Exploration of entropic uncertainty bound in a symmetric multi-qubit system under noisy channels

Abstract

Considering one of the particles as a quantum memory in a bipartite system can remarkably improve the measurement accuracy for two incompatible observables. Herein, we study quantum-memoryassisted entropic uncertainty bound for an arbitrary two-qubit X-state, and then we get a clear formula as the entropic uncertainty bound. In the following, we examine analytically and numerically the dynamics of entropic uncertainty bound in a symmetric multi-qubit system under four types of noisy channels, i.e. phase-flip, amplitude damping, phase-damping, and depolarizing channels. Our results show that the entropic uncertainty bound dynamics is related to the number of particles and especially the noise channel used. Noteworthy, our remarks reveal that under the amplitude damping channel, the entropic uncertainty bound can be suppressed during the time. It turns out that under an amplitude damping channel, these results can be important in practical goals where the minimum uncertainty is required such as quantum computation. † at all times. The uncertainty principle is one of the important and fundamental concepts in quantum theory. It defines the distinction between the classical and the quantum world. The uncertainty principle has been first introduced by Heisenberg [6]. Originally, he proved that the momentum and location of a particle could not be determined simultaneously with high accuracy. In fact, the accurate measurement of one observable reduces the accuracy of another observable measurement. Up to now, the uncertainty principle has been formulated in different ways. However, the most important and fundamental relation is presented by Schrödinger [7] and Robertson [8]. They claimed that the following relation is satisfied for two arbitrary incompatible observables U and V as RECEIVED

Controllable entropic uncertainty relation in an effective two-level non-Hermitian system

“…One is devoting to developing different forms like the Rényi entropy to improve the lower bound of EUR [16][17][18][19][20]. Another expends effort toward exploiting the effects of various forms of real environmental noises on the dynamics of EUR [21][22][23][24][25][26][27][28][29]. The third is focusing on the tripartite entropybased uncertainty relation with quantum memory [30][31][32][33].…”

Fidelity of quantum states in a correlated dephasing channel

“…The fact that quantum systems cannot be completely detached from their external mediums and face a wide range of disorders is the primary source of interest. These disorders result in a variety of noisy situations, and when they are superimposed on the system phase factor, cause the quantum states to deviate from their original encoded state [39][40][41][42][43]. Therefore, research into such areas can help to overcome the actual causes of quantum mechanical application shortcomings while also increasing the likelihood of relative success.…”

Witnessing criticality in non-Hermitian systems via entropic uncertainty relation

“…In fact, the EUR can be further improved with the assistance of a quantum memory, so that the outcomes of two incompatible measurements can be predicted precisely by an observer with access to the quantum memory if the initial states are maximally entangled [5,6]. At present, the EUR has received a great deal of attention [7][8][9][10][11][12][13][14][15][16][17][18] due to potential applications in quantum information processing tasks such as quantum entanglement witnessing [19][20][21][22], and quantum key distribution [23,24].…”