Related papers: Partially Unbiased Entangled Bases
We discuss the question of entanglement versus separability of pure quantum states in direct product Hilbert spaces and the relevance of this issue to physics. Different types of separability may be possible, depending on the particular…
In this thesis we study symmetric structures in Hilbert spaces known as symmetric informationally complete positive operator-valued measures (SIC-POVMs), mutually unbiased bases (MUBs), and MUB-balanced states. Our tools include symmetries…
The density matrix of a qudit may be reconstructed with optimal efficiency if the expectation values of a specific set of observables are known. In dimension six, the required observables only exist if it is possible to identify six…
It is well-known that any two pure quantum states (in the same Hilbert space) can be mapped to any other using unitary transformations. However, previous approaches to this problem required two explicit bases for the Hilbert space, one each…
We show that partial transposition for pure and mixed two-particle states in a discrete $N$-dimensional Hilbert space is equivalent to a change in sign of a "momentum-like" variable of one of the particles in the Wigner function for the…
We consider the notion of unitary transformations forming bases for subspaces of $M(d,\mathbb{C})$ such that the square of Hilbert-Schmidt inner product of matrices from the differing bases is a constant. Moving from the qubit case,…
We study genuine tripartite entanglement and multipartite entanglement in arbitrary $n$-partite quantum systems based on complete orthogonal basis (COB). While the usual Bloch representation of a density matrix uses three types of…
Entanglement for pure bipartite states is most commonly quantified in a state-by-state manner to each pure state of a bipartite system a scalar quantity, such as the von Neumann entropy of a reduced density matrix. This provides a precise…
Presence of entangled states is explicitly shown in Topological insulator (TI) $Bi_2Te_3$. The surface and bulk state are found to have the different structures of entanglement. The surface states live as maximally entangled states in the…
The efficient quantum state reconstruction algorithm described in [P. Six et al., Phys. Rev. A 93, 012109 (2016)] is experimentally implemented on the non-local state of two microwave cavities entangled by a circular Rydberg atom. We use…
The unextendible product basis (UPB) is generalized to the unextendible entangled basis with any arbitrarily given Schmidt number $k$ (UEBk) for any bipartite system $\mathbb{C}^d\otimes\mathbb{C}^{d'}$ ($2\leq k<d\leq d'$), which can also…
We present a systematic simple method for constructing deterministic remote operations on single and multiple systems of arbitrary discrete dimensionality. These operations include remote rotations, remote interactions and measurements. The…
A long-standing problem in quantum physics is to determine the minimal number of measurement bases required for the complete characterization of unknown quantum states, a question of particular relevance to high-dimensional quantum…
Two kinds of Bell-states diagonal (BSD) entanglement witnesses (EW) are constructed by using the algebra of Dirac $\gamma$ matrices in the space-time of arbitrary dimension $d$, where the first kind can detect some BSD relativistic and…
We present a systematic method to introduce free parameters in sets of mutually unbiased bases. In particular, we demonstrate that any set of m real mutually unbiased bases in dimension N>2 admits the introduction of (m-1)N/2 free…
A complete set of d+1 mutually unbiased bases exists in a Hilbert spaces of dimension d, whenever d is a power of a prime. We discuss a simple construction of d+1 disjoint classes (each one having d-1 commuting operators) such that the…
We propose a method for detecting bipartite entanglement in a many-body mixed state based on estimating moments of the partially transposed density matrix. The estimates are obtained by performing local random measurements on the state,…
In a multipartite scenario quantum entanglement manifests its most dramatic form when the state is genuinely entangled. Such a state is more beneficial for information theoretic applications if it contains distillable entanglement in every…
We give a criterion for a positive mapping on the space of operators on a Hilbert space to be indecomposable. We show that this criterion can be applied to two families of positive maps. These families of maps can then be used to form…
A set of orthogonal pure states is an unextendible biseparable basis (UBB), which means that its complementary subspace contains only genuinely entangled states. UBBs thus serve as an effective tool for constructing genuinely entangled…