Jensen-Shannon divergence as a measure of distinguishability between mixed quantum states

By A. P. Majtey, P. W. Lamberti, D. Prato. 2005

197 citations recorded by the source corpus.

We discuss an alternative to relative entropy as a measure of distance between mixed quantum states. The proposed quantity is an extension to the realm of quantum theory of the Jensen-Shannon divergence (JSD) between probability distributions. The JSD has several interesting properties. It arises in information theory and, unlike the Kullback-Leibler divergence, it is symmetric, always well-defined, and bounded. We show that the quantum JSD shares with the relative entropy most of the physically relevant properties, in particular those required for a 'good' quantum distinguishability measure. We relate it to other known quantum distances and we suggest possible applications in the field of the quantum information theory.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d62c21b6e92a0fb1a29106db8340d5c50eb3b77f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Lars Kunze
2. Alex Arenas
3. J. Briet
4. Michael Beetz
5. Ross Duncan
6. M. A. Porter
7. Peter Harremoës
8. Manlio De Domenico

In Atomic and Molecular Physics, and Optics

1. Alex Arenas
2. J. Briet
3. Michael Beetz
4. Ross Duncan
5. M. A. Porter
6. Peter Harremoës
7. Lars Kunze
8. Manlio De Domenico

In Statistical and Nonlinear Physics

1. M. A. Porter
2. Manlio De Domenico
3. Alex Arenas
4. J. Briet
5. Michael Beetz
6. Peter Harremoës
7. Lars Kunze
8. Santo Fortunato

Citations in the corpus

• Properties of Classical and Quantum Jensen-Shannon Divergence (2008, methodology): “[21, 23, 24] proposed to use the (classical) JD as a distance function for quantum states, but also introduced a quantum version based on the von Neumann entropy, which we denote by QJD.”
• Envisioning the qualitative effects of robot manipulation actions using simulation-based projections (2017, methodology): “This distance measure is known as the Jensen-Shannon divergence (Majtey et al., 2005) and used widely in information theory.”
• Multilayer Analysis and Visualization of Networks (2014, methodology): “For each pair of layers in the original multilayer network, muxViz calculates the quantum Jensen–Shannon divergence [47].”
• t|ket⟩: a retargetable compiler for NISQ devices (2020, methodology): “We instead use the Jenses–Shannon divergence DJS [91], which is closely related to DKL.”