[Paper Review] Bound entangled states provide overall convertibility of pure entangled states

Satoshi Ishizaka|arXiv (Cornell University)|Mar 2, 2004

Quantum Computing Algorithms and Architecture3 citations

TL;DR

This paper demonstrates that bound entangled states enable two distant parties to probabilistically convert a single copy of their pure entangled state into any other pure state using only stochastic local operations and classical communication (SLOCC), overcoming a known limitation of SLOCC alone. The key contribution is the first realization of bound entanglement enabling overall convertibility among pure states, with explicit optimal probabilities derived for several state classes.

ABSTRACT

I show that two distant parties can transform a single copy of their pure entangled state to arbitrary pure state by stochastic local operations and classical communication (SLOCC), if they share a single copy of bound entangled states. It has been known that this entanglement processing is impossible by SLOCC alone. This is the first example of the effect of bound entangled states on the entanglement processing for bipartite pure states. Further, I obtain the optimal attainable probability for several classes of states.

Motivation & Objective

• To investigate whether bound entangled states can overcome the limitations of SLOCC alone in transforming pure entangled states.
• To determine if shared bound entanglement enables universal probabilistic conversion between arbitrary pure entangled states.
• To derive the optimal success probabilities for state transformations within specific classes of pure states.

Proposed method

• Leverages the resource theory of entanglement to analyze SLOCC transformations with additional bound entangled states as a catalyst.
• Analyzes the structure of bipartite pure states and their convertibility under stochastic local operations.
• Applies known results on bound entanglement and entanglement catalysis to construct explicit protocols for state conversion.
• Derives optimal transformation probabilities using entanglement monotones and convex optimization techniques.
• Considers specific classes of pure states to compute analytically achievable success rates.

Experimental results

Research questions

• RQ1 Can bound entangled states enable the conversion of a single copy of a pure entangled state into any other pure entangled state via SLOCC?
• RQ2 What is the maximal achievable probability for such transformations when bound entanglement is shared?
• RQ3 How does the presence of bound entanglement alter the convertibility structure of pure entangled states compared to SLOCC alone?
• RQ4 For which classes of pure states can the optimal transformation probability be explicitly computed?

Key findings

• Bound entangled states serve as a catalyst for universal SLOCC convertibility among pure entangled states, enabling transformations otherwise impossible with SLOCC alone.
• The protocol achieves full convertibility between any two pure entangled states using a single copy of bound entangled states as a resource.
• Optimal transformation probabilities are derived for several classes of pure states, providing quantitative bounds on success rates.
• This work establishes the first known instance where bound entanglement directly enables processing of pure state entanglement, revealing a novel operational role for bound entanglement.