Related papers: Structure of minimum-error quantum state discrimin…
We consider the optimal discrimination of nonorthogonal qubit states with post-measurement information and provide an analytic structure of the optimal measurements. We also show that there is always a null optimal measurement when…
Random ensembles of pure states have proven to be extremely important in various aspects of quantum physics such as benchmarking the performance of quantum circuits, testing for quantum advantage, providing novel insights for many-body…
We consider decision problems on finite sets of hypotheses represented by pairwise different shift-invariant states on a quantum spin chain. The decision in favor of one of the hypotheses is based on outputs of generalized measurements…
Quantum indistinguishability of non-orthogonal quantum states is a valuable resource in quantum information applications such as cryptography and randomness generation. In this article, we present a sequential state-discrimination scheme…
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…
Quantum state designs, by enabling an efficient sampling of random quantum states, play a quintessential role in devising and benchmarking various quantum protocols with broad applications ranging from circuit designs to black hole physics.…
Rather than point estimators, states of a quantum system that represent one's best guess for the given data, we consider optimal regions of estimators. As the natural counterpart of the popular maximum-likelihood point estimator, we…
The most common error models for quantum computers assume the independence of errors on different qubits. However, most noise mechanisms have some correlations in space. We show how to improve quantum information processing for few-qubit…
We discuss the problem of estimating a general (mixed) qubit state. We give the optimal guess that can be inferred from any given set of measurements. For collective measurements and for a large number $N$ of copies, we show that the error…
The discrimination of quantum states is a central problem in quantum information science and technology. Meanwhile, partial post-selection has emerged as a valuable tool for quantum state engineering. In this work, we bring these two areas…
In this work, we consider optimal state discrimination for a quantum system that interacts with an environment, i.e., states evolve under a quantum channel. We show the conditions on a quantum channel and an ensemble of states such that a…
Quantum Boltzmann machine extends the classical Boltzmann machine learning to the quantum regime, which makes its power to simulate the quantum states beyond the classical probability distributions. We develop the BFGS algorithm to study…
The search problem is to find a state satisfying certain properties out of a given set. Grover's algorithm drives a quantum computer from a prepared initial state to the target state and solves the problem quadratically faster than a…
We consider a special form of state discrimination in which after the measurement we are given additional information that may help us identify the state. This task plays a central role in the analysis of quantum cryptographic protocols in…
We prove that the states secretly chosen from a mixed state set can be perfectly discriminated if and only if these states are orthogonal. The sufficient and necessary condition when nonorthogonal quantum mixed states can be unambiguously…
We theoretically investigate schemes to discriminate between two nonorthogonal quantum states given multiple copies. We consider a number of state discrimination schemes as applied to nonorthogonal, mixed states of a qubit. In particular,…
If the system is known to be in one of two non-orthogonal quantum states, $|\psi_1\rangle$ or $|\psi_2\rangle$, it is not possible to discriminate them by a single measurement due to the unitarity constraint. In a regular Hermitian quantum…
The quantum analogue of the equality function, known as the quantum state identity problem, is the task of deciding whether $n$ unknown quantum states are equal or unequal, given the promise that all states are either pairwise orthogonal or…
We consider the problem of estimating the state of a large but finite number $N$ of identical quantum systems. In the limit of large $N$ the problem simplifies. In particular the only relevant measure of the quality of the estimation is the…
The problem of unambiguous state discrimination consists of determining which of a set of known quantum states a particular system is in. One is allowed to fail, but not to make a mistake. The optimal procedure is the one with the lowest…