Entanglement catalysis for quantum states and noisy channels

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.

20 pages, 4 figures, Accepted in Quantum

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• Teleportation with Embezzling Catalysts
• Communication with Quantum Catalysts
• Transcendental properties of entropy-constrained sets: Part II
• $\chi$-Colorable Graph States: Closed-Form Expressions and Quantum Orthogonal Arrays
• A finite sufficient set of conditions for catalytic majorization