Unextendibility, uncompletability, and many-copy indistinguishable ensembles
Saronath Halder, Alexander Streltsov

TL;DR
This paper investigates unextendible and uncompletability concepts for operators positive under partial transpose, linking them to many-copy indistinguishable ensembles under LOCC, and introduces a unifying framework for their analysis.
Contribution
It introduces the notion of positive partial transpose uncompletability and connects it to many-copy indistinguishability, providing explicit constructions and simplifying proofs.
Findings
Maximum cardinality of nonorthogonal unextendible product bases (nUPBs) identified.
Many-copy indistinguishable ensembles can be characterized using unextendibility concepts.
Local indistinguishability increases as the number of mixed states decreases in certain ensembles.
Abstract
In this work, we explore the notions unextendible product basis and uncompletability for operators which remain positive under partial transpose. Then, we analyze their connections to the ensembles which are many-copy indistinguishable under local operations and classical communication (LOCC). We show that the orthogonal complement of any bipartite pure entangled state is spanned by product states which form a nonorthogonal unextendible product basis (nUPB) of maximum cardinality. This subspace has one to one correspondence with the maximum dimensional subspace where there is no orthonormal product basis. Due to these, the proof of indistinguishability of a class of ensembles under LOCC in many-copy scenario becomes simpler. Furthermore, it is now clear that there are several many-copy indistinguishable ensembles which are different construction-wise. But if we consider the technique of…
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Taxonomy
TopicsQuantum Information and Cryptography · Quantum Computing Algorithms and Architecture · Quantum Mechanics and Applications
