1. Introduction
Quantum discord has been introduced as a measure to quantify quantum correlations that go beyond the limitations of entanglement measures [1]. It is defined as the difference between the total correlation and classical correlation, based on a set of complete mutually orthogonal projectors, such as the von Neumann measurements [1, 2]. Its exploration documented in several studies, has unveiled unique properties in the realm of quantum information processing. Notably, the act of measuring an arbitrary quantum state using a projective measurement on some orthogonal basis results in the loss of coherence. Nevertheless, employing weak measurements to couple the system and the measuring device allows for a gradual disturbance of the system, enabling it to retain some level of coherence [3]. Lately, super quantum discord (SQD) [4, 5]—an extension of quantum discord under weak measurements—has emerged as a tool for capturing more complex and precise quantum correlations that traditional measures may not fully characterize [6]. This becomes particularly pertinent in the context of quantum information processing tasks, where comprehending and exploiting various forms of quantum correlations are crucial. Due to its distinctive advantages, super quantum discord has emerged as a subject of thorough investigation from various perspectives [3, 7–11].
In recent years, there has been an increasing focus on the study of coupled semiconductor quantum dots, owing to their versatile optical and electrical properties with significant implications for quantum information processing [12–15]. The exploration of these properties requires a thorough examination of various parameters, with the exciton–exciton interaction standing out as one of the most pertinent ones. This pertinence stems from the role of such interactions in first neighbors dots, providing a foundation for implementing schemes for quantum information processing on semiconductor quantum dots [16]. In this context, considerable efforts have been put to the exploration of systems involving coupled semiconductor quantum dots [17–21]. These efforts are propelled by the rapid advancements in the field of quantum information science [22]. For instance, in a study by Shojaei [18], researchers investigated the concurrence and the quantum discord between three excitons within semiconductor quantum dots. Additionally, a recent inquiry, referenced as [19], delves into the dynamics of quantum correlations within two excitonic qubits situated in two coupled semiconductor quantum dots, each independently interacting with dephasing reservoirs.
In this paper, we investigate the super quantum discord in an array of optically excited two coupled semiconductor quantum dots. Each quantum dot in the array is represented by an exciton modeled as an electric dipole. In this regard, we assess the robustness of this type of quantum correlation under the influence of thermal effect for different values of the measurement strength x. Moreover, we process the impact of varying the parameter x on its evolution against the external electric field and the Förster interaction. Our attention delves also into how these variations affect the characteristics of the defined system and the excitonic interactions within it.
This letter is structured as follows. In section 2 , we present the Hamiltonian and the model that we use in our system. In section 3 , we revise the definition of the weak measurement and the super quantum discord. The results and relevant discussions are given in section 4 . Finally, a brief summary is presented in section 5 .
