[Paper Review] Entanglement catalysis for quantum states and noisy channels

Chandan Datta, Tulja Varun Kondra+2 more|arXiv (Cornell University)|Feb 10, 2022

Quantum Information and Cryptography77 references4 citations

TL;DR

This paper establishes the existence of universal entanglement catalysts that enable all possible LOCC transformations between bipartite pure quantum states, demonstrating catalysis significantly enhances singlet distillation and quantum communication capacity. It proves that catalysis allows unbounded singlet extraction from non-iid state sequences and enables reliable qubit transmission through noisy channels, with catalytic capacity fully characterized by the von Neumann entropy of the channel's Choi state.

ABSTRACT

Many applications of the emerging quantum technologies, such as quantum teleportation and quantum key distribution, require singlets, maximally entangled states of two quantum bits. It is thus of utmost importance to develop optimal procedures for establishing singlets between remote parties. As has been shown very recently, singlets can be obtained from other quantum states by using a quantum catalyst, an entangled quantum system which is not changed in the procedure. In this work we take this idea further, investigating properties of entanglement catalysis and its role for quantum communication. For transformations between bipartite pure states, we prove the existence of a universal catalyst, which can enable all possible transformations in this setup. We demonstrate the advantage of catalysis in asymptotic settings, going beyond the typical assumption of independent and identically distributed systems. We further develop methods to estimate the number of singlets which can be established via a noisy quantum channel when assisted by entangled catalysts. For various types of quantum channels our results lead to optimal protocols, allowing to establish the maximal number of singlets with a single use of the channel.

Motivation & Objective

• To determine whether universal catalysts exist that can enable all possible LOCC transformations between bipartite pure states.
• To investigate the advantage of catalysis in asymptotic, non-iid settings where independent and identically distributed assumptions do not hold.
• To develop methods for estimating the catalytic quantum capacity of noisy quantum channels.
• To demonstrate that entanglement catalysis can turn entanglement-breaking channels into useful communication channels.
• To characterize the conditions under which a quantum channel can reliably transmit m qubits using catalysis.

Proposed method

• Proves the existence of a universal catalyst for all LOCC transformations between bipartite pure states using majorization theory and entanglement entropy criteria.
• Applies approximate catalysis theory to show that any transformation satisfying S(ψ^A) ≥ S(ϕ^A) can be catalytically achieved with an appropriate catalyst state.
• Uses the Choi-Jamiołkowski isomorphism to map quantum channels to density matrices and evaluates their catalytic capacity via von Neumann entropy of the Choi state.
• Derives bounds on catalytic capacity: a d-dimensional channel can transmit m qubits if S(ρ_choi) ≤ log₂d − m.
• Demonstrates that any 4-dimensional channel with a rank-2 Choi state can transmit at least one qubit perfectly when catalyzed.
• Introduces catalytic quantum communication protocols using intermediate nodes and local operations with classical communication (LOCC) to distribute entanglement through otherwise useless channels.

Experimental results

Research questions

• RQ1 Can there exist a single catalyst state that enables all possible LOCC transformations between bipartite pure states?
• RQ2 Does catalysis provide a significant advantage in asymptotic, non-iid settings where systems are not identically distributed?
• RQ3 What is the maximal number of qubits that can be reliably transmitted through a noisy quantum channel when assisted by an entangled catalyst?
• RQ4 Under what conditions can a noisy quantum channel be transformed into a noiseless one via catalysis?
• RQ5 Can entanglement be distributed through a single-qubit depolarizing channel that is otherwise entanglement-breaking, when catalysis is used?

Key findings

• A universal catalyst exists for all LOCC transformations between bipartite pure states, resolving an open problem in entanglement catalysis.
• Catalysis enables the extraction of an unbounded number of singlets from a sequence of non-iid two-qubit states, while the probability of obtaining even one singlet without catalysis is vanishingly small.
• Any quantum channel of dimension d can faithfully transmit m qubits if the von Neumann entropy of its Choi state is at most log₂d − m.
• For d ≥ 4, any quantum channel with a rank-2 Choi state can transmit at least one qubit perfectly when catalyzed.
• Catalysis allows entanglement distribution through a single-qubit depolarizing channel that is entanglement-breaking without catalysis, by using an intermediate node and a catalyst.
• The catalytic quantum capacity is strictly larger than the standard quantum capacity for certain channels, demonstrating a fundamental advantage of catalysis in communication protocols.