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General Approach to Quantum Channel Impossibility by Local Operations and Classical Communication
1Department of Physics, Portland State University, Portland, Oregon 97201, USA.
Physical Review Letters
|January 28, 2017
Summary
We present a method to determine if a quantum channel can be implemented using local operations and classical communication (LOCC). This approach uses linear equations and can design protocols when implementation is possible, simplifying quantum information processing analysis.
Area of Science:
- Quantum Information Science
- Quantum Computation
- Quantum Communication
Background:
- Implementing quantum channels via local operations and classical communication (LOCC) is a fundamental problem in quantum information science.
- Determining the implementability of quantum channels is computationally challenging, especially for complex channels or infinite rounds.
- Existing methods often struggle with channels on the boundary of the LOCC set or require prior knowledge of channel separability.
Purpose of the Study:
- To develop a general and computationally efficient method for proving the impossibility of implementing quantum channels via LOCC.
- To provide a constructive approach for designing LOCC protocols when implementation is possible within a finite number of rounds.
- To investigate the properties of the set of LOCC-implementable quantum channels, including its closure properties.
Main Methods:
- Formulating the problem of LOCC implementability as solving a set of linear equations.
- Developing a general framework applicable to any number of rounds, including infinite rounds.
- Applying the method to specific quantum channel examples to test its efficacy and explore boundary cases.
Main Results:
- A general method is established to prove LOCC impossibility by solving linear equations.
- The method enables the design of LOCC protocols for implementable channels in a finite number of rounds.
- Numerical evidence suggests the set of non-LOCC quantum channels is not closed, with boundary channels existing for 1-round and 3-round implementations.
- The method does not require prior knowledge of the channel's separability.
Conclusions:
- The developed method offers a powerful and efficient tool for analyzing quantum channel implementability via LOCC.
- The findings contribute to a deeper understanding of the boundaries and properties of LOCC-implementable quantum channels.
- This research simplifies the analysis of quantum channels, making it more accessible computationally than previously thought.
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