2. Thermal state of system
To investigate the evolution of weak quantum correlations in a semiconductor quantum dots system, we employ a model sample featuring a series of InAs coupled semiconductor quantum dots with small equal spacing between them along the axis [23]. In this model, we elucidate the energy transfer between semiconductor quantum dots through the dipolar interaction between the excitons, relying on the Förster mechanism [24]. In this case, the qubits are represented by the excitonic electric dipole moments situated in each quantum dot, which can only orient along ∣0⟩ or against ∣1⟩ the external electric fields. The Hamiltonian of the system in the presence of an external electric field $\left(\overrightarrow{E}\right)$ is given by [19], 1 ), ωi denotes the frequency of the excitons in the semiconductor quantum dots, and Ωi represents the frequency related to the excitonic dipole moment. This frequency is a function of the dipole moment and the external electric field $\left(\overrightarrow{E}\right)$ at the quantum dot number i,
$\begin{eqnarray}\begin{array}{rcl}H & = & {\hslash }\displaystyle \sum _{i=1}^{n}{\omega }_{i}\left[{S}_{z}^{i}+\displaystyle \frac{1}{2}\right]\\ & & +\,{\hslash }\displaystyle \sum _{i=1}^{n}{{\rm{\Omega }}}_{i}{S}_{z}^{i}+{\hslash }\displaystyle \sum _{\displaystyle \genfrac{}{}{0em}{}{i,j=1}{i\ne j}}^{n}{J}_{z}\left[{S}_{z}^{i}+\displaystyle \frac{1}{2}\right]\left[{S}_{z}^{j}+\displaystyle \frac{1}{2}\right]\\ & & +\,\displaystyle \frac{1}{2}\displaystyle \sum _{\displaystyle \genfrac{}{}{0em}{}{i,j=1}{i\ne j}}^{n}\lambda \left[{S}_{+}^{i}{S}_{-}^{j}+{S}_{-}^{j}{S}_{+}^{i}\right],\end{array}\end{eqnarray}$
with ${S}_{+}^{i}=\left(\begin{array}{cc}0 & 0\\ 1 & 0\end{array}\right)$, ${S}_{-}^{i}=\left(\begin{array}{cc}0 & 1\\ 0 & 0\end{array}\right)$, and ${S}_{z}^{i}=\tfrac{1}{2}\left(\begin{array}{cc}1 & 0\\ 0 & -1\end{array}\right).$ In equation ( $\begin{eqnarray}{\hslash }{{\rm{\Omega }}}_{i}=| \vec{d}\cdot \vec{E}| ,\end{eqnarray}$
with $\vec{d}$ being the electric dipole moment associated with the exciton (assumed to be the same for each quantum dot), λ represents the Förster interaction responsible for transferring an exciton from one quantum dot to another, and Jz is the exciton–exciton dipolar interaction energy. For two dipoles i and j, along the z-axis and separated by a distance rij, it is given by $\begin{eqnarray}{\hslash }{J}_{z}=\displaystyle \frac{{\vec{d}}^{2}(1-3\,\cos \,\theta )}{{\vec{r}}_{{ij}}^{3}},\end{eqnarray}$
with θ represents the angle between dipoles and z-axes.The state of the system, when in canonical thermal equilibrium at temperature T, is described by the density matrix,
$\begin{eqnarray}\rho =\exp \left[-\displaystyle \frac{\beta \hat{H}}{Z}\right],\end{eqnarray}$
with $\beta ={\left({K}_{{\rm{B}}}T\right)}^{-1}$, KB being the Boltzmann constant and T the temperature. The partition function Z is given by $\begin{eqnarray}{\rm{Z}}(T)=\mathrm{Tr}(\exp [-\beta H])\end{eqnarray}$
$\begin{eqnarray}=\displaystyle \sum _{i=1}^{N}{g}_{i}{{\rm{e}}}^{-\beta {E}_{i}},\end{eqnarray}$
Ei being the eigenvalues of the Hamiltonian, and gi is the degeneracy.The corresponding system state of the partition function Z(T) given in equation (6 ) can be written,
$\begin{eqnarray}\rho (T)=\displaystyle \frac{1}{{\rm{Z}}}\displaystyle \sum _{i=1}^{N}{{\rm{e}}}^{-\beta {E}_{i}}| {\phi }_{i,j}\rangle \langle {\phi }_{i,j}| ,\end{eqnarray}$
