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Distinguishability and indistinguishability by local operations and classical communication
1Quantum Computation and Information Project, ERATO, Japan Science and Technology Agency, Daini Hongo White Building 201, Hongo 5-28-3, Bunkyo-ku, Tokyo 113-0033, Japan.
Physical Review Letters
|June 1, 2004
Summary
Spatially separated quantum states, even if orthogonal, may be indistinguishable using only local operations and classical communication. However, a limited number of entangled states can be distinguished locally.
Area of Science:
- Quantum Information Science
- Quantum Communication
- Quantum Entanglement
Background:
- Orthogonal quantum states are typically perfectly distinguishable.
- Distinguishability changes when quantum states are shared between spatially separated parties.
Purpose of the Study:
- To investigate the local distinguishability of linearly independent quantum states shared by separated parties.
- To determine conditions under which these states can or cannot be discriminated using local operations and classical communication (LOCC).
Main Methods:
- Analysis of quantum states defined by generalized Pauli matrices.
- Application of local operations and classical communication (LOCC) principles.
- Derivation of conditions for local distinguishability of entangled states.
Main Results:
- A set of linearly independent quantum states cannot be discriminated deterministically or probabilistically via LOCC.
- A condition l(l-1) <= 2d is established for the local distinguishability of 'l' maximally entangled states.
- Explicit projecting measurements were derived for local discrimination.
Conclusions:
- Local distinguishability of shared quantum states is constrained by entanglement and LOCC limitations.
- The findings provide insights into the fundamental limits of quantum information processing in distributed systems.
- Four Werner states serve as an example of locally indistinguishable states.