Consider a quantum system Q described by a Hilbert space H. This allows us to build up a “unitary-like” map on a subspace into a full unitary operator – a handy fact in some mathematical arguments....

Consider a quantum system Q described by a Hilbert space H.

This allows us to build up a “unitary-like” map on a subspace into a full unitary operator – a handy fact in some mathematical arguments. For example:

(b) Start with a map E on density operators for Q that has the operator–sum form (Eq. 9.10) for a set of Kraus operators satisfying Eq. 9.12. Append a system E in state |0 and consider the following linear map on kets:

for an orthonormal set of E-states |ek. Show that there exists a unitary U(QE) that does this.
⁴The generalization of the no-cloning theorem to mixed states – called the no-broadcasting theorem – is outside the scope of this book. In other words, every E on Q that has a normalized operator–sum representation can be realized as the result of unitary evolution on a larger system QE.

Eq. 9.10

Eq. 9.12