with ∣φi,j⟩ is the ith eigenfunction. Hence, the temperature dependent system state can be written in the basis of the eigenvectors of the Hamiltonian as, $\begin{eqnarray}\begin{array}{l}{\rho }_{{AB}}(T)={\rho }_{11}| +,+\rangle \langle +,+| +{\rho }_{22}| +,-\rangle \\ \langle +,-| +{\rho }_{23}| -,+\rangle \langle +,-| \\ +\,{\rho }_{32}| +,-\rangle \langle -,+| +{\rho }_{33}| -,+\rangle \\ \langle -,+| +{\rho }_{44}| -,-\rangle \langle -,-| ,\end{array}\end{eqnarray}$
its matrix form is written as: $\begin{eqnarray*}{\rho }_{{AB}}(T)=\left(\begin{array}{cccc}{\rho }_{11} & 0 & 0 & 0\\ 0 & {\rho }_{22} & {\rho }_{23} & 0\\ 0 & {\rho }_{32} & {\rho }_{33} & 0\\ 0 & 0 & 0 & {\rho }_{44}\end{array}\right),\end{eqnarray*}$
where the elements ρ11, ρ22, ρ23, ρ32, ρ33 and ρ44 are expressed as a function of $\tfrac{1}{Z}{\sum }_{i=1}^{N}{{\rm{e}}}^{-\beta {E}_{i}}$. In which, $\begin{eqnarray}\begin{array}{l}{\rho }_{11}=\displaystyle \frac{1}{{\rm{Z}}}\displaystyle \sum _{i=1}^{N}{{\rm{e}}}^{-\beta {E}_{1}}\\ \quad =\,\tfrac{1}{{{\rm{e}}}^{\beta (-\lambda +2{\hslash }\mathrm{Jz}+{\hslash }\omega +{\hslash }{\rm{\Omega }})}+{{\rm{e}}}^{\beta (\lambda +2{\hslash }\mathrm{Jz}+{\hslash }\omega +{\hslash }{\rm{\Omega }})}+{{\rm{e}}}^{2\beta ({\hslash }\mathrm{Jz}+{\hslash }\omega +{\hslash }{\rm{\Omega }})}+1},\end{array}\end{eqnarray}$
$\begin{eqnarray}\begin{array}{l}{\rho }_{22}={\rho }_{33}=\displaystyle \frac{1}{{\rm{Z}}}\displaystyle \sum _{i=1}^{N}{{\rm{e}}}^{-\beta {E}_{2}}\\ \quad =\,\tfrac{\left({{\rm{e}}}^{2\beta \lambda }+1\right){{\rm{e}}}^{\beta (-\lambda +2{\hslash }\mathrm{Jz}+{\hslash }\omega +{\hslash }{\rm{\Omega }})}}{2\left({{\rm{e}}}^{\beta (-\lambda +2{\hslash }\mathrm{Jz}+{\hslash }\omega +{\hslash }{\rm{\Omega }})}+{{\rm{e}}}^{\beta (\lambda +2{\hslash }\mathrm{Jz}+{\hslash }\omega +{\hslash }{\rm{\Omega }})}+{{\rm{e}}}^{2\beta ({\hslash }\mathrm{Jz}+{\hslash }\omega +{\hslash }{\rm{\Omega }})}+1\right)},\end{array}\end{eqnarray}$
$\begin{eqnarray}\begin{array}{l}{\rho }_{23}={\rho }_{32}=\displaystyle \frac{1}{{\rm{Z}}}\displaystyle \sum _{i=1}^{N}{{\rm{e}}}^{-\beta {E}_{3}}\\ \quad =-\tfrac{\left({{\rm{e}}}^{2\beta \lambda }-1\right){{\rm{e}}}^{\beta (-\lambda +2{\hslash }\mathrm{Jz}+{\hslash }\omega +{\hslash }{\rm{\Omega }})}}{2\left({{\rm{e}}}^{\beta (-\lambda +2{\hslash }\mathrm{Jz}+{\hslash }\omega +{\hslash }{\rm{\Omega }})}+{{\rm{e}}}^{\beta (\lambda +2{\hslash }\mathrm{Jz}+{\hslash }\omega +{\hslash }{\rm{\Omega }})}+{{\rm{e}}}^{2\beta ({\hslash }\mathrm{Jz}+{\hslash }\omega +{\hslash }{\rm{\Omega }})}+1\right)},\end{array}\end{eqnarray}$
$\begin{eqnarray}\begin{array}{l}{\rho }_{44}=\displaystyle \frac{1}{{\rm{Z}}}\displaystyle \sum _{i=1}^{N}{{\rm{e}}}^{-\beta {E}_{4}}\\ \quad =\displaystyle \frac{{{\rm{e}}}^{2\beta ({\hslash }\mathrm{Jz}+{\hslash }\omega +{\hslash }{\rm{\Omega }})}}{{{\rm{e}}}^{\beta (-\lambda +2{\hslash }\mathrm{Jz}+{\hslash }\omega +{\hslash }{\rm{\Omega }})}+{{\rm{e}}}^{\beta (\lambda +2{\hslash }\mathrm{Jz}+{\hslash }\omega +{\hslash }{\rm{\Omega }})}+{{\rm{e}}}^{2\beta ({\hslash }\mathrm{Jz}+{\hslash }\omega +{\hslash }{\rm{\Omega }})}+1}.\end{array}\end{eqnarray}$
3. Weak measurements and super quantum discord (SQD)
The weak measurements theory can be articulated using pre- and post-selected quantum systems [25]. Additionally, it can be expressed in terms of the measurement operator formalism, as introduced by Oreshkov and Brun [26]. This latter approach offers a novel tool in quantum information theory, applicable to both weak and strong measurements. By considering dichotomic measurement operators, which represent measurements with two outcomes, one can construct quantum measurements with any number of outcomes as a sequence of such dichotomic measurements.
