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Results in Physics

Measurement uncertainty and dense coding in a two-qubit system: Combined effects of bosonic reservoir and dipole–dipole interaction

Saeed Haddadi, Ming‐Liang Hu, Youssef Khedif, Hazhir Dolatkhah, Mohammad Reza Pourkarimi, Mohammed Daoud A

Published Dec 3, 2021• 36 citations
Publisher

Abstract

The uncertainty principle imposes a limitation on the measurement accuracy of two incompatible observables and has potential applications in quantum information science. We explore the bipartite entropic uncertainty relation and dense coding for two qubits coupled via dipole–dipole interaction and subject to a bosonic reservoir. It is shown that there exists a trade-off between the uncertainty bound and the dense coding capacity which results in their opposite dynamical behaviors. Moreover, the behaviors of the measurement uncertainty and the dense coding capacity rely crucially on the initial system–reservoir correlation, the strength of the dipole–dipole interaction, and the degree of non-Markovianity, and one can reduce the measurement uncertainty and enhance the dense coding capacity by tuning these parameters to appropriate values.

DOI
10.1016/j.rinp.2021.105041

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The uncertainty principle imposes a limitation on the measurement accuracy of two incompatible observables and has potential applications in quantum information science. We explore the bipartite entropic uncertainty relation and dense coding for two qubits coupled via dipole–dipole interaction and subject to a bosonic reservoir. It is shown that there exists a trade-off between the uncertainty bound and the dense coding capacity which results in their opposite dynamical behaviors. Moreover, the behaviors of the measurement uncertainty and the dense coding capacity rely crucially on the initial system–reservoir correlation, the strength of the dipole–dipole interaction, and the degree of non-Markovianity, and one can reduce the measurement uncertainty and enhance the dense coding capacity by tuning these parameters to appropriate values.
Abstract The measurement precision for two incompatible observables in a typical quantum system can be improved by the aid of one particle as a quantum memory. In this work, we study the entropic uncertainty relation in the presence of quantum memory (EUR-QM) and dense coding capacity (DCC) for arbitrary two-qubit X-states, and then we obtain an explicit relationship between the lower bound of the uncertainty and DCC. As an example, we examine the thermal EUR-QM as well as DCC in two kinds of two-qubit spin squeezing models (one-axis twisting model and two-axis counter-twisting model) under an external magnetic field. In the following, we relate EUR-QM to DCC and show analytically that there is an anti-correlated relation between them, and especially in the ground state. Our results show that for both the models, the entropic uncertainty and its bound can be decreased by reinforcing the spin squeezing parameters or decreasing the temperature of the system. Notably, we reveal that the valid dense coding cannot carry out in the one-axis twisting model, nevertheless, if we properly choose the Hamiltonian parameters, the two-axis counter-twisting model not only carries out the valid dense coding but also the optimal dense coding surely can be achieved. Thereby, our observations might offer new insights into quantum measurement precision and the optimal dense coding for the regimes of various solid-state systems.
The uncertainty relation is a fundamental limit in quantum mechanics and is of great importance to quantum information processing as it relates to quantum precision measurement. Due to interactions with the surrounding environment, a quantum system will unavoidably suffer from decoherence. Here, we investigate the dynamic behaviors of the entropic uncertainty relation of an atom-cavity interacting system under a bosonic reservoir during the crossover between Markovian and non-Markovian regimes. Specifically, we explore the dynamic behavior of the entropic uncertainty relation for a pair of incompatible observables under the reservoir-induced atomic decay effect both with and without quantum memory. We find that the uncertainty dramatically depends on both the atom-cavity and the cavity-reservoir interactions, as well as the correlation time, τ, of the structured reservoir. Furthermore, we verify that the uncertainty is anti-correlated with the purity of the state of the observed qubit-system. We also propose a remarkably simple and efficient way to reduce the uncertainty by utilizing quantum weak measurement reversal. Therefore our work offers a new insight into the uncertainty dynamics for multi-component measurements within an open system, and is thus important for quantum precision measurements.
Abstract Optimal dense coding and entropic uncertainty relation of quantum memory (EUR‐QM) of the two‐qubit Heisenberg chain model influenced by atomic dipole and Kaplan–Shekhtman–Entin–Wohlman–Aharony interactions are studied. The temporal evolution of the two functions at the phase decoherence environment with the Werner state as the initial state is discussed. The results imply that the dense coding and EUR‐QM have a contrary relationship, and an increase in the phase decoherence rate reduces the behavior of the two functions. The growth in coupling dipole interaction plays a role in oscillating and increasing the minimum bounds of the dense coding capacity. On the other hand, the effect of a thermal bath on the two functions at finite temperatures is investigated. The coding capacity suffers from sudden death as the temperature increases. The possibility of restraining the sudden death induced by the temperature may be enhanced by increasing the strength of the symmetric cross interaction. As the coupling of dipole increases, the EUR‐QM decreases while the coding capacity rises to its maximum value.
The entropic uncertainty principle imposes a limit on how precisely two incompatible observables can be measured, which can be reduced when quantum memory is involved. We theoretically investigate the dynamics of the quantum-memory-assisted entropic uncertainty relation when either quantum memory alone or both the measured particle and the quantum memory interact with a squeezed-vacuum bath through energy-preserving interactions. We show that in both scenarios, the squeezing phase of the reservoir decreases the entropic uncertainty (EU), whereas the squeezing strength increases the EU. In addition, we find that EU can be significantly reduced when both the measured particle and quantum memory are subjected to a common squeezed-vacuum bath. Furthermore, we explore the key factors controlling the behavior of EU by exploring the competition between quantum discord and minimal missing information. Moreover, we examine the tightness of the entropic uncertainty bound (EUB) in both system-environment setups and observe that the EUB is less tight when both the measured particle and quantum memory are coupled to a common squeezed-vacuum bath.
The uncertainty principle sets a lower bound on the uncertainties of two incompatible observables measured on a particle. The uncertainty lower bound can be reduced by considering a particle as a quantum memory entangled with the measured particle. In this paper, we consider a tripartite scenario in which a quantum state has been shared among Alice, Bob, and Charlie. The aim of Bob and Charlie is to minimize Charlie's lower bound about Alice's measurement outcomes. To this aim, they concentrate their correlation with Alice in Charlie's side via a cooperative strategy based on local operations and classical communication. We obtain a lower bound for Charlie's uncertainty about Alice's measurement outcomes after concentrating information and compare it with the lower bound without concentrating information in some examples. We also provide a physical interpretation of the entropic uncertainty lower bound based on the dense coding capacity.
This paper investigates the intrinsic decoherence effect on quantum memory and coherence dynamics of two dipole-coupled qubits in a non-degenerate bimodel cavity. Entropic uncertainty, entropy, and concurrence are utilized to examine the dynamics of quantum-memory-assisted entropic uncertainty relations, mixedness, and entanglement. The results indicate that the nonlinear interactions between the two qubits and the cavity generate quantum-memory-assisted entropic uncertainty, mixedness, and entanglement, which are reliant not only on the qubit–qubit interaction but also on the intrinsic decoherence and coherence intensity of the initial two-mode cavity states. For specific values of the dipole–dipole interaction, non-classical correlations can be enhanced By reducing the initial intensity coherence, the stability of the quantum memory-assisted entropic uncertainty relations, as well as the two-qubit mixedness of the intrinsic decoherence, are accelerated.