Extended quantum conditional entropy and quantum uncertainty inequalities

Abstract

Quantum states can be subjected to classical measurements, whose incompatibility, or uncertainty, can be quantified by a comparison of certain entropies. There is a long history of such entropy inequalities between position and momentum. Recently these inequalities have been generalized to the tensor product of several Hilbert spaces and we show here how their derivations can be shortened to a few lines and how they can be generalized. All the recently derived uncertainty relations utilize the strong subadditivity (SSA) theorem; our contribution relies on directly utilizing the proof technique of the original derivation of SSA.

4 pages

References in corpus (5)

• Conjectured Strong Complementary Information Tradeoff
• Uncertainty relations from simple entropic properties
• Heisenberg-style bounds for arbitrary estimates of shift parameters including prior information
• Entropy and the uncertainty principle
• An entropic uncertainty principle for positive operator valued measures

Cited by in corpus (22)

• Entropic Uncertainty Relations and their Applications
• Experimental demonstration of Gaussian protocols for one-sided device-independent quantum key distribution
• Unconditional security of entanglement-based continuous-variable quantum secret sharing
• Entropic uncertainty and measurement reversibility
• Position-Momentum Uncertainty Relations in the Presence of Quantum Memory
• General entropy-like uncertainty relations in finite dimensions
• Quantifying high-dimensional entanglement with Einstein-Podolsky-Rosen correlations
• Wehrl entropy, entropic uncertainty relations and entanglement
• Measurement uncertainty relations for discrete observables: Relative entropy formulation
• Entanglement detection in quantum many-body systems using entropic uncertainty relations
• Entropic entanglement criteria in phase space
• Sequential sharing of two-qudit entanglement based on the entropic uncertainty relation
• Approximate tensorization of the relative entropy for noncommuting conditional expectations
• Relative entropic uncertainty relation
• Entropic Heisenberg limits and uncertainty relations from the Holevo information bound
• Quantum Brascamp-Lieb Dualities
• Uncertainty-Reality Complementarity and Entropic Uncertainty Relations
• Quantum preparation uncertainty and lack of information
• General Continuity Bounds for Quantum Relative Entropies
• Loss of Information in Quantum Guessing Game
• The generalized strong subadditivity of the von Neumann entropy for bosonic quantum systems
• Quantum Uncertainty and Entropy