Consider the weak measurement operators [26], which constitute a pair of complete mutually parametrized orthogonal operators. It is noteworthy that these operators are not necessarily idempotents. For any real x ≥ 0, let
$\begin{eqnarray}P(\pm x)=\sqrt{\displaystyle \frac{1\mp \tanh x}{2}}{{\rm{\Pi }}}_{0}+\sqrt{\displaystyle \frac{1\pm \tanh x}{2}}{{\rm{\Pi }}}_{1},\end{eqnarray}$
with P†(x)P(x) + P†( − x)P( − x) = I. Π0 and Π1 are two orthogonal projectors that satisfy Π0 + Π1 = I. In addition, ${\mathrm{lim}}_{x\to +\infty }P(-x)={{\rm{\Pi }}}_{0}$ and ${\mathrm{lim}}_{x\to +\infty }P(x)={{\rm{\Pi }}}_{1}$.The parameter x in equation (13 ) denotes the strength of the measurement process, it quantifies the interaction level between the quantum system and the measurement apparatus [25]. Understanding the measurement strength x is pivotal in optimizing weak measurements for quantum information processing. It enables precise control over how much the system is disturbed during the manipulation and measurement of quantum states, crucial for preserving their intrinsic properties. Interpreting x reveals distinct regimes: In the weak regime (x ≪ 1), the interaction minimally disturbs the system, allowing limited information extraction without significant state alteration. The intermediate regime (x ≈ 1) induces noticeable system changes, enhancing information retrieval at a higher disturbance cost. The strong regime (x ≫ 1) substantially collapses the system's wavefunction, maximizing information extraction with pronounced disturbance.
The super quantum discord Dw(ρAB) of a bipartite quantum state ρAB with weak measurements on the subsystem B is the difference between the quantum mutual correlation I(ρAB) and the classical correlation J(ρAB)[6]. Recall that the quantum mutual information is given by [27, 28],
$\begin{eqnarray}I({\rho }_{{AB}})=S({\rho }_{A})+S({\rho }_{B})-S({\rho }_{{AB}}),\end{eqnarray}$
where S(ρA), S(ρB) and S(ρAB) are the von Neumann entropies ($S(\rho )=-\mathrm{Tr}(\rho \,\mathrm{log}\,\rho )$) of the reduced state ${\rho }_{A}={\mathrm{Tr}}_{B}({\rho }_{{AB}}),{\rho }_{B}={\mathrm{Tr}}_{A}({\rho }_{{AB}})$, and the total state ρAB, respectively. The classical correlation represents the information obtained about subsystem A after carrying out the measurements PB(x) = P(x) on subsystem B [2] and it is expressed as, $\begin{eqnarray}J({\rho }_{{AB}})=S({\rho }_{A})-{\min }_{\left\{{P}^{B}(x)\right\}}{S}_{w}(A| \{{P}^{B}(x)\}).\end{eqnarray}$
Therefore, the super quantum discord denoted by Dw(ρAB) is defined as
$\begin{eqnarray}\begin{array}{l}{D}_{w}({\rho }_{{AB}})=I({\rho }_{{AB}})-J({\rho }_{{AB}})\\ \,=\,S({\rho }_{B})-S({\rho }_{{AB}})\\ \,+\,\mathop{\min }\limits_{\{{P}^{B}(x)\}}[{S}_{w}(A| \{{P}^{B}(x)\})],\end{array}\end{eqnarray}$
with {PB(x)} is weak measurement performed on subsystem B, and Sw(A∣{PB(x)}) represents the weak quantum conditional entropy [6] and it is given by $\begin{eqnarray}\begin{array}{l}{S}_{w}(A| \{{P}^{B}(x)\})=P(x)S({\rho }_{A| {P}^{B}(x)})\\ \quad +\,P(-x)S({\rho }_{A| {P}^{B}(-x)}),\end{array}\end{eqnarray}$
where $\begin{eqnarray}\begin{array}{l}{\rho }_{A| {P}^{B}(\pm x)}=\displaystyle \frac{1}{P(\pm x)}\\ {\mathrm{Tr}}_{B}\,\times \,[(I\otimes {P}^{B}(\pm x)){\rho }_{{AB}}(I\otimes {P}^{B}(\pm x))],\end{array}\end{eqnarray}$
and $\begin{eqnarray}\begin{array}{l}P(\pm x)\\ =\,{\mathrm{Tr}}_{{AB}}\,[(I\otimes {P}^{B}(\pm x)){\rho }_{{AB}}(I\otimes {P}^{B}(\pm x))].\end{array}\end{eqnarray}$
The two weak measurement projectors PB( ± x) in the above equation are written as,
$\begin{eqnarray*}{P}^{B}(-x)=\left(\begin{array}{cc}\chi \ \nu +\varphi \ {\rm{\Gamma }} & \eta \ \nu -\eta \ {\rm{\Gamma }}\\ \kappa \ \nu -\kappa \ {\rm{\Gamma }} & \varphi \ \nu +\chi \ {\rm{\Gamma }}\end{array}\right),\end{eqnarray*}$
$\begin{eqnarray*}{P}^{B}(+x)=\left(\begin{array}{cc}\varphi \ \nu +\chi \ {\rm{\Gamma }} & -\eta \ \nu +\eta \ {\rm{\Gamma }}\\ -\kappa \ \nu +\kappa \ {\rm{\Gamma }} & \chi \ \nu +\varphi \ {\rm{\Gamma }}\end{array}\right),\end{eqnarray*}$
