Constructions of Unextendible Maximally Entangled Bases in $${{\mathbb{C}}}^{d}\otimes {{\mathbb{C}}}^{d^{\prime} }$$ ℂ d ⊗ ℂ d ′

Unextendible maximally entangled bases and mutually unbiased bases

Locally unextendible non-maximally entangled basis

We introduce the concept of the locally unextendible non-maximally entangled basis (LUNMEB) in H ⊗ H. It is shown that such a basis consists of d orthogonal vectors for a non-maximally entangled state. However, there can be a maximum of (d − 1) orthogonal vectors for non-maximally entangled state if it is maximally entangled in (d− 1) dimensional subspace. Such a basis plays an important role i...

A note on locally unextendible non-maximally entangled basis

Received (received date) Revised (revised date) We study the locally unextendible non-maximally entangled basis (LUNMEB) in H d ⊗ H d. We point out that there exists an error in the proof of the main result of LUNMEB [Quant. Inf. Comput. 12, 0271(2012)], which claims that there are at most d orthogonal vectors in a LUNMEB, constructed from a given non-maximally entangled state. We show that bot...

Unextendible mutually unbiased bases from Pauli C\classes

We provide a construction of sets of d/2 + 1 mutually unbiased bases (MUBs) in dimensions d = 4, 8 using maximal commuting classes of Pauli operators. We show that these incomplete sets cannot be extended further using the operators of the Pauli group. What is more, specific examples of sets of MUBs obtained using our construction are shown to be strongly unextendible; that is, there does not e...

T D C C

In the k-set agreement problem, each process proposes a value and has to decide a value in such a way that a decided value is a proposed value and at most k different values are decided. This problem can easily be solved in synchronous systems or in asynchronous systems prone to t process crashes when t < k. In contrast, it has been shown that k-set agreement cannot be solved in asynchronous sy...