The uncertainty principle determines the distinction between the classical and quantum worlds. This principle states that it is not possible to measure two incompatible observables with the desired accuracy simultaneously. In quantum information theory, Shannon entropy has been used as an appropriate measure to express the uncertainty relation. According to the applications of entropic uncertainty relation, studying and trying to improve the bound of this relation is of great importance. Uncertainty bound can be altered by considering an extra quantum system as the quantum memory $B$ which is correlated with the measured quantum system $A$. One can extend the bipartite quantum memory assisted entropic uncertainty relation to tripartite quantum memory assisted entropic uncertainty relation in which the memory is split into two parts. In this work, we obtain a lower bound for the tripartite quantum memory assisted entropic uncertainty relation. Our lower bound has two additional terms compared to the lower bound in [Phys. Rev. Lett. 103, 020402 (2009)] which depending on the conditional von Neumann entropy, the Holevo quantity and mutual information. It is shown that the bound obtained in this work is more tighter than other bounds. In addition, using our lower bound, a lower bound for the quantum secret key rate has been obtained. The lower bound is also used to obtain the states for which the strong subadditivity inequality and Koashi-Winter inequality is satisfied with equality.
Quantum discord and quantum uncertainty are two important features of the quantum world. In this work, the relation between entropic uncertainty relation and the shareability of quantum discord is studied. First, by using tripartite quantum-memory-assisted entropic uncertainty relation, an upper bound for the shareability of quantum discord among different partites of a composite system is obtained. It is also shown that, for a specific class of tripartite states, the obtained relation could be expressed as monogamy of quantum discord. Moreover, it is illustrated that the relation could be gen…
The uncertainty principle sets limit on our ability to predict the values of two incompatible observables measured on a quantum particle simultaneously. This principle can be stated in various forms. In quantum information theory, it is expressed in terms of the entropic measures. Uncertainty bound can be altered by considering a particle as a quantum memory correlating with the primary particle. In this work, we provide a method for converting the entropic uncertainty relation in the absence of quantum memory to that in its presence. It is shown that the lower bounds obtained through the meth…
The effect of quantum steering describes a possible action at a distance via local measurements. Whereas many attempts on characterizing steerability have been pursued, answering the question as to whether a given state is steerable or not remains a difficult task. Here, we investigate the applicability of a recently proposed method for building steering criteria from generalized entropic uncertainty relations. This method works for any entropy which satisfy the properties of (i) (pseudo-) additivity for independent distributions; (ii) state independent entropic uncertainty relation (EUR); and…
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 pre…
In this paper, we study the interaction between a $Λ$-type three-level atom and two quantized electromagnetic fields which are simultaneously injected in a bichromatic cavity surrounded by a Kerr medium in the presence of the field-field interaction (parametric down conversion) and detuning parameters. By applying a canonical transformation, the introduced model is reduced to a well-known form of the generalized Jaynes-Cummings model. Under particular initial conditions which may be prepared for the atom and the field, the time evolution of state vector of the entire system is analytically eva…
We study the monogamy and polygamy inequalities of unified entanglement in multipartite quantum systems. We first derive the monogamy inequality of unified-$(q, s)$ entanglement for multi-qubit states under arbitrary bipartition, and then obtain the monogamy inequalities of the $α$th ($0\leqα\leq\frac{r}{2}, r\geq\sqrt{2}$) power of entanglement of formation for tripartite states and their generalizations in multi-qubit quantum states. We also generalize the polygamy inequalities of unified-$(q, s)$ entanglement for multi-qubit states under arbitrary bipartition. Moreover, we investigate polyg…
We show how to quantify tri-partite entanglement using entropies derived from experimental correlations. We use a multi-partite generalization of the entanglement of formation that is greater than zero if and only if the state is genuinely multi-partite entangled. We develop an entropic witness for tripartite entanglement, and show that the degree of violation of this witness places a lower limit on the tripartite entanglement of formation. We test our results in the three-qubit regime using the GHZ-Werner state and the W-Werner state, and in the high-dimensional pure-state regime using the tr…
