Related papers: Optimal Perfect Distinguishability between Unitari…
A reliable method for characterizing quantum operations that is suitable for improving and validating their accuracies is indispensable for realizing a practical quantum computer. Known methods are still not sufficient because they lack…
The Quantum Approximate Optimization Algorithm can naturally be applied to combinatorial search problems on graphs. The quantum circuit has p applications of a unitary operator that respects the locality of the graph. On a graph with…
Let $\rho_1, \rho_2$ be quantum states and $(\rho_1,\rho_2) \mapsto D(\rho_1, \rho_2)$ be a scalar function such as the trace norm, the fidelity, and the relative entropy, etc. We determine optimal bounds for $D(\rho_1, \Phi(\rho_2))$ for…
Measuring the distinguishability between quantum states is a basic problem in quantum information theory. In this paper, we develop optimal quantum algorithms that estimate both the trace distance and the (square root) fidelity between pure…
Operational consistent query answering (CQA) is a recent framework for CQA, based on revised definitions of repairs and consistent answers, which opens up the possibility of efficient approximations with explicit error guarantees. The main…
We establish a lower bound of $\Omega{(\sqrt{n})}$ on the bounded-error quantum query complexity of read-once Boolean functions, providing evidence for the conjecture that $\Omega(\sqrt{D(f)})$ is a lower bound for all Boolean functions.…
Maximal quantum $f$-divergences, defined via the commutant Radon--Nikodym derivative, form a fundamental class of distinguishability measures for quantum states associated with operator convex functions. In this paper, we study the…
One method to determine whether or not a system of partial differential equations is consistent is to attempt to construct a solution using merely the "algebraic data" associated to the system. In technical terms, this translates to the…
We present a number of results related to quantum algorithms with small error probability and quantum algorithms that are zero-error. First, we give a tight analysis of the trade-offs between the number of queries of quantum search…
We address quantum decision theory as a convenient framework to analyze process discrimination and estimation in qubit systems. In particular we discuss the following problems: i) how to discriminate whether or not a given unitary…
Nonlinear variants of quantum mechanics can solve tasks that are impossible in standard quantum theory, such as perfectly distinguishing nonorthogonal states. Here we derive the optimal protocol for distinguishing two states of a qubit…
We study a set of new functionals (called entanglement--breaking indices) which characterize how many local iterations of a given (local) quantum channel are needed in order to completely destroy the entanglement between the system of…
We present a generic study of unambiguous discrimination between two mixed quantum states. We derive operational optimality conditions and show that the optimal measurements can be classified according to their rank. In Hilbert space…
Efficient measures to determine similarity of quantum states, such as the fidelity metric, have been widely studied. In this paper, we address the problem of defining a similarity measure for quantum operations that can be…
We show that almost all n-bit Boolean functions have bounded-error quantum query complexity at least n/2, up to lower-order terms. This improves over an earlier n/4 lower bound of Ambainis, and shows that van Dam's oracle interrogation is…
Database theory is exciting because it studies highly general and practically useful abstractions. Conjunctive query (CQ) evaluation is a prime example: it simultaneously generalizes graph pattern matching, constraint satisfaction, and…
In the oracle identification problem, we are given oracle access to an unknown N-bit string x promised to belong to a known set C of size M and our task is to identify x. We present a quantum algorithm for the problem that is optimal in its…
As techniques for fault-tolerant quantum computation keep improving, it is natural to ask: what is the fundamental lower bound on redundancy? In this paper, we obtain a lower bound on the redundancy required for $\epsilon$-accurate…
The concept of antidistinguishability of quantum states has been studied to investigate foundational questions in quantum mechanics. It is also called quantum state elimination, because the goal of such a protocol is to guess which state,…
The quantum formalism permits one to discriminate sometimes between any set of linearly-independent pure states with certainty. We obtain the maximum probability with which a set of equally-likely, symmetric, linearly-independent states can…