scholarly journals Quantum vs. classical information: operator negativity as a probe of scrambling

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Jonah Kudler-Flam ◽  
Masahiro Nozaki ◽  
Shinsei Ryu ◽  
Mao Tian Tan
Keyword(s):  
Classical Information ◽  
Information Operator

scholarly journals Zero uncertainty states in the presence of quantum memory

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Huangjun Zhu
Keyword(s):  
Uncertainty Principle ◽  
Quantum States ◽  
Quantum Memory ◽  
System State ◽  
Von Neumann ◽  
Practical Applications ◽  
Classical Information ◽  
Fundamental Limit ◽  
Minimum Uncertainty ◽  
Incompatible Observables

AbstractThe uncertainty principle imposes a fundamental limit on predicting the measurement outcomes of incompatible observables even if complete classical information of the system state is known. The situation is different if one can build a quantum memory entangled with the system. Zero uncertainty states (in contrast with minimum uncertainty states) are peculiar quantum states that can eliminate uncertainties of incompatible von Neumann observables once assisted by suitable measurements on the memory. Here we determine all zero uncertainty states of any given set of nondegenerate observables and determine the minimum entanglement required. It turns out all zero uncertainty states are maximally entangled in a generic case, and vice versa, even if these observables are only weakly incompatible. Our work establishes a simple and precise connection between zero uncertainty and maximum entanglement, which is of interest to foundational studies and practical applications, including quantum certification and verification.

scholarly journals CALCULATING A MAXIMIZER FOR QUANTUM MUTUAL INFORMATION

2008 ◽  
Vol 06 (supp01) ◽  
pp. 745-750 ◽  
Author(s):  
T. C. DORLAS ◽  
C. MORGAN
Keyword(s):  
Mutual Information ◽  
State Capacity ◽  
Convex Combination ◽  
Product State ◽  
Not Given ◽  
Classical Information ◽  
Amplitude Damping Channel ◽  
Quantum Amplitude ◽  
Memoryless Channels ◽  
Quantum Mutual Information

We obtain a maximizer for the quantum mutual information for classical information sent over the quantum amplitude damping channel. This is achieved by limiting the ensemble of input states to antipodal states, in the calculation of the product state capacity for the channel. We also consider the product state capacity of a convex combination of two memoryless channels and demonstrate in particular that it is in general not given by the minimum of the capacities of the respective memoryless channels.

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