Generic local distinguishability and completely entangled subspaces

Generic local distinguishability and completely entangled subspaces

Entangled Subspaces and Quantum Symmetries

Entanglement is defined for each vector subspace of the tensor product of two finite-dimensional Hilbert spaces, by applying the notion of operator entanglement to the projection operator onto that subspace. The operator Schmidt decomposition of the projection operator defines a string of Schmidt coefficients for each subspace, and this string is assumed to characterize its entanglement, so tha...

Local and global distinguishability in quantum interferometry.

A statistical distinguishability based on relative entropy characterizes the fitness of quantum states for phase estimation. This criterion is employed in the context of a Mach-Zehnder interferometer and used to interpolate between two regimes of local and global phase distinguishability. The scaling of distinguishability in these regimes with photon number is explored for various quantum state...

A completely entangled subspace of maximal dimension

Consider a tensor product H = H1⊗H2⊗· · ·⊗Hk of finite dimensional Hilbert spaces with dimension of Hi = di, 1 ≤ i ≤ k. Then the maximum dimension possible for a subspace of H with no non-zero product vector is known to be d1d2 . . . dk− (d1 +d2 + · · ·+dk)+k−1. We obtain an explicit example of a subspace of this kind. We determine the set of product vectors in its orthogonal complement and sho...

Local distinguishability of multipartite unitary operations.

We show that any two different unitary operations acting on an arbitrary multipartite quantum system can be perfectly distinguished by local operations and classical communication when a finite number of runs is allowed. Intuitively, this result indicates that the lost identity of a nonlocal unitary operation can be recovered locally. No entanglement between distant parties is required.