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Optimal strategies for sending information through A quantum channel
1Grup de Fisica Teorica & IFAE, Facultat de Ciencies, Edifici Cn, Universitat Autonoma de Barcelona, 08193 Bellaterra (Barcelona), Spain.
Physical Review Letters
|December 2, 2000
Summary
This study introduces optimal quantum encoding for directional information using N spins (qubits). The fidelity of quantum encoding depends on the encoding space dimension and polynomial zeros.
Area of Science:
- Quantum Information Science
- Quantum Computing
- Mathematical Physics
Background:
- Quantum states offer a method for encoding directional information, represented by unit vectors.
- Utilizing multi-qubit systems for encoding is a key area in quantum information processing.
Purpose of the Study:
- To determine the optimal quantum encoding procedure for directional information using N spins (qubits).
- To analyze the fidelity of quantum encoding based on encoding space dimension and alternative methods like spatial rotations.
- To explore the relationship between encoding fidelity and information gain.
Main Methods:
- Development and analysis of an optimal encoding procedure for N-spin (qubit) quantum states.
- Investigation of spatial rotations as a natural encoding method.
- Mathematical derivation relating fidelity to Legendre and Jacobi polynomials for rotation-based encoding.
Main Results:
- The fidelity of the optimal N-qubit encoding procedure is solely determined by the dimension of the encoding space.
- For spatial rotations, encoding fidelity is directly linked to the largest zeros of Legendre and Jacobi polynomials.
- Results are discussed in the context of information gain.
Conclusions:
- The dimension of the encoding space is a critical factor in the fidelity of optimal quantum directional encoding.
- Spatial rotations provide a viable and potentially less demanding encoding strategy with fidelity linked to specific polynomial properties.
- The findings contribute to understanding quantum information encoding and its limitations.
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