Related papers: Toward Instance-Optimal State Certification With I…
We consider the apparatus in a quantum measurement process to be in a mixed state. We propose a simple upper bound on the probability of correctly distinguishing any number of mixed states. We use this to derive fundamental bounds on the…
One of the main challenges of quantum information is the reliable verification of quantum entanglement. The conventional detection schemes require repeated measurement on a large number of identically prepared systems. This is hard to…
Quantum learning from state samples is often benchmarked in a fixed-budget paradigm, relating error to a prescribed number of copies. We instead adopt a stopping-time viewpoint: in minimal-feedback learning, the learning completion can be…
This thesis aims to establish notions of symmetry for quantum states and channels as well as describe algorithms to test for these properties on quantum computers. Ideally, the work will serve as a self-contained overview of the subject. We…
This paper investigates symmetric composite binary quantum hypothesis testing (QHT), where the goal is to determine which of two uncertainty sets contains an unknown quantum state. While asymptotic error exponents for this problem are…
Various aspects of distillation of noisy entanglement and some associated effects in quantum error correction are considered. In particular we prove that if only one--way classical communication (from Alice to Bob) is allowed and the shared…
The idea of self-testing is to render guarantees concerning the inner workings of a device based on the measurement statistics. It is one of the most formidable quantum certification and benchmarking schemes. Recently it was shown by…
Experimentally quantifying entanglement and coherence are extremely important for quantum resource theory. However, because the quantum state tomography requires exponentially growing measurements with the number of qubits, it is hard to…
The accurate characterization of quantum systems is essential for the advancement of quantum technologies. In particular, certifying convex functions of quantum states plays a central role in many applications. We present a certification…
We demonstrate to what extent many copies of maximally entangled two-qubit states enable for generating a greater amount of certified randomness than that can be certified from a single copy. Although it appears that greater the dimension…
Symmetry is a unifying concept in physics. In quantum information and beyond, it is known that quantum states possessing symmetry are not useful for certain information-processing tasks. For example, states that commute with a Hamiltonian…
We extend a recent method to detect lower bounds to the quantum capacity of quantum communication channels by considering realistic scenarios with general input probe states and arbitrary detection procedures at the output. Realistic…
Certifying the fidelity of a prepared state to a target stabilizer state is a fundamental task in quantum information processing. Ref. [Phys. Rev. A 99, 042337 (2019)] gave the optimal worst-case lower bound from one fixed stabilizer…
Quantum-enhanced metrology can be achieved by entangling a probe with an auxiliary system, passing the probe through an interferometer, and subsequently making measurements on both the probe and auxiliary system. Conceptually, this…
Computing quantum state fidelity will be important to verify and characterize states prepared on a quantum computer. In this work, we propose novel lower and upper bounds for the fidelity $F(\rho,\sigma)$ based on the "truncated fidelity"…
Quantum state discrimination is a fundamental information processing task that serves as a building block for numerous applications and provides implications at the foundational level. In this work, we consider minimum error discrimination…
In this thesis we study the problem of unambiguously discriminating two mixed quantum states. We first present reduction theorems for optimal unambiguous discrimination of two generic density matrices. We show that this problem can be…
We study the composite sequential quantum hypothesis testing (SQHT) problem, where the objective is to distinguish a null quantum state from a set of alternative quantum states. We propose a mixture-sequential quantum probability ratio test…
Self-testing protocols are methods to determine the presence of shared entangled states in a device independent scenario, where no assumptions on the measurements involved in the protocol are made. A particular type of self-testing…
The problem of identifying measurement scenarios capable of revealing state-independent contextuality in a given Hilbert space dimension is considered. We begin by showing that for any given dimension $d$ and any measurement scenario…