Related papers: Compatibility of subsystem states and convex geome…
We study the separability of permutationally symmetric quantum states. We show that for bipartite symmetric systems most of the relevant entanglement criteria coincide. However, we provide a method to generate examples of bound entangled…
The convex feasibility problem (CFP) is to find a feasible point in the intersection of finitely many convex and closed sets. If the intersection is empty then the CFP is inconsistent and a feasible point does not exist. However,…
We present a method for describing and characterizing the state of N particles that may be distinguishable in principle but not in practice due to experimental limitations. The technique relies upon a careful treatment of the exchange…
We introduce a general method for the construction of quasiprobability representations for arbitrary notions of quantum coherence. Our technique yields a nonnegative probability distribution for the decomposition of any classical state.…
Suppose we have an unknown multipartite quantum state, how can we experimentally find out whether it is genuine multipartite entangled or not? Recall that even for a bipartite quantum state whose density matrix is known, it is already…
This paper improves the algorithms based on supporting halfspaces and quadratic programming for convex set intersection problems in our earlier paper in several directions. First, we give conditions so that much smaller quadratic programs…
Certifying entanglement for unknown quantum states experimentally is a fundamental problem in quantum computing and quantum physics. Because of being easy to implement, a most popular approach for this problem in modern quantum experiments…
Clarifying the relation between the whole and its parts is crucial for many problems in science. In quantum mechanics, this question manifests itself in the quantum marginal problem, which asks whether there is a global pure quantum state…
We investigate the optimal convex approximation of the quantum state with respect to a set of available states. By isometric transformation, we have presented the general mathematical model and its solutions together with a triple…
Using techniques developed in [Lasserre02], we show that some minimum cardinality problems subject to linear inequalities can be represented as finite sequences of semidefinite programs. In particular, we provide a semidefinite…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…
The well-known two-slit interference is understood as a special relation between observable (localization at the slits) and state (being on both slits). Relation between an observable and a quantum state is investigated in the general case.…
We consider bipartite quantum state discrimination using positive-partial-transpose measurements and show that minimum-error discrimination by positive-partial-transpose measurements is closely related to entanglement witness. By using the…
We discuss quantum correlations in systems of indistinguishable particles in relation to entanglement in composite quantum systems consisting of well separated subsystems. Our studies are motivated by recent experiments and theoretical…
After introducing the partially separable concept, we proved the equivalence between the partial separability of a given $m$-partite subsystem with $m$ qubits and the purity of states of this $m$-partite subsystem for a pure state in…
We examine the possible states of subsystems of a system of bits or qubits. In the classical case (bits), this means the possible marginal distributions of a probability distribution on a finite number of binary variables; we give necessary…
Ever since entanglement was identified as a computational and cryptographic resource, effort has been made to find an efficient way to tell whether a given density matrix represents an unentangled, or separable, state. Essentially, this is…
Entanglement witness is an effective method to detect entanglement in unknown states without doing full tomography. One of the most widespread schemes of witnessing entanglement is measuring its fidelity with respect to a pure entangled…
Entanglement, a critical resource for quantum information processing, needs to be witnessed in many practical scenarios. Theoretically, witnessing entanglement is by measuring a special Hermitian observable, called entanglement witness…
It is well known that a minimum error quantum measurement for arbitrary binary optical coherent states can be realized by a receiver that comprises interfering with a coherent reference light, photon counting, and feedback control. We show…