Related papers: Some Ulam's reconstruction problems for quantum st…
Concurrence, as one of entanglement measures, is a useful tool to characterize quantum entanglement in various quantum systems. However, the computation of the concurrence involves difficult optimizations and only for the case of two qubits…
We show that the covariance matrix of a quantum state can be reconstructed from position measurements using the simple notion of polar duality, familiar from convex geometry. In particular, all multidimensional Gaussian states (pure or…
As a striking manifestation of quantum entanglement, nonlocality has long played a pivotal role in shaping our understanding of the quantum world. When considering a Bell test involving three parties, we may even find a remarkable situation…
The Reconstruction Conjecture of Kelly and Ulam states that any graph $G$ with $n\geq 3$ vertices can be reconstructed from the multiset $\mathcal{D}(G)$ of unlabelled subgraphs $G-v$ for all $v\in V(G)$. We refer to $\mathcal{D}(G)$ as the…
Measurement based (MB) quantum computation allows for universal quantum computing by measuring individual qubits prepared in entangled multipartite states, known as graph states. Unless corrected for, the randomness of the measurements…
We determine the resource scaling of machine learning-based quantum state reconstruction methods, in terms of inference and training, for systems of up to four qubits when constrained to pure states. Further, we examine system performance…
Grid states form a discrete set of mixed quantum states that can be described by graphs. We characterize the entanglement properties of these states and provide methods to evaluate entanglement criteria for grid states in a graphical way.…
Graph states form a rich class of entangled states that exhibit important aspects of multi-partite entanglement. At the same time, they can be described by a number of parameters that grows only moderately with the system size. They have a…
We study in how far it is possible to reconstruct a graph from various Banach algebras associated to its universal covering, and extensions thereof to quantum statistical mechanical systems. It turns out that most the boundary operator…
We propose a method for constructing multi-qubit entangled quantum states representing weighted tripartite graphs. An expression for the entanglement distance for multi-qubit states corresponding to arbitrary tripartite graph structures is…
We study hypergraphs which represent finite quantum event structures. We contribute to results of graph theory, regarding bounds on the number of edges, given the number of vertices. We develop a missing one for 3-graphs of girth 4. As an…
We present a family of correlations constraints that apply to all multipartite quantum systems of finite dimension. The size of this family is exponential in the number of subsystems. We obtain these relations by defining and investigating…
This work studies how a suitably-designed classical system generates with a quantum-like (QL) state space mediated by a graph. The graph plays a special dual role by directing the topology of the classical network and defining a state space…
We present a general method to characterize the quantum correlations obtained after local measurements on multipartite systems. Sufficient conditions for a quantum system to be fully-nonlocal according to a given partition, as well as being…
Quantum state tomography, the ability to deduce the density matrix of a quantum system from measured data, is of fundamental importance for the verification of present and future quantum devices. It has been realized in systems with few…
The quantum state discrimination problem is to distinguish between non-orthogonal quantum states. This problem has many applications in quantum information theory, quantum communication and quantum cryptography. In this paper a quantum…
The principle of maximum likelihood reconstruction has proven to yield satisfactory results in the context of quantum state tomography for many-body systems of moderate system sizes. Until recently, however, quantum state tomography has…
We investigate whether pure entangled states can be associated to a measurement basis in which all vectors are local unitary transformations of the original state. We prove that for bipartite states with a local dimension that is either $2,…
The collapse of a quantum state can be understood as a mathematical way to construct a joint probability density even for operators that do not commute. We can formalize that construction as a non-commutative, non-associative collapse…
The reconstruction of quantum states from a sufficient set of experimental data can be achieved with arbitrarily weak measurement interactions. Since such weak measurements have negligible back-action, the quantum state reconstruction is…