Related papers: A quantum version of Wielandt's inequality
Quantum inequalities are lower bounds for local averages of quantum observables that have positive classical counterparts, such as the energy density or the Wick square. We establish such inequalities in general (possibly interacting)…
In this thesis we analyse the type of states and ensembles which achieve the capacity for certain quantum channels carrying classical information. We first concentrate on the product-state capacity of a particular quantum channel, that is,…
The information capacities and ``distillability'' of a quantum channel are studied in the presence of auxiliary resources. These include prior entanglement shared between the sender and receiver and free classical bits of forward and…
An upper limit is given to the amount of quantum information that can be transmitted reliably down a noisy, decoherent quantum channel. A class of quantum error-correcting codes is presented that allow the information transmitted to attain…
Quantum capacities are fundamental quantities that are notoriously hard to compute and can exhibit surprising properties such as superadditivity. Thus, a vast amount of literature is devoted to finding tight and computable bounds on these…
The data processing inequality is the most basic requirement for any meaningful measure of information. It essentially states that distinguishability measures between states decrease if we apply a quantum channel and is the centerpiece of…
We propose a general method to operationally quantify the resourcefulness of quantum channels via channel discrimination, an important information processing task. A main result is that the maximum success probability of distinguishing a…
We show that for the tensor product of an entanglement-breaking quantum channel with an arbitrary quantum channel, both the minimum entropy of an output of the channel and the Holevo-Schumacher-Westmoreland capacity are additive. In…
A new bound for the quantum capacity of the $d$-dimensional depolarizing channels is presented. Our derivation makes use of a flagged extension of the map where the receiver obtains a copy of a state $\sigma_0$ whenever the messages are…
Two quantum channels are called compatible if they can be obtained as marginals from a single broadcasting channel; otherwise they are incompatible. We derive a characterization of the compatibility relation in terms of concatenation and…
A collection of quantum channels is called incompatible if they cannot be obtained as marginals from a single channel. No-cloning theorem is the most prominent instance of incompatibility of quantum channels. We show that every collection…
We show that, for any system with a number of levels which can be identified with n qubits, there is an inequality for the correlations between three compatible dichotomic measurements which must be satisfied by any noncontextual theory,…
Starting from the Hamiltonian formulation for the inhomogeneous Mixmaster dynam- ics, we approach its quantum features through the link of the quasi-classical limit. We fix the proper operator-ordering which ensures that the WKB continuity…
The quantum capacity captures the value of a quantum channel for transmitting quantum information, establishing the fundamental limits on quantum communication. In spite of its central role in quantum information theory, the quantum…
Quantum technologies rely on the ability to coherently manipulate, process and transfer information, encoded in quantum states, along quantum channels. Decoherence induced by the environment introduces errors, thus setting limits on the…
In this work we analyze properties of generic quantum channels in the case of large system size. We use random matrix theory and free probability to show that the distance between two independent random channels converges to a constant…
We prove the quantum conditional Entropy Power Inequality for quantum additive noise channels. This inequality lower bounds the quantum conditional entropy of the output of an additive noise channel in terms of the quantum conditional…
Shared entanglement is a resource available to parties communicating over a quantum channel, much akin to public coins in classical communication protocols. Whereas shared randomness does not help in the transmission of information, or…
Quantum communications promises reliable transmission of quantum information, efficient distribution of entanglement and generation of completely secure keys. For all these tasks, we need to determine the optimal point-to-point rates that…
In this article new bounds on weighted p-norms of ambiguity functions and Wigner functions are derived. Such norms occur frequently in several areas of physics and engineering. In pulse optimization for Weyl--Heisenberg signaling in…