Tightening the tripartite quantum-memory-assisted entropic uncertainty relation

Quantum discord and quantum uncertainty are two important features of the quantum world. In this work, the relation between entropic uncertainty relation and the shareability of quantum discord is studied. By using tripartite quantum-memory-assisted entropic uncertainty relation, an upper bound for the shareability of quantum discord among different parties of a composite system is obtained. It is also shown that, for a specific class of tripartite states, the obtained relation could be expressed as monogamy of quantum discord. Moreover, it is illustrated that the relation could be generalized and an upper bound for the shareability of quantum discord for multipartite states is derived.

Section: Introductionmentioning

confidence: 99%

The tripartite quantum-memory-assisted entropic uncertainty relation and upper bound on shareability of quantum discord

Dolatkhah

Mohammadi

Haseli

2022

“…( 5 ), and Shannon entropy H ( X ) ( H ( Z )) of X ( Z ) measurement. In the same context, Dolatkhah et al 38 have proposed another lower bound of the tripartite uncertainty that is tighter than that suggested by Ming et al ( 8 ) for some states . Their formula reads in which …”

Section: Introductionmentioning

confidence: 85%

Tripartite entropic uncertainty relation under phase decoherence

Abdelghany

Mohamed

Tammam

et al. 2021

We formulate the tripartite entropic uncertainty relation and predict its lower bound in a three-qubit Heisenberg XXZ spin chain when measuring an arbitrary pair of incompatible observables on one qubit while the other two are served as quantum memories. Our study reveals that the entanglement between the nearest neighbors plays an important role in reducing the uncertainty in measurement outcomes. In addition we have shown that the Dolatkhah’s lower bound (Phys Rev A 102(5):052227, 2020) is tighter than that of Ming (Phys Rev A 102(01):012206, 2020) and their dynamics under phase decoherence depends on the choice of the observable pair. In the absence of phase decoherence, Ming’s lower bound is time-invariant regardless the chosen observable pair, while Dolatkhah’s lower bound is perfectly identical with the tripartite uncertainty with a specific choice of pair.

“…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 .…”

Section: Introductionmentioning

confidence: 99%

Suppressing measurement uncertainty in an inhomogeneous spin star system

Haddadi

Ghominejad

Akhound

et al. 2021

The uncertainty principle is known as a foundational element of quantum theory, providing a striking lower bound to quantify our prediction for the measured result of two incompatible observables. In this work, we study the thermal evolution of the entropic uncertainty bound in the presence of quantum memory for an inhomogeneous four-qubit spin-star system that is in the thermal regime. Intriguingly, our results show that the entropic uncertainty bound can be controlled and suppressed by adjusting the inhomogeneity parameter of the system.