Improved bounds on quantum uncommon information

Abstract

In classical information theory, channel capacity quantifies the maximum number of messages that can be reliably transmitted using shared information. An equivalent concept, termed uncommon information, represents the number of messages required to be exchanged to completely share all information in common. However, this equivalence does not extend to quantum information theory. Specifically, quantum uncommon information is operationally defined as the minimal amount of entanglement required for the quantum communication task of quantum state exchange, where two parties exchange quantum states to share all quantum messages in common. Currently, an analytical closed-form expression for the quantum uncommon information remains undetermined. In this work, by investigating underlying characterization of the quantum uncommon information, we derive improved bounds on it. To obtain these bounds, we develop a subspace exchange strategy that leverages a common subspace of two parties to identify the unnecessary qubits for exchange. We also consider a referee-assisted exchange, wherein a referee aids two parties in efficiently performing the quantum state exchange. Our bounds provide more precise estimations for the quantum uncommon information. Furthermore, we demonstrate that the subspace technique is a versatile tool for characterizing uncommon information not only in the bipartite scenario but also in various multi-partite ones.

24 pages, 7 figures, typos were corrected and readability was improved

References in corpus (17)

• Three qubits can be entangled in two inequivalent ways
• Distributed Quantum Computation over Noisy Channels
• Quantum information can be negative
• A Sharp Fannes-type Inequality for the von Neumann Entropy
• Quantum state merging and negative information
• Distributed quantum dense coding
• The exact cost of redistributing multipartite quantum states
• The non-local content of quantum operations
• Optimal quantum source coding with quantum information at the encoder and decoder
• Characterization of non-local gates
• Fundamental rate-loss tradeoff for the quantum internet
• Conditions for optimal construction of two-qubit non-local gates
• Reversible combination of inequivalent kinds of multipartite entanglement
• State exchange with quantum side information
• The SWAP Imposter: Bidirectional Quantum Teleportation and its Performance
• One-shot quantum state exchange
• Quantum state rotation: Circularly transferring quantum states of multiple users