Quantum-memory-assisted entropic uncertainty principle, teleportation, and entanglement witness in structured reservoirs

Abstract

We relate the principle of quantum-memory-assisted entropic uncertainty to quantum teleportation and show geometrically that any two-qubit state which lowers the upper bound of this uncertainty relation is useful for teleportation. We also explore the efficiency of this entropic uncertainty principle on witnessing entanglement in a general class of bosonic structured reservoirs. The entanglement regions witnessed by different estimates are determined, which may have no relation with the explicit form of the spectral density of the reservoir for certain special chosen sets of the initial states. DOI: null PACS number(s): 03.67.Mn, 03.65.Ta, 03.65.Yz

Entropic uncertainty relations and their applications

“…Here, δ T is the gap between the left and right hand sides in the uncertainty relation (165). Further connections between quantum correlations and entropic uncertainty relations have been elucidated in the context of non-Markovian dynamics (Karpat et al, 2015), entanglement creation (Coles, 2012a), teleportation (Hu and Fan, 2012), and monogamy (Hu and Fan, 2013a).…”

Entropic Uncertainty in Spin XY Model with Long-Range Interactions

“…More recently, a new type of Heisenberg relation, i.e., the quantum memory assisted entropic uncertainty relation, has been derived [ 12 ] according to the conjecture of Renes and Boileau [ 13 ]. Owing to its versatile applications, entropic uncertainty relation can be potentially applied to quantum key distribution [ 14 , 15 ], probing quantum correlations [ 16 , 17 , 18 , 19 , 20 ], quantum randomness [ 21 ], cryptographic security [ 22 , 23 ], entanglement witness [ 24 , 25 , 26 , 27 , 28 , 29 ], and quantum metrology [ 30 , 31 , 32 ]. It is worth mentioning that the close relation between mixedness and uncertainty has been discussed widely as a concerned topic [ 33 , 34 , 35 , 36 , 37 ].…”

Suppressing measurement uncertainty in an inhomogeneous spin star system

“…Till date, the EUR-QM has been the topic of much work 8 – 48 and many attempts have been made to tighten this inequality 49 – 60 . Moreover, many efforts have been made to generalize the various entropic uncertainty relations to more than two measurements 61 – 67 .…”