Virtual Quantum Subsystems

@inproceedings{Foundation2001VirtualQS,
  title={Virtual Quantum Subsystems},
  author={Paolo Zanardi Institute for Scientific Interchange Foundation and Istituto Nazionale per la Fisica della Materia},
  year={2001}
}
The physical resources available to access and manipulate the degrees of freedom of a quantum system define the set A of operationally relevant observables. The algebraic structure of A selects a preferred tensor product structure i.e., a partition into subsystems. The notion of compoundness for quantum system is accordingly relativized. Universal control over virtual subsystems can be achieved by using quantum noncommutative holonomies 
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Let us consider two qubits and the family by U λ := exp(i λ S) = cos λ 1 1 + i sin λ S where S |ψ ⊗ |φ = |φ ⊗ |ψ). If X1 := σx ⊗ 1 1 one has X1(U λ ) = cos 2 λ X1 + sin 2 λ 1 1 ⊗ σx + i
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    ) implies A2 ⊂ ⊕J Mn J (C) ⊗ 1 1 d J then A1 ∨ A2 = ⊕J Mn J (C) ⊗ M d J (C). A comparison of the dimension of this latter algebra
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