Dynamics of the measurement uncertainty in an open system and its controlling

Abstract

The uncertainty principle is one of the most remarkable features of quantum mechanics, originally expressed in terms of the standard deviation of two incompatible observables. Alternatively, it can be modified and written in the form of entropy to eliminate the defect in the form of standard deviation, and can also be generalized by including a memory particle that is entangled with the particle to be measured. Herein we consider a realistic scenario where the particle A to be measured is in an open environment and B as quantum memory is under an environment typically characterized by non-Markovian regimes. Specifically, it shows that the quantum memory and the non-Markovian effect can essentially inhibit the increase of uncertainty, however, the quantum memory-assisted uncertainty will finally inflate inevitably, due to that the quantum correlation of the system will be damaged gradually by the noise from the surrounding environments. To be explicit, we study the dynamic evolution of the entropic uncertainty and correlation in open system where both particles experience the noise channels. Meanwhile, we put forward some effective operation strategies to reduce the magnitude of the measurement uncertainty under the open systems. Furthermore, we explore the applications of the uncertainty relation investigated on entanglement witness and quantum channel capacity. Thus, our investigations might offer an insight into quantum measurement estimation in open systems.

Tripartite entropic uncertainty relation under phase decoherence

“…The great relevance between bipartite QMA-EUR and quantum correlation 19 – 28 encouraged us to include entanglement in our study, by considering the residual entanglement to quantify simultaneous entanglement between all qubits in a multi-qubit system. For a three-qubit system, the residual entanglement can be expressed as: where the negativity of tripartite and bipartite systems can be expressed, respectively, as and , is the trace norm of , represents the partial transpose of with respect to the qubit .…”

“…These new formulations of the uncertainty principle have facilitated the emergence of many potential applications in the field of quantum information, including cryptography 9 , 10 , quantum metrology 11 , 12 , quantum randomness 13 , 14 and entanglement witness 15 – 18 . Much interest has been focused on clarifying how the QMA-EUR evolves in various systems including Heisenberg spin models 19 – 28 , Unruh–DeWitt detector model 29 , 30 , neutrino oscillations 31 and some open quantum systems 21 , 31 – 35 .…”

Dense Coding and Quantum Memory Assisted Entropic Uncertainty Relations in a Two‐Qubit State Influenced by Dipole and Symmetric Cross Interactions

“…[22] In solid-state and open quantum systems, such as Heisenberg models, the connection between EUR-QM and some quantum correlations has been studied. [23][24][25][26][27][28][29] The dynamics and correlations of EUR-QM, entanglement and mixedness for the Heisenberg chain model with with Dzyaloshinskii-Moriya (DM) interaction have been studied. [30] In the presence of a perfectly reflecting plane boundary, the dynamics of EUR-QM for a two-level atom interacted with fluctuating electromagnetic field have been investigated.…”

Measurement Uncertainty and Its Connection to Quantum Coherence in an Inertial Unruh–DeWitt Detector

“…[25][26][27] Additionally, the EUR can yield promising results when considering the effect of the environment. [28][29][30][31][32][33] It is well known that de Sitter space is the foundation of inflationary cosmology and can be approximately considered to reflect the current accelerating universe. [34] Therefore, it is crucial to study the measurement dynamics in de Sitter space in the frame of relativistic quantum information science.…”

“…[ 25–27 ] Additionally, the EUR can yield promising results when considering the effect of the environment. [ 28–33 ]…”