The power of quantum catalytic local operations

Abstract

A key result in entanglement theory is that the addition of a catalyst dramatically enlarges the set of possible state transformations via local operations and classical communication (LOCC). However, it remains unclear what is the interplay between classical communication and quantum catalysis. Here our aim is to disentangle the effect of the catalyst from that of classical communication. To do so, we explore a class of state transformations termed catalytic local operations (CLO) and compare it to LOCC and to stochastic LOCC augmented by bounded quantum communication. We show that these classes are incomparable and capture different facets of quantum state transformations.

Figures (1)

• Figure 1: We consider three operational frameworks: catalytic local operations with bounded Schmidt number of the catalyst, $\text{CLO}^{(d)}$; local operations and classical communication, LOCC; and stochastic local operations with bounded quantum communication, $\text{SLOCCQ}^{(d)}$. By construction, every $\text{CLO}^{(d)}$ protocol can be simulated within $\text{SLOCCQ}^{(d)}$. However, our results demonstrate strict separations: there are transformations in $\text{CLO}^{(d)}$ that cannot be realized by $\text{SLOCCQ}^{(d-1)}$, and conversely, some tasks possible with LOCC cannot be reproduced by catalytic protocols, regardless of the catalyst’s dimension. Thus, these three classes capture genuinely different aspects of bipartite quantum state manipulation.

Theorems & Definitions (8)

• Definition 1: SLOCCQ$^{(d)}$
• Definition 2: Schmidt number terhal2000sanpera2001
• Definition 3: CLO$^{(d)}$
• Theorem 1
• Lemma 1
• Lemma 2
• proof
• proof