where ${\rm{\Gamma }}=\sqrt{\tfrac{1+\tanh (x)}{2}}$, $\nu =\sqrt{\tfrac{1-\tanh (x)}{2}}$, $\eta =\cos \theta \sin \theta {{\rm{e}}}^{{\rm{i}}\phi }$, $\kappa =\cos \theta \sin \theta {{\rm{e}}}^{-{\rm{i}}\phi }$, $\ \ \varphi ={\sin }^{2}\theta $, and $\chi ={\cos }^{2}\theta $.Interestingly, in the strong measurement limit (i.e. when $\mathrm{lim}x\to \infty $), super quantum discord becomes the normal quantum discord under von Neumann measurements. Consequently, its computation can be exceedingly challenging, as discord involves a complex optimization problem over a parametrized manifold with a boundary.
4. Main results
We investigate the behavior of super quantum discord within a system consisting of two excitonic qubits positioned inside two coupled semiconductor quantum dots. Our exploration is focused on the influence of the weak measurement on its robustness as well as on the non-classicality of system against thermal effects. To delve into this, we present in figure 1 its evolution as a function of temperature T for various values of the measurement strength x when the electric field is deactivated ℏΩ = 0 meV (Figure 1(a)) and when it is activated ℏΩ = 3 meV (figure 1(b)).
Figure 1. Super quantum discord as a function of temperature T for different values of the measurement strength x for fixed values of Förster parameter λ = 5meV and the coupling ℏJz = 2.5 meV. |
In figure 1(a), where the electric field is deactivated, it is seen that, for very small values of the measurement strength x, the super quantum discord decreases until reaching a stabilized value at higher temperatures. This reflects its robustness within the coupled semiconductor quantum dots system, even at elevated temperatures, ensuring that its quantumness remains intact despite thermal effects. Nevertheless, for higher values of the parameter x (x ≥ 5), the super quantum discord diminishes with increasing this parameter until it vanishes. Indeed, the variation of measurement strength x significantly influences its sensitivity to thermal effects, leading certainly to a change in the system's characteristics. On the other hand, in figure 1(b), when the electric field is activated, the super quantum discord exhibits a behavior similar to the plot in figure 1(a), albeit with reduced amplitudes at lower temperatures. Noteworthy is that, for elevated temperature values, the amplitude remains constant. This confirms that the influence of the external electric field ℏΩ can be nullified under higher temperature conditions [19]. Additionally, both plots reveal that decreasing the measurement strength x leads to an increase in the quantity of super quantum correlation, as the exciton–exciton interaction is enhanced. Also, they indicate that higher values of this parameter disrupt the non-classical nature of the coupled semiconductor quantum dots system. Considering all this, from figure 1, one can deduce that adjusting this parameter to lower values turns weak measurements into a mechanism that not only strengthens the non-classicality of the system but also fortifies the robustness of its super quantum correlations against thermal effects.
Physically, the robustness of super quantum discord is enhanced through several mechanisms. Weaker measurements reduce the system's interaction with the environment, mitigating thermal noise and preserving quantum correlations. They conserve more of the system's initial energy, avoiding the disruption caused by stronger measurements, and disturb the system less, allowing more information about quantum correlations to persist despite thermal noise. To validate this, an experimental setup could use a well-characterized quantum system such as entangled qubits, trapped ions, superconducting qubits, or quantum dots, with a tunable measurement apparatus to vary x. The system would be placed in a precisely regulated thermal environment, and weak, intermediate, and strong measurements would be performed under different thermal conditions. Super quantum discord would be measured at various x values, with data analysis identifying patterns that support the enhanced robustness.
Besides, a comprehensive exploration of the super quantum discord between the two excitonic qubits has been performed to address comparatively the impact of varying the measurement strength x on its sensitivity to both the external electric field effect and the Förster interaction effect. This exploration is visually illustrated in figure 2, where we present the 3D evolution of super quantum discord against x and ℏΩ in figure 2(a) and as a function of x and λ in figure 2(b).
