7 research outputs found
Recoverability for Holevo's just-as-good fidelity
Holevo's just-as-good fidelity is a similarity measure for quantum states
that has found several applications. One of its critical properties is that it
obeys a data processing inequality: the measure does not decrease under the
action of a quantum channel on the underlying states. In this paper, I prove a
refinement of this data processing inequality that includes an additional term
related to recoverability. That is, if the increase in the measure is small
after the action of a partial trace, then one of the states can be nearly
recovered by the Petz recovery channel, while the other state is perfectly
recovered by the same channel. The refinement is given in terms of the trace
distance of one of the states to its recovered version and also depends on the
minimum eigenvalue of the other state. As such, the refinement is universal, in
the sense that the recovery channel depends only on one of the states, and it
is explicit, given by the Petz recovery channel. The appendix contains a
generalization of the aforementioned result to arbitrary quantum channels.Comment: 6 pages, submission to ISIT 201
On the strong converses for the quantum channel capacity theorems
A unified approach to prove the converses for the quantum channel capacity
theorems is presented. These converses include the strong converse theorems for
classical or quantum information transfer with error exponents and novel
explicit upper bounds on the fidelity measures reminiscent of the Wolfowitz
strong converse for the classical channel capacity theorems. We provide a new
proof for the error exponents for the classical information transfer. A long
standing problem in quantum information theory has been to find out the strong
converse for the channel capacity theorem when quantum information is sent
across the channel. We give the quantum error exponent thereby giving a
one-shot exponential upper bound on the fidelity. We then apply our results to
show that the strong converse holds for the quantum information transfer across
an erasure channel for maximally entangled channel inputs.Comment: Added the strong converse for the erasure channel for maximally
entangled inputs and corrected minor typo
A family of generalized quantum entropies: definition and properties
We present a quantum version of the generalized (h, φ)-entropies, introduced by SalicrĂş et al. for the study of classical probability distributions.We establish their basic properties and show that already known quantum entropies such as von Neumann, and quantum versions of RĂ©nyi, Tsallis, and unified entropies, constitute particular classes of the present general quantum SalicrĂş form. We exhibit that majorization plays a key role in explaining most of their common features. We give a characterization of the quantum (h, φ)-entropies under the action of quantum operations and study their properties for composite systems. We apply these generalized entropies to the problem of detection of quantum entanglement and introduce a discussion on possible generalized conditional entropies as well.Facultad de Ciencias ExactasInstituto de FĂsica La Plat