Related papers: Permutation and Its Partial Transpose

We introduce a recoupling theory for virtual braided trees. This recoupling theory can be utilized to incorporate swap gates into anyonic models of quantum computation.

In order to compute the Schmidt decomposition of $A\in M_k\otimes M_m$, we must consider an associated self-adjoint map. Here, we show that if $A$ is positive under partial transposition (PPT) or symmetric with positive coefficients (SPC)…

The Quantum Inverse Scattering Method is a scheme for solving integrable models in $1+1$ dimensions, building on an $R$-matrix that satisfies the Yang--Baxter equation and in terms of which one constructs a commuting family of transfer…

The interplay between the algebraic structure (operator algebras) for the quantum observables and the convex structure of the state space has been explored for a long time and most advanced results are due to Alfsen and Shultz. Here we…

We propose a gate-based quantum algorithm for the prediction step of Bayesian state estimation based on the Fokker-Planck equation on a discretized position-velocity state space. The probability density is encoded in the amplitudes of a…

Efficient methods to access the entanglement of a quantum many-body state, where the complexity generally scales exponentially with the system size $N$, have long a concern. Here we propose the Schmidt tensor network state (Schmidt TNS)…

Loop braid groups characterize the exchange of extended objects, namely loops, in three dimensional space generalizing the notion of braid groups that describe the exchange of point particles in two dimensional space. Their interest in…

The Transformer architecture is shown to provide a powerful framework as an end-to-end model for building expression trees from online handwritten gestures corresponding to glyph strokes. In particular, the attention mechanism was…

We introduce a reversible theory of exact entanglement manipulation by establishing a necessary and sufficient condition for state transfer under trace-preserving transformations that completely preserve the positivity of partial transpose…

We establish a generalisation of the fundamental state convertibility theorem in quantum information to the context of bipartite quantum systems modelled by commuting semi-finite von Neumann algebras. Namely, we establish a generalisation…

Port-based teleportation (PBT) is a variation of regular quantum teleportation that operates without a final unitary correction. However, its behavior for higher-dimensional systems has been hard to calculate explicitly beyond dimension…

For a system of N identical particles in a random pure state, there is a threshold k_0 = k_0(N) ~ N/5 such that two subsystems of k particles each typically share entanglement if k > k_0, and typically do not share entanglement if k < k_0.…

The partition algebras are algebras of diagrams (which contain the group algebra of the symmetric group and the Brauer algebra) such that the multiplication is given by a combinatorial rule and such that the structure constants of the…

Partial transposition of state operator is a well known tool to detect quantum correlations between two parts of a composite system. In this letter, the global partial transpose (GPT) is linked to conceptually multipartite underlying…

For every quantized Lie algebra there exists a map from the tensor square of the algebra to itself, which by construction satisfies the set-theoretic Yang-Baxter equation. This map allows one to define an integrable discrete quantum…

We introduce twisted permutation-equivariant GW-invariants, and compute them in terms of untwisted ones. The computation is based on Grothendieck-like RR formula corresponding to Adams' operations from K-theory to itself, and the result can…

In this paper we indicate one method of construction of linear representations of groups and algebras with translation invariant (except, maybe , finite number) defining relationships. As an illustration of this method, we give one approach…

Borrowing ideas from the relation between simply laced Lie algebras and Dynkin diagrams, a weighted graph theory representation of quantum information is addressed. In this way, the density matrix of a quantum state can be interpreted as a…

Lattice gauge theories of permutation groups with a simple topological action (henceforth permutation-TFTs) have recently found several applications in the combinatorics of quantum field theories (QFTs). They have been used to solve…

It is quite common to use the generalized probabilistic theories (GPTs) as generic models to reconstruct quantum theory from a few basic principles and to gain a better understanding of the probabilistic or information theoretic foundations…