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In quantum systems, entanglement corresponds to nonclassical correlation of nonlocal observables. Thus, entanglement (or, to the contrary, separability) of a given quantum state is not uniquely determined by properties of the state, but may…
Summary. A simple derivation of finite Schmidt decomposition of pure states describing finite dimensional systems interacting with the infinite dimensional ones is presented. In particular, maximally entangled pure states in such systems…
The situation of two independent observers conducting measurements on a joint quantum system is usually modelled using a Hilbert space of tensor product form, each factor associated to one observer. Correspondingly, the operators describing…
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…
We investigate the inseparability of states generated by superposition of a multipartite pure entangled state with a product state. In particular, we identify specific multipartite entangled states that will always produce inseparability…
Tensor network methods as presented in our open source Matrix Product States software have opened up the possibility to study many-body quantum physics in one and quasi-one-dimensional systems in an easily accessible package similar to…
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…
We discuss why regular observables can not be proper entanglement measures, and how observables in a generalized setting can be used to make an entanglement monotone a directly observable quantity for the case of pure states. For the case…
It is pointed out that every mixed state statistical operator is, up to a normalization constant, a super state vector in the Hilbert space of linear Hilbert-Schmidt operators acting in the state space of the quantum system. Hence, the well…
Mathematical foundation of the novel concept of quantum tensor product by Zanardi et al is rigorously established. The concept of relative quantum entanglement is naturally introduced and its meaning is made clear both mathematically and…
In closed systems, dynamical symmetries lead to conservation laws. However, conservation laws are not applicable to open systems that undergo irreversible transformations. More general selection rules are needed to determine whether, given…
Any single system whose space of states is given by a separable Hilbert space is automatically equipped with infinitely many hidden tensor-like structures. This includes all quantum mechanical systems as well as classical field theories and…
We introduce the idea that the knowable quantum reality depends not only on the state but also on measurements. Mathematically, we map the states from the ordinary Hilbert space into new states in what we call the measurement space. The…
We report the creation of a wide range of quantum states with controllable degrees of entanglement and entropy using an optical two-qubit source based on spontaneous parametric downconversion. The states are characterised using measures of…
Construction of genuinely entangled multipartite subspaces with certain characteristics has become a relevant task in various branches of quantum information. Here we show that such subspaces can be obtained from an arbitrary collection of…
We work out a classification scheme for quantum modeling in Hilbert space of any kind of composite entity violating Bell's inequalities and exhibiting entanglement. Our theoretical framework includes situations with entangled states and…
We derive an exact uncertainty relation for arbitrary quantum states of finite-dimensional Hilbert spaces. For any given $k$-partition of a $d$-dimensional multipartite system, we introduce the total uncertainty as the sum of the…
We discuss the uniqueness of quantum states compatible with given results for measuring a set of observables. For a given pure state, we consider two different types of uniqueness: (1) no other pure state is compatible with the same…
We show that the global infinitesimal change in the multi-particle pure product state gives rise to an entangled state. This suggests that even if there is no interaction present between the subsystems, i.e., at each time instant the state…
A nice and interesting property of any pure tensor-product state is that each such state has distillable entangled states at an arbitrarily small distance $\epsilon$ in its neighborhood. We say that such nearby states are…