Exploring entropic uncertainty relation and dense coding capacity in a two-qubit X-state

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.

Coherence freezing strictly incoherent operations

“…An interesting question is to classify coherence freezing strictly incoherent operations on quantum states with less nonzero off-diagonal elements. The typical example of such states are X states which frequently used as important resources for the realization of various tasks related to quantum communication and computation [2,33,34].…”

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

“…Many theoretical and experimental studies have been devoted to the dense coding capacity. [2][3][4][5][6][7][8] Generally, the amount of encoded classical information that might be transferred via chosen channel has been the Holevo quantity, where the maximum capacity of dense coding is expressed as [9] DOI: 10.1002/andp.202200204…”

“…Many theoretical and experimental studies have been devoted to the dense coding capacity. [ 2–8 ] Generally, the amount of encoded classical information that might be transferred via chosen channel has been the Holevo quantity, where the maximum capacity of dense coding is expressed as [ 9 ] $$\begin{equation} \qquad\qquad\qquad\qquad\qquad\mathcal {\chi }=\mathcal {S}(\bar{\rho }_{AB})- \mathcal {S}(\rho _{AB}) \end{equation}$$where $$ \mathcal {S}(\bullet )=- \bullet \log _2 \bullet$$ is the von Neumann entropy. $$ \bar{\rho }_{AB}$$ denotes the average density state of the single ensemble for a two‐qubit channel state, where the sender encodes his information by performing a set of mutually orthogonal unitary transformations.…”

“…[ 11 ] The effect of Dzyaloshinskii–Moriya interaction and external magnetic field using different types of Heisenberg chain models have been discussed. [ 7,12,13 ] The optimal simultaneous dense coding protocol influenced by the fluctuating massless scalar field has been proposed. [ 14 ] The channel capacity of coding information of two non‐identical charge qubits and the accelerated frame has been investigated.…”

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].…”