Determining the asymptotic algebraic complexity of matrix multiplication, succinctly
represented by the matrix multiplication exponent $\omega $, is a central problem in …

We present a polynomial time algorithm to approximately scale tensors of any format to
arbitrary prescribed marginals (whenever possible). This unifies and generalizes a …

Scaling problems have a rich and diverse history, and thereby have found numerous
applications in several fields of science and engineering. For instance, the matrix scaling …

The asymptotic restriction problem for tensors s and t is to find the smallest β≥ 0 such that
the n th tensor power of t can be obtained from the (β n+ o (n)) th tensor power of s by …

We introduce a family of tensor network states that we term semi-injective Projected
Entangled-Pair States (PEPSs). They extend the class of injective PEPSs and include other …

When some of the parties of a multipartite entangled pure state are lost, the question arises
whether the residual mixed state is also entangled, in which case the initial entangled pure …

We undertake experimental detection of the entanglement present in arbitrary three-qubit
pure quantum states on an NMR quantum information processor. Measurements of only four …

Matrix rank is well-known to be multiplicative under the Kronecker product, additive under
the direct sum, normalised on identity matrices and non-increasing under multiplying from …

In the practical context of quantum networks, the most reliable method of transmitting
quantum information is via teleportation because quantum states are highly sensitive …

We prove that the generic element of the fifth secant variety σ _5 (Gr (P^ 2, P^ 9)) ⊂ P (⋀^ 3
C^ 10) σ 5 (G r (P 2, P 9))⊂ P (⋀ 3 C 10) of the Grassmannian of planes of P^ 9 P 9 has …