• Corpus ID: 245986469

Test-measured R\'enyi divergences

  title={Test-measured R\'enyi divergences},
  author={Mil{\'a}n Mosonyi and Fumio Hiai},
One possibility of defining a quantum Rényi α -divergence of two quantum states is to optimize the classical Rényi α -divergence of their post-measurement probability distributions over all possible measurements (measured Rényi divergence), and maybe regularize these quantities over multiple copies of the two states (regularized measured Rényi α -divergence). A key observation behind the theorem for the strong converse exponent of asymptotic binary quantum state discrimination is that the… 



Quantum Rényi divergences and the strong converse exponent of state discrimination in operator algebras

The main tool is an approximation theorem (martingale convergence) for the sandwiched Rényi divergences, which may be used for the extension of various further results from the finite-dimensional to the von Neumann algebra setting.

Pretty good measures in quantum information theory

A reverse Araki-Lieb-Thirring inequality is proved that implies a new relation between these two families of divergences, namely that αD<inf>α</inf>(ρ‖σ) for α ∊ [0, 1] and where ρ and σ are density operators.

The strong converse exponent of discriminating infinite-dimensional quantum states

This paper answers questions in the positive for density operators on an infinite-dimensional Hilbert space, using a simple finite-dimensional approximation technique and begins the study of the sandwiched Rényi divergences, and the related problem of the strong converse exponent.

On variational expressions for quantum relative entropies

A new variational expression is created for the measured Rényi relative entropy, which is exploited to show that certain lower bounds on quantum conditional mutual information are superadditive.

Quantum Hypothesis Testing and the Operational Interpretation of the Quantum Rényi Relative Entropies

This work shows that the new quantum extension of Rényi’s α-relative entropies have an operational interpretation in the strong converse problem of quantum hypothesis testing, and obtains a new simple proof for their monotonicity under completely positive trace-preserving maps.

Different quantum f-divergences and the reversibility of quantum operations

This paper compares the standard and the maximal $f-divergences regarding their ability to detect the reversibility of quantum operations, and studies the monotonicity of the Renyi divergences under the special class of bistochastic maps that leave one of the arguments of theRenyi divergence invariant.

Strong Converse Exponent for Classical-Quantum Channel Coding

The exact strong converse exponent of classical-quantum channel coding, for every rate above the Holevo capacity, is determined, an exact analogue of Arimoto’s, given as a transform of the Rényi capacities with parameters α>1.

Defining quantum divergences via convex optimization

This work introduces a new quantum Renyi divergence defined in terms of a convex optimization program that has several desirable computational and operational properties such as an efficient semidefinite programming representation for states and channels, and a chain rule property.

Correlation detection and an operational interpretation of the Rényi mutual information

This work shows that the Rényi mutual information attains operational significance in the context of composite hypothesis testing, when the null hypothesis is a fixed bipartite state and the alternate hypothesis consists of all product states that share one marginal with thenull hypothesis.

Interpolating between symmetric and asymmetric hypothesis testing

If arbitrarily many identical copies of the system are assumed to be available, then the minimal error probability of s-hypothesis testing is shown to decay exponentially in the number of copies, with a decay rate given by a quantum divergence which the authors denote as ξs(ρ‖σ), and which satisfies a host of interesting properties.