Related papers: Random measurement bases, quantum state distinctio…
Quantum state tomography (QST) is a fundamental task in quantum information science that aims to reconstruct unknown quantum states from measurement data. However, the exponential growth of Hilbert-space dimension with system size makes…
We introduce a new method to estimate unknown pure $d$-dimensional quantum states using the probability distributions associated with only three measurement bases. Measurement results of $2d$ projectors are employed to generate a set of…
A central challenge in quantum metrology is identifying optimal measurements that saturate the quantum Cramer-Rao bound under realistic constraints, e.g., local measurements. We show that symmetries of the probe state provide a general…
We consider the problem of designing an optimal quantum detector to minimize the probability of a detection error when distinguishing between a collection of quantum states, represented by a set of density operators. We show that the design…
Quantum tomography is a fundamental technique for characterizing, benchmarking, and verifying quantum states and devices. It plays a crucial role in advancing quantum technologies and deepening our understanding of quantum mechanics.…
Mutually unbiased bases (MUBs) and symmetric informationally complete (SIC) positive operator-valued measurements (POVMs) are two related topics in quantum information theory. They are generalized to mutually unbiased measurements (MUMs)…
We derive the class of covariant measurements which are optimal according to the maximum likelihood criterion. The optimization problem is fully resolved in the case of pure input states, under the physically meaningful hypotheses of…
We establish three impossibility results regarding our knowledge of the quantum state of the universe. Suppose the universal quantum state is a typical unit vector in a high-dimensional subspace $\mathscr{H}_0$ of Hilbert space…
We develop a sufficient condition for the least-squares measurement (LSM), or the square-root measurement, to minimize the probability of a detection error when distinguishing between a collection of mixed quantum states. Using this…
We address perfect discrimination of two separable states. When available states are restricted to separable states, we can theoretically consider a larger class of measurements than the class of measurements allowed in quantum theory. The…
Distinguishing different quantum states is a fundamental task having practical applications for information processing. Despite the efforts devoted so far, however, strategies for optimal discrimination are known only for specific examples.…
We address the problem of characterizing the steerability of quantum states under restrictive measurement scenarios, i.e., the problem of determining whether a quantum state can demonstrate steering when subjected to $N$ measurements of $k$…
Quantum State Tomography is the task of determining an unknown quantum state by making measurements on identical copies of the state. Current algorithms are costly both on the experimental front -- requiring vast numbers of measurements --…
We study the quantum communication protocol of remote state preparation (RSP) for pure states of qubits encoded in single photons transmitted through a double slit, the so-called spatial qubits. Two measurement strategies that one can adopt…
We consider a fixed quantum measurement performed over $n$ identical copies of quantum states. Using a rigorous notion of distinguishability We consider a fixed quantum measurement performed over $n$ identical copies of quantum states.…
We address a problem of identifying a given pure state with one of two reference pure states, when no classical knowledge on the reference states is given, but a certain number of copies of them are available. We assume the input state is…
We present a new method to measure the work $w$ performed on a driven quantum system and to sample its probability distribution $P(w)$. The method is based on a simple fact that remained unnoticed until now: Work on a quantum system can be…
The optimization conditions for minimum error discrimination of linearly independent pure states comprise of two kinds: stationary conditions over the space of rank one projective measurements and the global maximization conditions. A…
We study the problem of quantum-state tomography under the assumption that the state of the system is close to pure. In this context, an efficient measurements that one typically formulates uniquely identify a pure state from within the set…
We study how useful random states are for quantum metrology, i.e., surpass the classical limits imposed on precision in the canonical phase estimation scenario. First, we prove that random pure states drawn from the Hilbert space of…