Related papers: Information-theoretic lower bounds for quantum sor…
Lin and Lin have recently shown how starting with a classical query algorithm (decision tree) for a function, we may find upper bounds on its quantum query complexity. More precisely, they have shown that given a decision tree for a…
Quantum error-correcting codes are analyzed from an information-theoretic perspective centered on quantum conditional and mutual entropies. This approach parallels the description of classical error correction in Shannon theory, while…
Hemaspaandra, Hempel, and Wechsung [cs.CC/9909020] initiated the field of query order, which studies the ways in which computational power is affected by the order in which information sources are accessed. The present paper studies, for…
The complexity of the following numerical problem is studied in the quantum model of computation: Consider a general elliptic partial differential equation of order 2m in a smooth, bounded domain Q\subset \R^d with smooth coefficients and…
Information theory provides tools to predict the performance of a learning algorithm on a given dataset. For instance, the accuracy of learning an unknown parameter can be upper bounded by reducing the learning task to hypothesis testing…
Quantum state estimation (or state tomography) is an indispensable task in quantum information processing. Because full state tomography that determines all elements of the density matrix is computationally demanding, one usually takes the…
Quantum span program algorithms for function evaluation sometimes have reduced query complexity when promised that the input has a certain structure. We design a modified span program algorithm to show these improvements persist even…
Partial orders have been used to model several experimental setups, going from classical thermodynamics and general relativity to the quantum realm with its resource theories. In order to study such experimental setups, one typically…
We introduce information-theoretic definitions for noise and disturbance in quantum measurements and prove a state-independent noise-disturbance tradeoff relation that these quantities have to satisfy in any conceivable setup. Contrary to…
In this paper, we consider the parameterized quantum query complexity for graph problems. We design parameterized quantum query algorithms for $k$-vertex cover and $k$-matching problems, and present lower bounds on the parameterized quantum…
For many years, the intuitions underlying partial-order planning were largely taken for granted. Only in the past few years has there been renewed interest in the fundamental principles underlying this paradigm. In this paper, we present a…
Understanding the power of quantum data in machine learning is central to many proposed applications of quantum technologies. While access to quantum data can offer exponential advantages for carefully designed learning tasks and often…
This paper deals with the problem of the requirements for quantum systems that enable one to design efficient quantum algorithms. We rise the issue of the possibility to utilise the non-complete networks for algorithmic purposes. In…
Quantification of quantum entanglement plays a crucial role in the study of quantum information tasks. We present analytical lower bounds for both concurrence and 2-concurrence based on the correlation matrices of bipartite quantum states.…
In a partially observed quantum or classical system the information that we cannot access results in our description of the system becoming mixed even if we have perfect initial knowledge. That is, if the system is quantum the conditional…
We prove a new lower bound on the algorithmic information content of points lying on a line in $\mathbb{R}^n$. More precisely, we show that a typical point $z$ on any line $\ell$ satisfies \begin{equation*} K_r(z)\geq \frac{K_r(\ell)}{2} +…
What kind of object is a quantum state? Is it an object that encodes an exponentially growing amount of information (in the size of the system) or more akin to a probability distribution? It turns out that these questions are sensitive to…
Branching programs are quite popular for studying time-space lower bounds. Bera et al. recently introduced the model of generalized quantum branching program aka. GQBP that generalized two earlier models of quantum branching programs. In…
Information must take up space, must weigh, and its flux must be limited. Quantum limits on communication and information storage leading to these conclusions are here described. Quantum channel capacity theory is reviewed for both steady…
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…