arXiv subjects

Pranjal Agarwal

Publications and source records attributed to Pranjal Agarwal.

3 recordsLinked to original sources

arXiv2026

Detection of patterns in a discrete-outcome sensor network

A discrete outcome quantum sensor network is one in which we are only interested in which detectors are activated. This can be studied in either the strong or weak interaction regime. If the detectors interact strongly with the environment, it is possible to definitely find which ones were activated. If the interaction is weaker, there is a possibility of making an error, and the object is to minimize the probability of this happening. Here we will be interested in this weaker interaction regime. We will also assume that only certain patterns of detectors will be activated, different patterns being translated versions of a fundamental one. Our object will be to find which pattern has been activated. We will look at both one and two-dimensional detector arrays and make use of techniques from minimum-error state discrimination.

quant-ph↗

arXiv2025

Interference and Measurement: Changing amplitude phase information to amplitude magnitude information

There are quantum procedures that encode the solutions to a problem in the phases of quantum amplitudes. This happens in some quantum optimization algorithms in which the value of a function to be maximized or minimized is represented by a phase. An example of this is the QAOA algorithm for the MaxCut problem in which one encodes the number of edges connecting the sets resulting from a partition of the vertices of a graph into phases of amplitudes of a quantum state. Another is the minimum vertex cover problem in which the number of edges included in the cover is encoded in phases. Here we want to see what can be done if we only use simple aspects of quantum mechanics, interference and measurement, to manipulate the magnitudes of the amplitudes whose phases encode the relevant information. The idea is to use constructive interference to enhance the amplitudes that contain useful information and destructive interference to suppress those that do not. We examine examples, both analytically and numerically. We also show how the results of sequences of measurements can be used to gain information about the landscape of solutions.

quant-ph↗

arXiv2025

State learning from pairs of states

Suppose you receive a sequence of qubits where each qubit is guaranteed to be in one of two pure states, but you do not know what those states are. Your task is to determine the states. This can be viewed as a kind of quantum state learning -- or quantum state estimation. A problem is that, without more information, all that can be determined is the density matrix of the sequence and, in general, density matrices can be decomposed into pure states in many different ways. To solve the problem, additional information, either classical or quantum, is required. We show that if an additional copy of each qubit is supplied -- that is, one receives pairs of qubits, both in the same state, rather than single qubits -- the task can be accomplished. This is possible because the mixed two-qubit state has a unique decomposition into pure product states. For illustration, we simulate numerically the symmetric, informationally complete measurement of a sequence of qubit pairs and show that the unknown states and their respective probabilities of occurrence can be inferred from the data with high accuracy. Finally, we propose an experiment that employs a product measurement and can be realized with existing technology, and we demonstrate how the data tell us the states and their probabilities. We find that it is enough to detect a few thousand qubit pairs.

quant-ph↗