A New Quantum Data Processing Inequality

Abstract

Quantum data processing inequality bounds the set of bipartite states that can be generated by two far apart parties under local operations; Having access to a bipartite state as a resource, two parties cannot locally transform it to another bipartite state with a mutual information greater than that of the resource state. But due to the additivity of quantum mutual information under tensor product, the data processing inequality gives no bound when the parties are provided with arbitrary number of copies of the resource state. In this paper we introduce a measure of correlation on bipartite quantum states, called maximal correlation, that is not additive and gives the same number when computed for multiple copies. Then by proving a data processing inequality for this measure, we find a bound on the set of states that can be generated under local operations even when an arbitrary number of copies of the resource state is available.

12 pages, removed a claim about the hermicity of optimal operators and added an example

Cited by in corpus (12)

• The Arbitrarily Varying Wiretap Channel - Secret Randomness, Stability and Super-Activation
• Generic bound coherence under strictly incoherent operations
• Monotone Measures for Non-Local Correlations
• Impossibility of Local State Transformation via Hypercontractivity
• Arbitrarily Small Amounts of Correlation for Arbitrarily Varying Quantum Channels
• Tensorization of the strong data processing inequality for quantum chi-square divergences
• Continual Test-Time Adaptation for Single Image Defocus Deblurring via Causal Siamese Networks
• Network mechanism for generating genuinely correlative Gaussian states
• Axiomatic approach to measures of total correlations
• Maximal Entanglement - A New Measure of Entanglement
• Nonlocal games with noisy maximally entangled states are decidable
• Capacity-Achieving Entanglement Purification Protocol for Pauli Dephasing Channel