rotation $R$. The task of Bob is to estimate these parameters of the rotation $R$ by the best possible measurements. Based on the Quantum Fisher Information, we show that Greenberger-Horne-Zeilinger (GHZ) states are near optimal states for this task. Compared to the optimal states proposed before, the advantage of $GHZ$ states are that they can be more easily prepared experimentally, and more importantly, we show concrete measurements which will allow Bob to determine the rotation $R$. We also study the robustness of these states in keeping their encoded information, against common sources of noises.

quant-ph↗