Related papers: The unextendible product bases of four qubits: Has…
The construction of multipartite unextendible product bases (UPBs) is a basic problem in quantum information. We respectively construct two families of $2\times2\times4$ and $2\times2\times2\times4$ UPBs of size eight by using the existing…
Unextendible product bases have been shown to have many important uses in quantum information theory, particularly in the qubit case. However, very little is known about their mathematical structure beyond three qubits. We present several…
An important problem in quantum information is to construct multiqubit unextendible product bases (UPBs). By using the unextendible orthogonal matrices, we construct a 7-qubit UPB of size 11. It solves an open problem in [Quantum…
In quantum information theory, it is a fundamental problem to construct multipartite unextendible product bases (UPBs). We show that there exist two families UPBs in Hilbert space…
The unextendible orthogonal matrices (UPBs) can be used for various problems in quantum information. We provide an algorithm to check if two UPBs are non-equivalent to each other. We give a method to construct UPBs and we apply this method…
The 4-qubit unextendible product basis (UPB) has been recently studied by [Johnston, J. Phys. A: Math. Theor. 47 (2014) 424034]. From this result we show that there is only one UPB of size $6$ and six UPBs of size $9$ in…
We studied the construction problem of the unextendible product basis (UPB). We mainly give a method to construct a UPB of a quantum system through the UPBs of its subsystem. Using this method and the UPBs which are known for us, we…
Unextendible product bases (UPBs) play a key role in the study of quantum entanglement and nonlocality. A famous open question is whether there exist genuinely unextendible product bases (GUPBs), namely multipartite product bases that are…
We show that there are six inequivalent $4\times4$ unextendible product bases (UPBs) of size eight, when we consider only 4-qubit product vectors. We apply our results to construct Positive-Partial-Transpose entangled states of rank nine.…
Unextendible product bases (UPBs) provide a versatile tool with various applications across different areas of quantum information theory. Their comprehensive characterization is thus of great importance and has been a subject of vital…
Unextendible product bases (UPBs) are interesting mathematical objects arising in composite Hilbert spaces that have found various applications in quantum information theory, for instance in a construction of bound entangled states or Bell…
An unextendible product basis (UPB) for a multipartite quantum system is an incomplete orthogonal product basis whose complementary subspace contains no product state. We give examples of UPBs, and show that the uniform mixed state over the…
We investigate the problem of constructing unextendible product bases in the qubit case - that is, when each local dimension equals 2. The cardinality of the smallest unextendible product basis is known in all qubit cases except when the…
We investigate the open problem of the existence of genuinely unextendible product bases (GUPBs), that is, multipartite unextendible product bases (UPBs) which remain unextendible even with respect to biproduct vectors across all…
An unextendible product basis (UPB) is a set of orthogonal product states which span a subspace of a given Hilbert space while the complementary subspace contains no product state. These product bases are useful to produce bound entangled…
It is known that the $n$-qubit system has no unextendible product bases (UPBs) of cardinality $2^n-1$, $2^n-2$ and $2^n-3$. On the other hand the $n$-qubit UPBs of cardinality $2^n-4$ exist for all $n\ge3$. We prove that they do not exist…
We discuss the concept of unextendible product basis (UPB) and generalized UPB for fermionic systems, using Slater determinants as an analogue of product states, in the antisymmetric subspace $\wedge^ N \bC^M$. We construct an explicit…
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 bipartite quantum systems of dimension 3x3 entangled states that are positive under partial transposition (PPT) can be constructed with the use of unextendible product bases (UPB). As discussed in a previous publication all the lowest…
We completely characterize the condition when a tile structure provides an unextendible product basis (UPB), and construct UPBs of different large sizes in $\mathbb{C}^m\otimes\mathbb{C}^n$ for any $n\geq m\geq 3$. This solves an open…