Figure 2. Super quantum discord as a function of ℏΩ and λ for fixed temperature; T = 70. |
Figure 2(a) shows that the quantity of super quantum discord decreases whenever we increase the electric field parameter ℏΩ. Physically, this decrease is attributed to the alignment of all dipoles in a singular direction under the influence of an external electric field. This alignment results in an intensified dipole-dipole repulsive interaction, precipitating a reduction in Coulomb-induced correlations [29]. Furthermore, it shows that the pace of this decrease is broadly influenced by the variation of the measurement strength. Interestingly, in this figure, we observe that the super quantum discord attains notably smaller values at larger x even when the electric field is deactivated, which is particularly intriguing because under typical conditions, one would anticipate it to reach its maximum value. Additionally, we observe that at smaller values of x, this super quantum correlation diminishes slowly with the increase of the electric field parameter, and even for large values of this parameter its quantity remains considerable. These observations imply that weak measurement slows up the influence of external electric field on super quantum correlation. Moving into figure 2(b), it is seen that increasing the Förster interaction parameter λ amplifies the super quantum correlation in the system, a consequence of the heightened exciton–exciton interaction. Further, it is seen that for higher measurement strength x, this correlation vanishes whenever this parameter vanishes then increases until reaching its stabilized value, however, for vanishing or weak measurement strength x, it is present even for vanishing Förster interaction and it attains its zenith for large values of this latter. Besides, figure 2(c) illustrates that an increase in the exciton–exciton dipole interaction energy enhances the super quantum discord (SQD) between the excitonic qubits of the system. Furthermore, it demonstrates that for smaller or vanishing values of the parameter x, this correlation reaches its maximum. Interestingly, despite the decrease in the coupling ℏJz, it manages to maintain its higher values. However, as this parameter attains higher values, the super quantum discord (SQD) quantity reaches its minimum, even in the presence of larger coupling ℏJz. As a matter of fact, from the three plots of figure 2 we state that the influence of varying the measurement strength x significantly surpasses the effects of Förster interaction, exciton–exciton dipole interaction energy and external electric field on the system. In light of these findings, we deem that our system and its exciton–exciton interactions can be controlled by manipulating the measurement strength x parameter.
5. Conclusion
In our investigation, we have addressed the super quantum discord between two excitonic qubits placed inside a coupled semiconductor quantum dots system. Our purpose is to reveal the weak measurement effect on this system and its interactions. For that fact, we have processed the variation of measurement strength x and its influence on the evolution of this super quantum correlation concerning temperature, external electric field, exciton–exciton dipole interaction energy and Förster interaction. Specifically, we have found that decreasing the measurement strength x leads to an increase in the quantity of super quantum correlation, as the exciton–exciton interaction is enhanced. Its robustness against temperature variation is assured when x takes on smaller values. In fact, we have deduced that by adjusting the measurement strength x in lower values, the weak measurement can be transformed into a catalyst, ensuring the non-classicality of the coupled semiconductor quantum dots system. Additionally, we have found that the variations in x exert an extensive influence on the quantum characteristics of this system. Interestingly, the effect of x on super quantum correlation outweighs the effects of associated quantum parameters; Förster interaction, exciton–exciton dipole interaction energy and external electric field. Indeed, we deem that through the strategic control of measurement strength x, weak measurements can serve as a powerful tool for managing our system and controlling exciton–exciton interactions within it.
Role of weak measurements in studying coupled semiconductor quantum dots, contributing to increased efficiency in the fields of quantum information processing and quantum computing. The utilization of these measurements can open new pathways for engineering quantum systems with tailored functionalities. Our findings present a promising avenue for designing advanced quantum devices and information processing technologies, marking an exciting frontier in the rapidly evolving landscape of quantum technology. Furthermore, our study demonstrates that changes in the measurement strength x correlate with changes in the physical properties of the system in several significant ways. This parameter affects both the amount of information extracted from the system and the disturbance it experiences, impacting quantum correlations, coherence, and thermal stability. Adjusting x in quantum dots can therefore influence their quantum properties similarly to observations in monolayer transition metal dichalcogenides (TMDs). Building on extensive research into magneto-polarons in monolayer TMDs over the past decade [30], our next study will explore the effects of weak measurements on such systems. This research promises deeper insights into their quantum behaviors and potential applications.