Consider four binary +-1 variables A, B, C and D for which classical reasoning implies ABCD = 1. In this case the knowledge of A, B, C automatically provides knowledge of D because D = ABC. However, the Greenberger-Horne-Zeilinger paradox shows that despite classical prediction one can find quantum states and observables with well defined outcomes for which D = -ABC. In this work we formulate an information-theoretic version of this paradox. We show that for a tripartite quantum system one can find a set of four properties for which classical reasoning implies that D = ABC, yet quantum theory …
Uncertainty principle is a striking and fundamental feature in quantum mechanics distinguishing from classical mechanics. It offers an important lower bound to predict outcomes of two arbitrary incompatible observables measured on a particle. In quantum information theory, this uncertainty principle is popularly formulized in terms of entropy. Here, we present an improvement of tripartite quantum-memory-assisted entropic uncertainty relation. The uncertainty's lower bound is derived by considering mutual information and Holevo quantity. It shows that the bound derived by this method will be ti…
The uncertainty principle sets 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 between 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 …
A Holevo measure is used to discuss how much information about a given POVM on system $a$ is present in another system $b$, and how this influences the presence or absence of information about a different POVM on $a$ in a third system $c$. The main goal is to extend information theorems for mutually unbiased bases or general bases to arbitrary POVMs, and especially to generalize "all-or-nothing" theorems about information located in tripartite systems to the case of \emph{partial information}, in the form of quantitative inequalities. Some of the inequalities can be viewed as entropic uncertai…
By using the quantum-memory-assisted entropic uncertainty relation (EUR), we derive a computable tight upper bound for quantum discord, which applies to an arbitrary bipartite state. Detailed examples show that this upper bound is tighter than other known bounds in a wide regime. Furthermore, we show that for any tripartite pure state, the quantum-memory-assisted EUR imposes a constraint on the shareability of quantum correlations among the constituent parties. This conclusion amends the well accepted result that quantum discord is not monogamous.
The entropic uncertainty relation with quantum side information (EUR-QSI) from [Berta et al., Nat. Phys. 6, 659 (2010)] is a unifying principle relating two distinctive features of quantum mechanics: quantum uncertainty due to measurement incompatibility, and entanglement. In these relations, quantum uncertainty takes the form of preparation uncertainty where one of two incompatible measurements is applied. In particular, the "uncertainty witness" lower bound in the EUR-QSI is not a function of a post-measurement state. An insightful proof of the EUR-QSI from [Coles et al., Phys. Rev. Lett. 10…
We investigate quantum Rényi entropic quantities, specifically those derived from 'sandwiched' divergence. This divergence is one of several proposed Rényi generalisations of the quantum relative entropy. We may define Rényi generalisations of the quantum conditional entropy and mutual information in terms of this divergence, from which they inherit many desirable properties. However, these quantities lack some of the convenient structure of their Shannon and von Neumann counterparts. We attempt to bridge this gap by establishing divergence inequalities for valid combinations of Rényi order wh…
Recently a new quantum generalization of the Renyi divergence and the corresponding conditional Renyi entropies was proposed. Here we report on a surprising relation between conditional Renyi entropies based on this new generalization and conditional Renyi entropies based on the quantum relative Renyi entropy that was used in previous literature. Our result generalizes the well-known duality relation H(A|B) + H(A|C) = 0 of the conditional von Neumann entropy for tripartite pure states to Renyi entropies of two different kinds. As a direct application, we prove a collection of inequalities that…
We prove two new fundamental uncertainty relations with quantum memory for the Wehrl entropy. The first relation applies to the bipartite memory scenario. It determines the minimum conditional Wehrl entropy among all the quantum states with a given conditional von Neumann entropy and proves that this minimum is asymptotically achieved by a suitable sequence of quantum Gaussian states. The second relation applies to the tripartite memory scenario. It determines the minimum of the sum of the Wehrl entropy of a quantum state conditioned on the first memory quantum system with the Wehrl entropy of…
