Related papers: Unextendible Maximally Entangled Bases in $\mathbb…
An important problem in quantum information theory is to understand what makes entangled quantum systems non-local or hard to simulate efficiently. In this work we consider situations in which various parties have access to a restricted set…
We use formal matrices whose entries we view as vector variables taking unit vectors values in one-qubit Hilbert spaces of a multiqubit quantum system. We construct many unextendible product bases (UPBs) of new sizes in such systems and…
In dimension $d$, Mutually Unbiased Bases (MUBs) are a collection of orthonormal bases over $\mathbb{C}^d$ such that for any two vectors $v_1, v_2$ belonging to different bases, the scalar product $|\braket{v_1|v_2}| = \frac{1}{\sqrt{d}}$.…
An entangled basis with fixed Schmidt number $k$ (EBk) is a set of orthonormal basis states with the same Schmidt number $k$ in a product Hilbert space $\mathbb{C}^d\otimes\mathbb{C}^{d'}$. It is a generalization of both the product basis…
We investigate the relation between unextendible product bases (UPB) and Bell inequalities found recently in [R. Augusiak et al., Phys. Rev. Lett. 107, 070401 (2011)]. We first review the procedure introduced there that associates to any…
Using the concept of non-degenerate Bell inequality, we show that quantum entanglement, the critical resource for various quantum information processing tasks, can be quantified for any unknown quantum states in a semi-device-independent…
In this work we provide a method for generating quantum circuits preparing maximally multipartite entangled states using genetic programming. The presented method is faster that known realisations thanks to the applied fitness function and…
Quite recently, Cai et al. [arXiv:2006.07165v1] proposed a new concept "absolutely entangled set" for bipartite quantum systems: for any possible choice of global basis, at least one state of the set is entangled. There they presented a…
Absolutely maximally entangled (AME) states are typically defined in homogeneous systems. However, the quantum system is more likely to be heterogeneous in a practical setup. In this work we pay attention to the construction of AME states…
For finite-dimensional bipartite quantum systems, we find the exact size of the largest balls, in spectral $l_p$ norms for $1 \le p \le \infty$, of separable (unentangled) matrices around the identity matrix. This implies a simple and…
We consider the actions of protocols involving local quantum operations and classical communication (LQCC) on a single system consisting of two separated qubits. We give a complete description of the orbits of the space of states under LQCC…
We introduce orthogonal quantum Latin squares, which restrict to traditional orthogonal Latin squares, and investigate their application in quantum information science. We use quantum Latin squares to build maximally entangled bases, and…
Mutually unbiased bases (MUB) are an elusive discrete structure in Hilbert spaces. Many (complete sets of) MUB are group covariant, but little is known whether they can be sharply covariant in the sense that the generating groups can have…
Entanglement-assisted quantum error correcting codes (EAQECCs) play a significant role in protecting quantum information from decoherence and quantum noise. Recently, constructing entanglement-assisted quantum maximum distance separable…
Quantum computers promise ultrafast performance of certain tasks. Experimentally appealing, measurement-based quantum computation (MBQC) requires an entangled resource called a cluster state, with long computations requiring large cluster…
Measurement-based quantum computation (MQC) is a leading paradigm for building a quantum computer. Cluster states being used in this context act as one-way quantum computers. Here, we consider Z-states as a type of highly entangled states…
It is not always possible to distinguish multipartite orthogonal states if only local operation and classical communication (LOCC) are allowed. We prove that we cannot distinguish the states of an unextendible product basis (UPB) by LOCC…
We construct a large family of Planar Maximally Entangled (PME) states which are a wider class of multi-partite entangled states than Absolutely Maximally Entangled (AME) states. These are states in which any half of the qudits are in a…
In this paper we describe a new connection between UPB (unextendable product bases) and P (positive) maps which are not CP (completely positive). We show that inner automorphisms of the set of P maps which are not CP, produce extremal…
Quantum data hiding stores classical information in bipartite quantum states that are, in principle, perfectly distinguishable, yet remain almost indistinguishable without access to a quantum communication channel. Here, we investigate…