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We address a broad class of optimization problems of finding quantum measurements, which includes the problems of finding an optimal measurement in the Bayes criterion and a measurement maximizing the average success probability with a…
We consider the problem of designing an optimal quantum detector that distinguishes unambiguously between a collection of mixed quantum states. Using arguments of duality in vector space optimization, we derive necessary and sufficient…
We study the local implementation of POVMs when we require only the faithful reproduction of the statistics of the measurement outcomes for all initial states. We first demonstrate that any POVM with separable elements can be implemented by…
Quantum states have high affinity for errors and hence error correction is of utmost importance to realise a quantum computer. Laflamme showed that 5 qubits are necessary to correct a single error on a qubit. In a Pauli error model, four…
According to the geometric characterization of measurement assemblages and local hidden state (LHS) models, we propose a steering criterion which is both necessary and sufficient for two-qubit states under arbitrary measurement sets. A…
Determining when the multiparameter quantum Cram\'er--Rao bound (QCRB) is saturable with experimentally relevant single-copy measurements is a central open problem in quantum metrology. Here we establish an equivalence between QCRB…
Quantum detector tomography is a fundamental technique for calibrating quantum devices and performing quantum engineering tasks. In this paper, we design optimal probe states for detector estimation based on the minimum upper bound of the…
We develop error-tolerant quantum state discrimination(QSD) strategies that maintain reliable performance under moderate noise. Two complementary approaches are proposed: CrossQSD, which generalizes unambiguous discrimination with tunable…
A geometrically uniform (GU) ensemble is a uniformly weighted quantum state ensemble generated from a fixed state by a unitary representation of a finite group $G$. In this work we analyze the problem of discriminating GU ensembles from…
Quantum algorithms use the principles of quantum mechanics, as for example quantum superposition, in order to solve particular problems outperforming standard computation. They are developed for cryptography, searching, optimisation,…
We derive a general lower bound on the minimum-error probability for {\it ambiguous discrimination} between arbitrary $m$ mixed quantum states with given prior probabilities. When $m=2$, this bound is precisely the well-known Helstrom…
Detecting genuine multipartite entanglement (GME) is a state-characterization task that benchmarks coherence and experimental control in quantum systems. Existing GME tests often require joint measurements on many qubits, posing challenges…
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…
Quantum state tomography (QST) remains the gold standard for benchmarking and verification of near-term quantum devices. While QST for a generic quantum many-body state requires an exponentially large amount of resources, most physical…
In this paper we consider the optimal discrimination of two mixed qubit states for a measurement that allows a fixed rate of inconclusive results(FRIR). Our strategy for the problem is to transform the FRIR of two qubit states into a…
Geometric quantum computation offers a practical strategy toward robust quantum computation due to its inherently error tolerance. However, the rigorous geometric conditions lead to complex and/or error-disturbed quantum controls,…
Quantum machine learning (QML) algorithms have obtained great relevance in the machine learning (ML) field due to the promise of quantum speedups when performing basic linear algebra subroutines (BLAS), a fundamental element in most ML…
A group theoretic framework is introduced that simplifies the description of known quantum error-correcting codes and greatly facilitates the construction of new examples. Codes are given which map 3 qubits to 8 qubits correcting 1 error, 4…
In a general optimized measurement scheme for discriminating between nonorthogonal quantum states, the error rate is minimized under the constraint of a fixed rate of inconclusive outcomes (FRIO). This so-called optimal FRIO measurement…
Examples of geometric phases abound in many areas of physics. They offer both fundamental insights into many physical phenomena and lead to interesting practical implementations. One of them, as indicated recently, might be an inherently…