Implications of Qudit Superselection rules for the Theory of Decoherence-free Subsystems

Abstract

The use of d-state systems, or qudits, in quantum information processing is discussed. Three-state and higher dimensional quantum systems are known to have very different properties from two-state systems, i.e., qubits. In particular there exist qudit states which are not equivalent under local unitary transformations unless a selection rule is violated. This observation is shown to be an important factor in the theory of decoherence-free, or noiseless, subsystems. Experimentally observable consequences and methods for distinguishing these states are also provided, including the explicit construction of new decoherence-free or noiseless subsystems from qutrits. Implications for simulating quantum systems with quantum systems are also discussed.

13 pages, 1 figures, Version 2: Typos corrected, references fixed and new ones added, also includes referees suggested changes and a new example

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Cited by in corpus (11)

• Reference frames, superselection rules, and quantum information
• Robust and Reliable Transfer of a Quantum State Through a Spin Chain
• Numerical method for finding decoherence-free subspaces and its applications
• Compatible Transformations for a Qudit Decoherence-free/Noiseless Encoding
• Minimal noise subsystems
• Geometry of pure states of N spin-J system
• Methods for Producing Decoherence-Free States and Noiseless Subsystems Using Photonic Qutrits
• Cooperative behavior of qutrits with dipole-dipole interactions
• The Role of Rotational Invariance in the Properties of Hamiltonians
• Casimir Invariants for Systems Undergoing Collective Motion
• Recursive encoding and decoding of the noiseless subsystem for qudits