Physics – Quantum Physics
Scientific paper
2008-05-15
Quantum Information and Computation, 9:739--764, 2009
Physics
Quantum Physics
25 pages, 11pt font, full page compilation of final journal version. v3: strong NP-hardness result added, other minor revision
Scientific paper
Multi-party local quantum operations with shared quantum entanglement or shared classical randomness are studied. The following facts are established: (i) There is a ball of local operations with shared randomness lying within the space spanned by the no-signaling operations and centred at the completely noisy channel. (ii) The existence of the ball of local operations with shared randomness is employed to prove that the weak membership problem for local operations with shared entanglement is strongly NP-hard. (iii) Local operations with shared entanglement are characterized in terms of linear functionals that are ``completely'' positive on a certain cone K of separable Hermitian operators, under a natural notion of complete positivity appropriate to that cone. Local operations with shared randomness (but not entanglement) are also characterized in terms of linear functionals that are merely positive on that same cone K. (iv) Existing characterizations of no-signaling operations are generalized to the multi-party setting and recast in terms of the Choi-Jamiolkowski representation for quantum super-operators. It is noted that the standard nonlocal box is an example of a no-signaling operation that is separable, yet cannot be implemented by local operations with shared entanglement.
No associations
LandOfFree
Properties of Local Quantum Operations with Shared Entanglement does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Properties of Local Quantum Operations with Shared Entanglement, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Properties of Local Quantum Operations with Shared Entanglement will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-509308