Related papers: A Geometric Approach to Quantum State Separation
One of the most important questions in quantum information theory is the so-called separability problem. It involves characterizing the set of separable (or, equivalently entangled) states among mixed states of a multipartite quantum…
We investigate generalized measurements, based on positive-operator-valued measures, and von Neumann measurements for the unambiguous discrimination of two mixed quantum states that occur with given prior probabilities. In particular, we…
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…
We address the problem of distinguishing among a finite collection of quantum states, when the states are not entirely known. For completely specified states, necessary and sufficient conditions on a quantum measurement minimizing the…
We investigate quantum state discrimination with confidentiality. $N$ observers share a given quantum state belonging to a finite set of known states. The observers want to determine the state as accurately as possible and send a…
There has been much work in the recent past in developing the idea of quantum geometry to characterize and understand the structure of many-particle states. For mean-field states, the quantum geometry has been defined and analysed in terms…
An arbitrary quantum-optical process (channel) can be completely characterized by probing it with coherent states using the recently developed coherent-state quantum process tomography (QPT) [Lobino et al., Science 322, 563 (2008)]. In…
We present a theoretical study of minimum error probability discrimination, using quantum- optical probe states, of M optical phase shifts situated symmetrically on the unit circle. We assume ideal lossless conditions and full freedom for…
We consider the discrimination of two-party quantum states and provide a quantum data-hiding scheme using two-qubit separable states. We first provide a bound on the optimal local discrimination of two-party quantum states, and establish a…
We derive a necessary condition for the existence of a completely-positive, linear, trace-preserving map which deterministically transforms one finite set of pure quantum states into another. This condition is also sufficient for…
There are fundamental limits to the accuracy with which one can determine the state of a quantum system. I give an overview of the main approaches to quantum state discrimination. Several strategies exist. In quantum hypothesis testing, a…
The outcomes of quantum mechanical experiments are inherently random. It is therefore necessary to develop stringent methods for quantifying the degree of statistical uncertainty about the results of quantum experiments. For the…
We address the following state comparison problem: is it possible to design an experiment enabling us to unambiguously decide (based on the observed outcome statistics) on the sameness or difference of two unknown state preparations without…
We extend quantum state tomography with minimal cumulative disturbance, first investigated in [arXiv:2406.18370], to arbitrary finite-dimensional pure states. A learner sequentially receives fresh copies of an unknown pure state, chooses a…
Quantum state discrimination underlies various applications in quantum information processing tasks. It essentially describes the distinguishability of quantum systems in different states, and the general process of extracting classical…
We investigate local distinguishability of quantum states by use of the convex analysis about joint numerical range of operators on a Hilbert space. We show that any two orthogonal pure states are distinguishable by local operations and…
Quantum state estimation aims at determining the quantum state from observed data. Estimating the full state can require considerable efforts, but one is often only interested in a few properties of the state, such as the fidelity with a…
One of the many interesting features of quantum nonlocality is that the states of a multipartite quantum system cannot always be distinguished as well by local measurements as they can when all quantum measurements are allowed. In this…
We study quantum state estimation problems where the reference system with respect to which the state is measured should itself be treated quantum mechanically. In this situation, the difference between the system and the reference tends to…
This is a review of the geometry of quantum states using elementary methods and pictures. Quantum states are represented by a convex body, often in high dimensions. In the case of n-qubits, the dimension is exponentially large in n. The…