相关论文: Entropy and Geometry of Quantum States

The problem of quantum state discrimination between two wave functions of a particle in a square well potential is considered. The optimal minimum-error probability for the state discrimination is known to be given by the Helstrom bound. 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…

We consider the class of metrics that can be obtained from those of nonextreme black holes by limiting transitions to the extreme state such that the near-horizon geometry expands into a whole manifold. These metrics include, in particular,…

The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…

Precision and accuracy, as two crucial criteria for quantum metrology, have previously lacked rigorous definitions and distinctions. In this paper, we provide a unified definition of precision and accuracy from the perspective of…

An important task for quantum information processing is optimal discrimination between two non-orthogonal quantum states, which until now has only been realized optically. Here, we present and compare experimental realizations of optimal…

We investigate the behavior of vortex bound states in the quantum limit by self-consistently solving the Bogoliubov-de Gennes equation. We find that the energies of the vortex bound states deviates from the analytical result…

Employing the volume of quantum steering ellipsoids (QSEs) as a measure on the fifteen-dimensional convex set of two-qubit states, we estimate the ratio of the integral of the measure over the separable states to its integral over all…

The distinguishability between two quantum states can be defined in terms of their trace distance. The operational meaning of this definition involves a maximization over measurement projectors. Here we introduce an alternative definition…

Braunstein and Caves (1994) proposed to use Helstrom's {\em quantum information} number to define, meaningfully, a metric on the set of all possible states of a given quantum system. They showed that the quantum information is nothing else…

Every sufficiently rich set of measurements on a fixed quantum system defines a statistical norm on the states of that system via the optimal bias that can be achieved in distinguishing the states using measurements from that set (assuming…

We prove the second law of thermodynamics and the nonequilibirum fluctuation theorem for pure quantum states.The entire system obeys reversible unitary dynamics, where the initial state of the heat bath is not the canonical distribution but…

The asymptotic discrimination problem of two quantum states is studied in the setting where measurements are required to be invariant under some symmetry group of the system. We consider various asymptotic error exponents in connection with…

Due to the potential of quantum advantage to surpass the standard quantum limit (SQL), the nonlinear interferometers have garnered significant attention from researchers in the field of precision measurement. However, many practical…

Using the quantum Hamiltonian for a gravitational system with boundary, we find the partition function and derive the resulting thermodynamics. The Hamiltonian is the boundary term required by functional differentiability of the action for…

A version of quantum Cram\'{e}r-Rao bound dictates that the covariance of any set of operators is bounded by a product of the derivatives of expectation values and the inverse of quantum metric. We elaborate that because quantum metric…

A survey of various concepts in quantum information is given, with a main emphasis on the distinguishability of quantum states and quantum correlations. Covered topics include generalized and least square measurements, state discrimination,…

The Bell state measurement (BSM) is the projection of two qubits onto four orthogonal maximally entangled states. Here, we first propose how to appropriately define more general BSMs, that have more than four possible outcomes, and then…

Nonequilibrium dynamics of quantum many-body systems is challenging for classical computing, providing opportunities for demonstrating practical quantum computational advantage with analogue quantum simulators. Owing to the intimate…

We consider the estimation of an unknown parameter $\theta$ through a quantum probe at thermal equilibrium. The probe is assumed to be in a Gibbs state according to its Hamiltonian $H_\theta$, which is divided in a parameter-encoding term…