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Are all noisy quantum states obtained from pure ones?
L Henderson1, N Linden, S Popescu
1Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom.
Physical Review Letters
|December 12, 2001
Summary
Not all mixed quantum states can be created from initially pure states corrupted by noise. Even with local actions and classical communication, some mixed states are inaccessible. This limits quantum state generation and manipulation.
Area of Science:
- Quantum Information Science
- Quantum Many-Body Systems
Background:
- Quantum information processing relies on the properties of quantum states.
- Shared pure quantum states are a valuable resource for quantum information tasks.
- Noise and local operations can transform pure states into mixed states.
Purpose of the Study:
- To investigate the types of mixed quantum states that can be generated from initially pure states subjected to noise.
- To determine if all possible mixed quantum states are accessible through this process.
Main Methods:
- Analysis of quantum state transformations under noise.
- Consideration of local operations and classical communication (LOCC).
Main Results:
- Demonstration that not all mixed quantum states can arise from noisy pure states.
- Proof that even with active local degradation and classical communication, certain mixed states remain unattainable.
Conclusions:
- The set of mixed quantum states producible from pure states via noise is restricted.
- Understanding these limitations is crucial for designing quantum protocols and error correction.