Felix Leditzky

Felix Leditzky
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Felix Leditzky

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Quantum Physics (9)
Mathematics - Mathematical Physics (2)
Mathematics - Information Theory (2)
Mathematical Physics (2)
Computer Science - Information Theory (2)

Publications Authored By Felix Leditzky

We determine both the quantum and the private capacities of low-noise quantum channels to leading orders in the channel's distance to the perfect channel. It has been an open problem for more than 20 years to determine the capacities of some of these low-noise channels such as the depolarizing channel. We also show that both capacities are equal to the single-letter coherent information of the channel, again to leading orders. Read More

We derive general upper bounds on the distillable entanglement of a mixed state under one-way and two-way LOCC. In both cases, the upper bound is based on a convex decomposition of the state into 'useful' and 'useless' quantum states. By 'useful', we mean a state whose distillable entanglement is non-negative and equal to its coherent information (and thus given by a single-letter, tractable formula). Read More

This dissertation investigates relative entropies, also called generalized divergences, and how they can be used to characterize information-theoretic tasks in quantum information theory. The main goal is to further refine characterizations of the optimal rates for quantum source coding, state redistribution, and measurement compression with quantum side information via second order asymptotic expansions and strong converse theorems. The dissertation consists of a mathematical and an information-theoretic part. Read More

The $\alpha$-sandwiched R\'enyi divergence satisfies the data processing inequality, i.e. monotonicity under quantum operations, for $\alpha\geq 1/2$. Read More

We use a R\'enyi entropy method to prove strong converse theorems for certain information-theoretic tasks which involve local operations and quantum or classical communication between two parties. These include state redistribution, coherent state merging, quantum state splitting, measurement compression with quantum side information, randomness extraction against quantum side information, and data compression with quantum side information. The method we employ in proving these results extends ideas developed by Sharma [arXiv:1404. Read More

We obtain a lower bound on the maximum number of qubits, $Q^{n, \varepsilon}({\mathcal{N}})$, which can be transmitted over $n$ uses of a quantum channel $\mathcal{N}$, for a given non-zero error threshold $\varepsilon$. To obtain our result, we first derive a bound on the one-shot entanglement transmission capacity of the channel, and then compute its asymptotic expansion up to the second order. In our method to prove this achievability bound, the decoding map, used by the receiver on the output of the channel, is chosen to be the {\em{Petz recovery map}} (also known as the {\em{transpose channel}}). Read More

The simplest example of a quantum information source with memory is a mixed source which emits signals entirely from one of two memoryless quantum sources with given a priori probabilities. Considering a mixed source consisting of a general one-parameter family of memoryless sources, we derive the second order asymptotic rate for fixed-length visible source coding. Furthermore, we specialize our main result to a mixed source consisting of two memoryless sources. Read More

We introduce two variants of the information spectrum relative entropy defined by Tomamichel and Hayashi which have the particular advantage of satisfying the data-processing inequality, i.e. monotonicity under quantum operations. Read More

Recently, an interesting quantity called the quantum Renyi divergence (or "sandwiched" Renyi relative entropy) was defined for pairs of positive semi-definite operators $\rho$ and $\sigma$. It depends on a parameter $\alpha$ and acts as a parent quantity for other relative entropies which have important operational significances in quantum information theory: the quantum relative entropy and the min- and max-relative entropies. There is, however, another relative entropy, called the 0-relative Renyi entropy, which plays a key role in the analysis of various quantum information-processing tasks in the one-shot setting. Read More