The entangling power of non-entangling channels

Abstract

There are processes that cannot generate entanglement but may, nevertheless, amplify entanglement already present in a system. Here, we show that a non-entangling operation can increase the Schmidt number of a quantum state only if it can generate entanglement with some non-zero probability. This is in stark contrast to the case where the parties of a quantum network are only able to control their joint state by local operations and classical communication (LOCC). There, being able to apply operations probabilistically (stochastic LOCC) does not increase the Schmidt number. Our findings show that certain non-entangling operations become entangling when selecting on specific measurement outcomes. This naturally leads us to the class of stochastically non-entangling maps, being those that cannot generate entanglement even probabilistically. Intrigued by this finding, we devise a Schmidt number for quantum channels that quantifies whether a channel can generate entanglement probabilistically. Moreover, we show that a channel is non-entangling if and only if its dual map is witness-preserving -- it takes entanglement witnesses to witnesses. Based on this finding, we derive Bell-like inequalities whose violation signals that a process generates entanglement.

References in corpus (19)

• Entanglement detection
• Ground-to-satellite quantum teleportation
• Increasing entanglement between Gaussian states by coherent photon subtraction
• Quantifying Entanglement with Witness Operators
• Strategies for enhancing quantum entanglement by local photon subtraction
• Bound entanglement provides convertibility of pure entangled states
• Classical simulatability, entanglement breaking, and quantum computation thresholds
• Entanglement-annihilating and entanglement-breaking channels
• Ultrafine Entanglement Witnessing
• Pure-state transformations and catalysis under operations that completely preserve positivity of partial transpose
• SLOCC Convertibility between Two-Qubit States
• Entanglement transformations using separable operations
• Entanglement resource theory of quantum channel
• Censorship of Quantum Resources in Quantum Networks
• Separability Lindblad equation for dynamical open-system entanglement
• Unbreakable and breakable quantum censorship
• Restricted Monte Carlo wave function method and Lindblad equation for identifying entangling open-quantum-system dynamics
• When quantum channel preserves product states
• Censorship of quantum resources against catalytic account sharing