Related papers: Building separable approximations for quantum stat…
We show that the manifold of quantum states is endowed with a rich and nontrivial geometric structure. We derive the Fubini-Study metric of the projective Hilbert space of a multi-qubit quantum system, endowing it with a Riemannian metric…
Quantifying entanglement for multipartite quantum state is a crucial task in many aspects of quantum information theory. Among all the entanglement measures, relative entropy of entanglement $E_{R}$ is an outstanding quantity due to its…
To better understand complexity in neural networks, we theoretically investigate the idealised phenomenon of lossless network compressibility, whereby an identical function can be implemented with fewer hidden units. In the setting of…
We propose protocols for determining the distances in Hilbert space between pure and mixed quantum states prepared on a quantum computer. In the case of pure quantum states, the protocol is based on measuring the square of modulus of scalar…
We provide quantitative bounds on the characterisation of multiparticle separable states by states that have locally symmetric extensions. The bounds are derived from two-particle bounds and relate to recent studies on quantum versions of…
In this paper, in terms of the relation between the state and the reduced states of it, we obtain two inequalities which are valid for all separable states in infinite-dimensional bipartite quantum systems. One of them provides an…
In this paper, an intuitive approach is employed to generalize the full separability criterion of tripartite quantum states of qubits to the higher-dimensional systems (Phys. Rev. A \textbf{72}, 022333 (2005)). A distinct characteristic of…
We give a new separability criterion, a necessary condition for separability of $N$-partite quantum states. The criterion is based on the Bloch representation of a $N$-partite quantum state and makes use of multilinear algebra, in…
We present an approach to characterize genuine multiparticle entanglement using appropriate approximations in the space of quantum states. This leads to a criterion for entanglement which can easily be calculated using semidefinite…
Statistical verification of a quantum state aims to certify whether a given unknown state is close to the target state with confidence. So far, sample-optimal verification protocols based on local measurements have been found only for…
We construct a simplex for multipartite qubit states of even number n of qubits, which has the same geometry concerning separability, mixedness, kind of entanglement, amount of entanglement and nonlocality as the bipartite qubit states. We…
We explore quantum search from the geometric viewpoint of a complex projective space $CP$, a space of rays. First, we show that the optimal quantum search can be geometrically identified with the shortest path along the geodesic joining a…
We examine the necessary and sufficient complexity of neural networks to approximate functions from different smoothness spaces under the restriction of encodable network weights. Based on an entropy argument, we start by proving lower…
We introduce a geometric framework for studying Bell nonlocality in Hilbert space, where, for a given quantum state, nonlocality is quantified by the distance between the state and the set of local states. This approach applies to any Bell…
We design quantum compression algorithms for parametric families of tensor network states. We first establish an upper bound on the amount of memory needed to store an arbitrary state from a given state family. The bound is determined by…
Several proposals to produce {\it tripartite} $W$-type entanglement are probabilistic even if no imperfections are considered in the processes. We provide a deterministic way to remotely create $W$ states out of an EPR source. The proposal…
We consider entanglement-based quantum networks, where multipartite entangled resource states are distributed and stored among the nodes and locally manipulated upon request to establish the desired target configuration. Separating the…
Every entangled state can be perturbed, for instance by decoherence, and stay entangled. For a large class of pure entangled states, we show how large the perturbation can be. Our class includes all pure bipartite and all maximally…
Production and verification of multipartite quantum state are an essential step in quantum information processing. In this work, we propose an efficient method to decompose symmetric multipartite observables, which are invariant under…
We investigate entanglement in two-qubit systems using a geometric representation based on the minimum of essential parameters. The latter is achieved by requiring subsystems with the same entropy, regardless of whether the state of the…