## 2 Quantum Uncertainty: The Problem and the Solution
### The Solution  
In this work, we explain a novel solution to the problem discussed above about reducing the quantum noise induced by the measurement process. We argue in this paper that such noise can be eliminated by modifying the quantum device to accommodate \(N\rightarrow\infty\) electrons, simultaneously. We will show that the dispersion of a random distribution of the (normalized) electrical current of \(N\rightarrow\infty\) electrons tends to zero, which implies eliminating the quantum noise. Let us consider an original or unmodified quantum electron device (before applying our protocol) that has only one transport electron, at each time, responsible for the measured current. Such electron at time \(t_{in}\) is described by a single particle quantum state \(|\psi^{1}(t_{in})\rangle\) where the superindex \(1\) refers to this first electron. We are measuring the current through a single particle operator \(\hat{I}^{1}\). If the state \(|\psi^{1}(t_{in})\rangle\) is not an eigenstate of the operator \(\hat{I}\), then, the measurement of the \(I\) gives rise to the quantum noise discussed in the previous subsection (we notice again that the generalization to more electrons is done in Appendix A). The solution that we propose to minimize the quantum noise requires designing a new quantum device (that we will refer to as the modified quantum device or just the quantum device) so that this new device satisfies the following two conditions:  
* **Condition 1:** We enlarge the original quantum electron device in order to accommodate a large number of electrons \(N\rightarrow\infty\) simultaneously. Then, the many-particle wave function \(\Psi_{T}(t_{in})\) that defines this \(N\) electrons at time \(t_{in}\) is: \[|\Psi_{T}(t_{in})\rangle=|\psi^{1}(t_{in})\rangle\otimes|\psi^{2}(t_{in}) \rangle\otimes....\otimes|\psi^{N}(t_{in})\rangle,\] (1) where the wave function \(|\psi^{i}(t_{in})\rangle\) is the single electron wave function that corresponds to the \(i\)-th electron prepared under the same conditions that we have used to prepare the wave function \(|\psi^{1}(t_{in})\rangle\) in the original quantum electron device. Strictly speaking, the condition \(N\rightarrow\infty\) is inaccessible in a practical scenario. We will see numerically in the following sections that a finite number of electrons is enough to drastically reduce the quantum noise. Identically, if the number of transport electrons in the original (unmodified) quantum electron device is already larger than one, the solution proposed here is still perfectly valid. See Appendix A for a generalization of the present protocol to more than one electron in the unmodified electron device. Finally, as can be seen in Equation (1), we assume a many-particle wave function of non-interacting electrons. This is obviously an approximation in realistic quantum devices since these electrons will suffer exchange and Coulomb interactions. In Appendix D, we test our protocol under the exchange symmetry for two electrons. Under the assumption of an initial negligible overlap of the wavepackets our protocol does not deviate from the actual result. These issues will be further elaborated in the practical implementation of this protocol in next two section. We mention that some (small) variation in the preparation of the state \(|\psi^{1}(t_{in})\rangle,|\psi^{2}(t_{in})\rangle,...\) forming \(\Psi_{T}(t_{in})\) is allowed. For example, the time delay between the injection of different single electron wave packets can vary. Also the central position of the wave packets along the lateral dimension of the device can be different. Similarities between different wave packets have to be enough to justify that the probability distribution of the values of the current is identical for all single electron wave packets.