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The uncertainty principle and entanglement are two fundamental, but yet not well understood, features of quantum theory. The uncertainty relation reflects the capability limit in acquiring the knowledge of different physical properties of a…
We investigate entanglement properties of a recently introduced class of macroscopic quantum superpositions in two-mode mixed states. One of the tools we use in order to infer the entanglement in this non-Gaussian class of states is the…
Heisenberg's uncertainty principle implies fundamental constraints on what properties of a quantum system can we simultaneously learn. However, it typically assumes that we probe these properties via measurements at a single point in time.…
Uncertainty relations play a central role in quantum mechanics. Entropic uncertainty relations in particular have gained significant importance within quantum information, providing the foundation for the security of many quantum…
In this paper we give a new way to quantify the folklore notion that quantum measurements bring a disturbance to the system being measured. We consider two observers who initially assign identical mixed-state density operators to a…
We compute R\'enyi entropies for the statistics of a noisy simultaneous observation of two complementary observables in two-dimensional quantum systems. The relative amount of uncertainty between two states depends on the uncertainty…
We present a new paradigm for capturing the complementarity of two observables. It is based on the entanglement created by the interaction between the system observed and the two measurement devices used to measure the observables…
We relate the principle of quantum-memory-assisted entropic uncertainty to quantum teleportation and show geometrically that any two-qubit state which lowers the upper bound of this uncertainty relation is useful for teleportation. We also…
The measurement outcomes of two incompatible observables on a particle can be precisely predicted when it is maximally entangled with a quantum memory, as quantified recently [Nature Phys. 6, 659 (2010)]. We explore the behavior of the…
Uncertainty relations give upper bounds on the accuracy by which the outcomes of two incompatible measurements can be predicted. While established uncertainty relations apply to cases where the predictions are based on purely classical data…
Detection of entanglement in bipartite states is a fundamental task in quantum information. The first method to verify entanglement in mixed states was the partial-transpose criterion. Subsequently, numerous quantifiers for bipartite…
Uncertainty relations based on information theory for both discrete and continuous distribution functions are briefly reviewed. We extend these results to account for (differential) R\'{e}nyi entropy and its related entropy power. This…
Since the uncertainty about an observable of a system prepared in a quantum state is usually described by its variance, when the state is mixed, the variance is a hybrid of quantum and classical uncertainties. Besides that, complementarity…
We provide a generalized treatment of uncertainties, von Neumann entropy, and squeezing in entangled bipartite pure state of two-level atoms. We observe that when the bipartite state is entangled, though the von Neumann entropy of the…
An universal approximation technique for analysis of different characteristics of states of composite infinite-dimensional quantum systems is proposed and used to prove general results concerning the properties of correlation and…
Similarity-sensitive entropy measures the uncertainty of a probability law relative to a similarity kernel that encodes the distinguishability between states. We develop a measure-theoretic treatment covering both finite similarity matrices…
A tight information-theoretic measurement uncertainty relation is experimentally tested with neutron spin-1/2 qubits. The noise associated to the measurement of an observable is defined via conditional Shannon entropies and a tradeoff…
The uncertainty relation for continuous variables due to Byalinicki-Birula and Mycielski expresses the complementarity between two $n$-uples of canonically conjugate variables $(x_1,x_2,\cdots x_n)$ and $(p_1,p_2,\cdots p_n)$ in terms of…
A special feature of the ground state in a topologically ordered phase is the existence of large scale correlations depending only on the topology of the regions. These correlations can be detected by the topological entanglement entropy or…
Entropies are fundamental measures of uncertainty with central importance in information theory and statistics and applications across all the quantitative sciences. Under a natural set of operational axioms, the most general form of…