Related papers: On the maximal dimension of a completely entangled…

We consider a quantum system with a finite number of distinguishable quantum states, which may be partitioned freely by a number of quantum particles, assumed to be maximally entangled. We show that if we partition the system into a number…

A completely entangled subspace of a tensor product of Hilbert spaces is a subspace with no non-trivial product vector. K. R. Parthasarathy determined the maximum dimension possible for such a subspace. Here we present a simple explicit…

A subspace of a multipartite Hilbert space is completely entangled if it contains no product states. Such subspaces can be large with a known maximum size, S, approaching the full dimension of the system, D. We show that almost all…

Let $V$ be a norm-closed subset of the unit sphere of a Hilbert space $H$ that is stable under multiplication by scalars of absolute value 1. A {\em maximal vector} (for $V$) is a unit vector $\xi\in H$ whose distance to $V$ is maximum…

A major difficulty in quantum computation is the ability to implement fault tolerant computations, protecting information against undesired interactions with the environment. Stabiliser codes were introduced as a means to protect…

I generalize the concept of balancedness to qudits with arbitrary dimension $d$. It is an extension of the concept of balancedness in New J. Phys. {\bf 12}, 075025 (2010) [1]. At first, I define maximally entangled states as being the…

We consider the question of how large a subspace of a given bipartite quantum system can be when the subspace contains only highly entangled states. This is motivated in part by results of Hayden et al., which show that in large d x…

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…

The normalized separable states of a finite-dimensional multipartite quantum system, represented by its Hilbert space ${\cal H}$, form a closed convex set ${\cal S}_1$. The set ${\cal S}_1$ has two kinds of faces, induced and non-induced.…

In this paper we describe a class of highly entangled subspaces of a tensor product of finite dimensional Hilbert spaces arising from the representation theory of free orthogonal quantum groups. We determine their largest singular values…

We present a complete classification of the geometry of the mutually complementary sets of entangled and separable states in three-dimensional Hilbert subspaces of bipartite and multipartite quantum systems. Our analysis begins by finding…

Genuine entanglement is the strongest form of multipartite entanglement. Genuinely entangled pure states contain entanglement in every bipartition and as such can be regarded as a valuable resource in the protocols of quantum information…

We introduce a class of entangled subspaces: completely entangled subspaces of entanglement depth $k$ ($k$-CESs). These are subspaces of multipartite Hilbert spaces containing only pure states with an entanglement depth of at least $k$. We…

For a multipart quantum system, a locally maximally entangled (LME) state is one where each elementary subsystem is maximally entangled with its complement. This paper is a sequel to arXiv:1708.01645, which gives necessary and sufficient…

Determining whether a subspace spanned by certain quantum states is entangled and its entanglement dimensionality remains a fundamental challenge in quantum information science. This paper introduces a geometric measure of $r$-bounded rank,…

Every Maximally Entangled State (MES) of two d-dimensional particles is shown to be a product state of suitably chosen collective coordinates. The state may be viewed as defining a "point" in a "phase space" like d^2 array representing d^2…

In quantum physics, multiparticle systems are described by quantum states acting on tensor products of Hilbert spaces. This product structure leads to the distinction between product states and entangled states; moreover, one can quantify…

Quantum entangled states of light are essential for quantum technologies and fundamental tests of physics. While quantum information science has relied on systems with entanglement in 2D degrees of freedom, e.g. quantum bits with…

Starting from arbitrary Hilbert spaces, we reduce the problem to verify entanglement of any bipartite quantum state to finite dimensional subspaces. Hence, entanglement is a finite dimensional property. A generalization for multipartite…

We introduce the notion of entanglement of subspaces as a measure that quantify the entanglement of bipartite states in a randomly selected subspace. We discuss its properties and in particular we show that for maximally entangled subspaces…