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Local discrimination of mixed States
J Calsamiglia1, J I de Vicente, R Muñoz-Tapia
1Física Teòrica, Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain.
Physical Review Letters
|September 28, 2010
Summary
Local operations assisted with classical communication (LOCC) protocols for distinguishing mixed quantum states are less efficient than collective strategies. Achieving the same accuracy may require twice as many copies for LOCC compared to collective methods.
Area of Science:
- Quantum Information Science
- Quantum Communication
- Quantum State Discrimination
Background:
- Distinguishing quantum states is fundamental in quantum information processing.
- Local operations assisted by classical communication (LOCC) represent a key class of quantum information tasks.
- Understanding the limitations of LOCC compared to collective strategies is crucial for resource optimization.
Purpose of the Study:
- To derive bounds on the average error probability for multiple-copy discrimination of mixed qubit states using LOCC.
- To compare the performance of LOCC protocols with general collective quantum strategies.
- To quantify the resource overhead associated with LOCC in state discrimination tasks.
Main Methods:
- Development of rigorously computable and tight bounds for error probability.
- Analysis of average error probability for multiple-copy discrimination.
- Numerical simulations to assess the gap between LOCC and collective error rates.
Main Results:
- LOCC protocols for mixed state discrimination are strictly less effective than collective protocols.
- A persistent gap exists between LOCC and collective error rates, even in the asymptotic limit.
- LOCC strategies may necessitate up to double the number of quantum copies to match the accuracy of collective protocols.
Conclusions:
- The study establishes performance limitations for LOCC in mixed state discrimination.
- The findings highlight a significant resource disadvantage for LOCC compared to collective approaches.
- The developed techniques offer a general framework for bounding LOCC capabilities in related quantum information settings.
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