Abstract
We review the geometric features of negative conditional entropy and the properties of the conditional amplitude operator proposed by Cerf and Adami for two qubit states in comparison with entanglement and nonlocality of the states. We identify the region of negative conditional entropy in the tetrahedron of locally maximally mixed two-qubit states. Within this set of states, negative conditional entropy implies nonlocality and entanglement, but not vice versa, and we show that the Cerf–Adami conditional amplitude operator provides an entanglement witness equivalent to the Peres–Horodecki criterion. Outside of the tetrahedron this equivalence is generally not true.
Highlights
The feature of entanglement is the basis for many fascinating phenomena in quantum information and quantum communication, such as quantum teleportation [1, 2] or quantum cryptography [3,4,5]
We review the geometric features of negative conditional entropy and the properties of the conditional amplitude operator proposed by Cerf and Adami for two qubit states in comparison with entanglement and nonlocality of the states
We have reviewed the geometry of entanglement for two-qubit systems
Summary
The feature of entanglement is the basis for many fascinating phenomena in quantum information and quantum communication, such as quantum teleportation [1, 2] or quantum cryptography [3,4,5]. A plethora of inequivalent criteria and measures is available for the detection and classification of entanglement [6,7,8]. The spectrum of available methods ranges from entanglement monotones such as the concurrence [9,10,11] or negativity [12], and geometric entanglement detection criteria in the form of so-called entanglement witnesses [13,14,15,16], to measures that directly quantify the utility of a state for specific tasks requiring entanglement.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of Physics A: Mathematical and Theoretical
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
