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.

arXiv comment20 pages, 4 figures, Accepted in Quantum

References in corpus (63)

• Quantum entanglement
• Entanglement of Formation of an Arbitrary State of Two Qubits
• Mixed State Entanglement and Quantum Error Correction
• A computable measure of entanglement
• Concentrating Partial Entanglement by Local Operations
• Quantifying Entanglement
• Quantum Coherence as a Resource
• On the volume of the set of mixed entangled states
• Conditions for a class of entanglement transformations
• Distillation of secret key and entanglement from quantum states
• The capacity of the noisy quantum channel
• The second laws of quantum thermodynamics
• Quantum data processing and error correction
• General Entanglement Breaking Channels
• Catalytic Coherence
• "Squashed Entanglement" - An Additive Entanglement Measure
• Information transmission through a noisy quantum channel
• The resource theory of informational nonequilibrium in thermodynamics
• Entanglement-assisted local manipulation of pure quantum states
• A Survey on Quantum Channel Capacities
• Quantum Channel Capacity of Very Noisy Channels
• Continuity of quantum conditional information
• Quantum cloning and the capacity of the Pauli channel
• Quantum Capacities of Bosonic Channels
• The quantum capacity of channels with arbitrarily correlated noise
• Embezzling Entangled Quantum States
• Approximate transformations and robust manipulation of bipartite pure state entanglement
• Necessary and Sufficient Conditions for the Trumping Relation
• Catalytic Conversion Probabilities for Bipartite Pure States
• Quantum privacy and quantum coherence
• Universal observable detecting all two-qubit entanglement and determinant based separability tests
• The quantum capacity with symmetric side channels
• Von Neumann entropy from unitarity
• Catalytic quantum teleportation and beyond
• Quantum thermodynamics of correlated-catalytic state conversion at small-scale
• Distilling entanglement from arbitrary resources
• The trumping relation and the structure of the bipartite entangled states
• Unified approach to quantum capacities: towards quantum noisy coding theorem
• Coherence and asymmetry cannot be broadcast
• Catalytic coherence transformations
• Catalytic Transformations of Pure Entangled States
• Catalysis of entanglement and other quantum resources
• Multiple-copy entanglement transformation and entanglement catalysis
• Quantum and private capacities of low-noise channels
• Correlation in Catalysts Enables Arbitrary Manipulation of Quantum Coherence
• Entropy and reversible catalysis
• Catalysis of entanglement manipulation for mixed states
• Catalytic majorization and ${\ell }_p$ norms
• Fundamental Limits on Correlated Catalytic State Transformations
• Experimental detection of quantum channel capacities
• All states are universal catalysts in quantum thermodynamics
• Necessary conditions on entanglement catalysts
• Is there a finite complete set of monotones in any quantum resource theory?
• Is coherence catalytic?
• Energy-constrained two-way assisted private and quantum capacities of quantum channels
• Detecting lower bounds to quantum channel capacities
• Infinite Shannon entropy
• Renormalising entanglement distillation
• Simple criteria for noise resistance of two qudit entanglement
• Progress towards a unified approach to entanglement distribution
• Catalytic leverage of correlations and mitigation of dissipation in Information erasure
• Catalytic Transformations in Coherence Theory
• Bounds On Entanglement Catalysts

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• Coherence manipulation in asymmetry and thermodynamics
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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