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Register a new userHolevo bound of entropic uncertainty relation under Unruh channel in the context of open quantum systems
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The uncertainty principle is the most important feature of quantum mechanics, which can be called the heart of quantum mechanics. This principle sets a lower bound on the uncertainties of two incompatible measurement. In quantum information theory, this principle is expressed in terms of entropic measures. Entropic uncertainty bound can be altered by considering a particle as a quantum memory. In this work we investigate the entropic uncertainty relation under the relativistic motion. In relativistic uncertainty game Alice and Bob agree on two observables, $hat{Q}$ and $hat{R}$, Bob prepares a particle constructed from the free fermionic mode in the quantum state and sends it to Alice, after sending, Bob begins to move with an acceleration $a$, then Alice does a measurement on her particle $A$ and announces her choice to Bob, whose task is then to minimize the uncertainty about the measurement outcomes. we will have an inevitable increase in the uncertainty of the Alics measurement outcome due to information loss which was stored initially in B. In this work we look at the Unruh effect as a quantum noise and we will characterize it as a quantum channel.
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The uncertainty principle is an inherent characteristic of quantum mechanics. This principle can be formulated in various form. Fundamentally, this principle can be expressed in terms of the standard deviation of the measured observables. In quantum information theory the preferred mathematical quantity to express the entropic uncertainty relation is the Shannons entropy. In this work, we consider the generalized entropic uncertainty relation in which there is an additional particle as a quantum memory. Alice measures on her particle $A$ and Bob, with memory particle $B$, predicts the Alices measurement outcomes. We study the effects of the environment on the entropic uncertainty lower bound in the presence of weak measurement and measurement reversal. The dynamical model that is intended in this work is as follows: First the weak measurement is performed, Second the decoherence affects on the system and at last the measurement reversal is performed on quantum system . Here we consider the generalized amplitude damping channel and depolarizing channel as environmental noises. We will show that in the presence of weak measurement and measurement reversal, despite the presence of environmental factors, the entropic uncertainty lower bound dropped to an optimal minimum value. In fact, weak measurement and measurement reversal enhance the quantum correlation between the subsystems $A$ and $B$ thus the uncertainty of Bob about Alices measurement outcomes reduces.
The uncertainty principle is a fundamental principle in quantum physics. It implies that the measurement outcomes of two incompatible observables can not be predicted simultaneously. In quantum information theory, this principle can be expressed in terms of entropic measures. Berta emph{et al}. [href{http://www.nature.com/doifinder/10.1038/nphys1734}{ Nature Phys. 6, 659 (2010) }] have indicated that uncertainty bound can be altered by considering a particle as a quantum memory correlating with the primary particle. In this article, we obtain a lower bound for entropic uncertainty in the presence of a quantum memory by adding an additional term depending on Holevo quantity and mutual information. We conclude that our lower bound will be tighten with respect to that of Berta emph{et al.}, when the accessible information about measurements outcomes is less than the mutual information of the joint state. Some examples have been investigated for which our lower bound is tighter than the Bertas emph{et al.} lower bound. Using our lower bound, a lower bound for the entanglement of formation of bipartite quantum states has obtained, as well as an upper bound for the regularized distillable common randomness.
Gaussian distribution of a quantum state with continuous spectrum is known to maximize the Shannon entropy at a fixed variance. Applying it to a pair of canonically conjugate quantum observables $hat x$ and $hat p$, quantum entropic uncertainty relation can take a suggestive form, where the standard deviations $sigma_x$ and $sigma_p$ are featured explicitly. From the construction, it follows in a transparent manner that: (i) the entropic uncertainty relation implies the Kennard-Robertson uncertainty relation in a modifed form, $sigma_xsigma_pgeqhbar e^{cal N}/2$; (ii) the additional factor ${cal N}$ quantifies the quantum non-Gaussianity of the probability distributions of two observables; (iii) the lower bound of the entropic uncertainty relation for non-gaussian continuous variable (CV) mixed state becomes stronger with purity. Optimality of specific non-gaussian CV states to the refined uncertainty relation has been investigated and the existance of new class of CV quantum state is identified.
Quantum uncertainty relations are formulated in terms of relative entropy between distributions of measurement outcomes and suitable reference distributions with maximum entropy. This type of entropic uncertainty relation can be applied directly to observables with either discrete or continuous spectra. We find that a sum of relative entropies is bounded from above in a nontrivial way, which we illustrate with some examples.
The uncertainty principle is one of the most important issues that clarify the distinction between classical and quantum theory. This principle sets a bound on our ability to predict the measurement outcome of two incompatible observables precisely. Uncertainty principle can be formulated via Shannon entropies of the probability distributions of measurement outcome of the two observables. It has shown that the entopic uncertainty bound can be improved by considering an additional particle as the quantum memory $B$ which has correlation with the measured particle $A$. In this work we consider the memory assisted entropic uncertainty for the case in which the quantum memory and measured particle are topological qubits. In our scenario the topological quantum memory $B$, is considered as an open quantum system which interacts with its surrounding. The motivation for this model is associated with the fact that the basis of the memory-assisted entropic uncertainty relation is constructed on the correlation between quantum memory $B$ and measured particle $A$. In the sense that, Bob who holds the quantum memory $B$ can predict Alices measurement results on particle $A$ more accurately, when the amount of correlation between $A$ and $B$ is great. Here, we want to find the influence of environmental effects on uncertainty bound while the quantum memory interacts with its surrounding. In this work we will consider Ohmic-like Fermionic and Bosonic environment. We have also investigate the effect of the Fermionic and Bosonic environment on the lower bounds of the amount of the key that can be extracted per state by Alice and Bob for quantum key distribution protocols.
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