Quantum-memory-assisted entropic uncertainty relation under noise

Entropic Uncertainty Relation and Information Exclusion Relation for multiple measurements in the presence of quantum memory

The Heisenberg uncertainty principle shows that no one can specify the values of the non-commuting canonically conjugated variables simultaneously. However, the uncertainty relation is usually applied to two incompatible measurements. We present tighter bounds on both entropic uncertainty relation and information exclusion relation for multiple measurements in the presence of quantum memory. As...

A Tight High-Order Entropic Quantum Uncertainty Relation with Applications

We derive a new entropic quantum uncertainty relation involving min-entropy. The relation is tight and can be applied in various quantum-cryptographic settings. Protocols for quantum 1-out-of-2 Oblivious Transfer and quantum Bit Commitment are presented and the uncertainty relation is used to prove the security of these protocols in the boundedquantum-storage model according to new strong secur...

Entropic Uncertainty Relations in Quantum Physics

Entropic Uncertainty Relations in Quantum Physics

Uncertainty relations have become the trademark of quantum theory since they were formulated by Bohr and Heisenberg. This review covers various generalizations and extensions of the uncertainty relations in quantum theory that involve the Rényi and the Shannon entropies. The advantages of these entropic uncertainty relations are pointed out and their more direct connection to the observed pheno...

Controlling entropic uncertainty bounds through memory effects

where H(X ) = −∑x p(x) log2 p(x) quantifies the amount of uncertainty about the observable X before the result of its measurement is known to us. Here, the probability of the outcome x is denoted by p(x) when a state ρ is measured in X -basis. Complementarity of the observables Q and R is given by 1/c = 1/maxi, j |〈ψi |φ j〉|2, where |ψi〉 and |φ j〉 are the eigenstates of the observables Q and R,...