A-unital Operations and Quantum Conditional Entropy
arXiv:2110.12527 · doi:10.22331/q-2022-02-02-641
Abstract
Negative quantum conditional entropy states are key ingredients for information theoretic tasks such as superdense coding, state merging and one-way entanglement distillation. In this work, we ask: how does one detect if a channel is useful in preparing negative conditional entropy states? We answer this question by introducing the class of A-unital channels, which we show are the largest class of conditional entropy non-decreasing channels. We also prove that A-unital channels are precisely the completely free operations for the class of states with non-negative conditional entropy. Furthermore, we study the relationship between A-unital channels and other classes of channels pertinent to the resource theory of entanglement. We then prove similar results for ACVENN: a previously defined, relevant class of states and also relate the maximum and minimum conditional entropy of a state with its von Neumann entropy. The definition of A-unital channels naturally lends itself to a procedure for determining membership of channels in this class. Thus, our work is valuable for the detection of resourceful channels in the context of conditional entropy.
arXiv commentAccepted for publication in Quantum journal (https://quantum-journal.org/). See also the related independent work by Brandsen et. al. at arXiv:2110.15330
References in corpus (31)
- Quantum entanglement
- Introducing Quantum Discord
- Classical, quantum and total correlations
- Entanglement Measures and Purification Procedures
- Quantum Resource Theories
- Distillation of secret key and entanglement from quantum states
- The Uncertainty Principle in the Presence of Quantum Memory
- General Entanglement Breaking Channels
- Quantum information can be negative
- From Classical to Quantum Shannon Theory
- Negative entropy and information in quantum mechanics
- Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask)
- An improved bound on distillable entanglement
- Quantum state merging and negative information
- Entangling operations and their implementation using a small amount of entanglement
- Geometry of entangled states
- Distributed quantum dense coding
- Unital Quantum Channels - Convex Structure and Revivals of Birkhoff's Theorem
- A multipartite generalization of quantum discord
- Geometry of two-qubit states with negative conditional entropy
- Von Neumann entropy and majorization
- One-shot entanglement distillation beyond local operations and classical communication
- Non-negativity of conditional von Neumann entropy and global unitary operations
- Exclusion Principle for Quantum Dense Coding
- Quantum channel detection
- Distributed Private Randomness Distillation
- Characterizing the boundary of the set of absolutely separable states and their generation via noisy environments
- Witnessing Negative Conditional Entropy
- Detecting mixed-unitary quantum channels is NP-hard
- Truncated moment sequences and a solution to the channel separability problem
- Quantum conditional entropy from information-theoretic principles