One-way LOCC indistinguishable lattice states via operator structures

Operator and Graph Theoretic Techniques for Distinguishing Quantum States via One-Way LOCC

“…Remark 3. As discussed further in [12], this result is new and can be extended to the so-called 'generalized Pauli states', where a new proof is given of an established result, and which leads to an improvement for a studied subclass of states [26]. The following example illustrates the approach.…”

“…We have also been able to use the 'operator structure road map' outlined above to find sets of lattice states [8,9,25] that are indistinguishable under one-way LOCC. The following is taken from [12].…”

“…The communication paradigm called local (quantum) operations and classical communication, usually denoted by its acronym LOCC, is fundamental to quantum information theory, and includes many central topics such as quantum teleportation, data hiding, and many of their derivations [1][2][3]. The somewhat more restricted version called one-way LOCC, in which communicating parties must perform their measurements in a prescribed order, has received expanded attention due it being more tractable mathematically while still capturing many of the more important communication scenarios [4][5][6][7][8][9][10][11][12][13]. A particularly important subclass of problems in this field involves the determination of when sets of known quantum states can be distinguished using only LOCC operations or some subset thereof.…”

“…Our work in the theory of LOCC [10][11][12][13] has for the first time brought techniques and tools from operator theory, operator algebras, and graph theory to the basic theory of quantum state distinguishability in one-way LOCC. Given the overlapping nature of some of our results and applications, including improvements on some results as our work progressed, we felt a review paper bringing together a selection of main features from our work could be a useful contribution to the literature.…”

“…In Section 2, we give necessary preliminaries, including the mathematical description of one-way LOCC in terms of operator relations. Section 3 includes a brief introduction to the relevant operator structures in our analysis, and then we present some of our main results and applications from [10][11][12]. We finish in Section 4 by first giving a brief introduction to our necessary notions from graph theory, then we present one of our main results from [13] and some examples, and we derive a new graph-theoretic description for the case of a single-qubit sender.…”