Related papers: On Strong Converse Theorems for Quantum Hypothesis…
We study the problem of communication over a compound quantum channel in the presence of entanglement. Classically such channels are modeled as a collection of conditional probability distributions wherein neither the sender nor the…
We analyze a task in which classical and quantum messages are simultaneously communicated via a noisy quantum channel, assisted with a limited amount of shared entanglement. We derive direct and converse bounds for the one-shot capacity…
One possibility of defining a quantum R\'enyi $\alpha$-divergence of two quantum states is to optimize the classical R\'enyi $\alpha$-divergence of their post-measurement probability distributions over all possible measurements (measured…
In this paper, we provide a simple framework for deriving one-shot achievable bounds for some problems in quantum information theory. Our framework is based on the joint convexity of the exponential of the collision relative entropy, and is…
With the recent development of quantum information theory, some attempts exist to construct information theory beyond quantum theory. Here we consider hypothesis testing relative entropy and one-shot classical capacity, that is, the optimal…
Quantum hypothesis testing concerns the discrimination between quantum states. This paper introduces a novel lower bound for asymmetric quantum hypothesis testing that is based on the Nussbaum-Szko{\l}a mapping. The lower bound provides a…
An uncertainty relation for the R\'enyi entropies of conjugate quantum observables is used to obtain a strong Heisenberg limit of the form ${\rm RMSE} \geq f(\alpha)/(\langle N\rangle+\frac12)$, bounding the root mean square error of any…
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…
We study hypothesis testing under communication constraints, where each sample is quantized before being revealed to a statistician. Without communication constraints, it is well known that the sample complexity of simple binary hypothesis…
Past works on remote lossy source coding studied the rate under average distortion and the error exponent of excess distortion probability. In this work, we look into how fast the excess distortion probability converges to 1 at small rates,…
The fully quantum reverse Shannon theorem establishes the optimal rate of noiseless classical communication required for simulating the action of many instances of a noisy quantum channel on an arbitrary input state, while also allowing for…
We revisit a fundamental open problem in quantum information theory, namely whether it is possible to transmit quantum information at a rate exceeding the channel capacity if we allow for a non-vanishing probability of decoding error. Here…
In statistical inference problems, we wish to obtain lower bounds on the minimax risk, that is to bound the performance of any possible estimator. A standard technique to obtain risk lower bounds involves the use of Fano's inequality. In an…
Reverse Shannon theorems concern the use of noiseless channels to simulate noisy ones. This is dual to the usual noisy channel coding problem, where a noisy (classical or quantum) channel is used to simulate a noiseless one. The Quantum…
We describe some applications of quantum information theory to the analysis of quantum limits on measurement sensitivity. A measurement of a weak force acting on a quantum system is a determination of a classical parameter appearing in the…
A strong converse bound for constant composition codes of the form $P_{e}^{(n)} \geq 1- A n^{-0.5(1-E_{sc}'(R,W,p))} e^{-n E_{sc}(R,W,p)}$ is established using the Berry-Esseen theorem through the concepts of Augustin information and…
We prove the strong converse for the $N$-source Gaussian multiple access channel (MAC). In particular, we show that any rate tuple that can be supported by a sequence of codes with asymptotic average error probability less than one must lie…
The strong exponential-time hypothesis (SETH) is a commonly used conjecture in the field of complexity theory. It states that CNF formulas cannot be analyzed for satisfiability with a speedup over exhaustive search. This hypothesis and its…
Achievability in information theory refers to demonstrating a coding strategy that accomplishes a prescribed performance benchmark for the underlying task. In quantum information theory, the crafted Hayashi-Nagaoka operator inequality is an…
In the simple quantum hypothesis testing problem, upper bound with asymmetric setting is shown by using a quite useful inequality by Audenaert et al, quant-ph/0610027, which was originally invented for symmetric setting. Using this upper…