Related papers: Estimating expectation values using approximate qu…
This thesis seeks to develop a general method for solving so-called quantum realizability problems, which are questions of the following form: under which conditions does there exist a quantum state exhibiting a given collection of…
We study the discrimination of N mixed quantum states in an optimal measurement that maximizes the probability of correct results while the probability of inconclusive results is fixed at a given value. After considering the discrimination…
Many quantum information measures can be written as an optimization of the quantum relative entropy between sets of states. For example, the relative entropy of entanglement of a state is the minimum relative entropy to the set of separable…
It is a central fact in quantum mechanics that non-orthogonal states cannot be distinguished perfectly. This property ensures the security of quantum key distribution. It is therefore an important task in quantum communication to design and…
We describe a technique for self consistently characterizing both the quantum state of a single qubit system, and the positive-operator-valued measure (POVM) that describes measurements on the system. The method works with only ten…
The states of the qubit, the basic unit of quantum information, are $2 \times 2$ positive semi-definite Hermitian matrices with trace 1. We contribute to the program to axiomatize quantum mechanics by characterizing these states in terms of…
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…
Quantum state preparation involving a uniform superposition over a non-empty subset of $n$-qubit computational basis states is an important and challenging step in many quantum computation algorithms and applications. In this work, we…
Cat states are an important resource for fault-tolerant quantum computing, where they serve as building blocks for a variety of fault-tolerant primitives. Consequently, the ability to prepare high-quality cat states at large fault distances…
Impressive progress has been made in the past decade in the study of technological applications of varied types of quantum systems. With industry giants like IBM laying down their roadmap for scalable quantum devices with more than…
Protecting a quantum object against irreversible accidental measurements from its surroundings is necessary for controlled quantum operations. This becomes especially challenging or unfeasible if one must simultaneously measure or reset a…
New algorithm for quantum state estimation based on the maximum likelihood estimation is proposed. Existing techniques for state reconstruction based on the inversion of measured data are shown to be overestimated since they do not…
Debugging quantum states transformations is an important task of modern quantum computing. The use of quantum tomography for these purposes significantly expands the range of possibilities. However, the presence of preparation and…
Quantum state tomography and other measures of the global properties of a quantum state are indispensable tools in understanding many body physics through quantum simulators. Unfortunately, the number of experimental measurements of the…
We propose a single observable to witness the nonzero quantum discord of an unknown quantum state provided that we have four copies of the state. The expectation value of this observable provides a necessary and sufficient condition for…
We estimate the resources required to prepare the ground state of a quantum many-body system on a quantum computer of intermediate size. This estimate is made possible using a combination of quantum many-body methods and analytic upper…
Quantum state preparation (QSP) is a fundamental task in quantum computation to prepare a quantum state for a given classical description of the quantum state. The classical description of an $n$-qubit quantum state may have $\exp(O(n))$…
We propose a learning method for estimating unknown pure quantum states. The basic idea of our method is to learn a unitary operation $\hat{U}$ that transforms a given unknown state $|\psi_\tau\rangle$ to a known fiducial state $|f\rangle$.…
We obtain the optimal scheme for estimating unknown qubit mixed states when an arbitrary number N of identically prepared copies is available. We discuss the case of states in the whole Bloch sphere as well as the restricted situation where…
$W$ states are quantum correlated states possessing both bipartite and multipartite entanglement, which makes them useful for several quantum algorithms. We propose a protocol to generate these states by exploiting {\it topological ring…