相关论文: Estimating Pre- and Post-Selected Ensembles

The framework of postselection is becoming more and more important in various recent directions in Quantum Computation research. Postselection renders simple computational models able to perform general quantum computation. This was first…

Quantum chaos in many-body systems provides a bridge between statistical and quantum physics with strong predictive power. This framework is valuable for analyzing properties of complex quantum systems such as energy spectra and the…

Estimating properties of a quantum state is an indispensable task in various applications of quantum information processing. To predict properties in the post-processing stage, it is inherent to first perceive the quantum state with a…

Non-orthogonal quantum states pose a fundamental challenge in quantum information processing, as they cannot be distinguished with absolute certainty. Conventionally, the focus has been on minimizing error probability in quantum state…

To elucidate ideal measurements, one must explain how individual events emerge from quantum theory which deals with statistical ensembles, and how different may end up with different final states. This so-called "measurement problem" is…

To describe the pre- and post-selected quantum ensembles, a complex quantity called the weak value of an operator is used. The weak value is highly controversial due to the fact that it is not bounded by the possible eigenvalues of the…

The guesswork of a quantum ensemble quantifies the minimum number of guesses needed in average to correctly guess the state of the ensemble, when only one state can be queried at a time. Here, we derive analytical solutions of the guesswork…

Random Quantum States are presently of interest in the fields of quantum information theory and quantum chaos. Moreover, a detailed study of their properties can shed light on some foundational issues of the quantum statistical mechanics…

A new ensemble interpretation of quantum mechanics is proposed according to which the ensemble associated to a quantum state really exists: it is the ensemble of all the systems in the same quantum state in the universe. Individual systems…

Suppose you receive a sequence of qubits where each qubit is guaranteed to be in one of two pure states, but you do not know what those states are. Your task is to determine the states. This can be viewed as a kind of quantum state learning…

We build a general quantum state tomography framework that makes use of machine learning techniques to reconstruct quantum states from a given set of coincidence measurements. For a wide range of pure and mixed input states we demonstrate…

Quantum state tomography is a fundamental tool in quantum information processing. It allows us to estimate the state of a quantum system by measuring different observables on many identically prepared copies of the system. This is, in…

A quantum ensemble $\{(p_x, \rho_x)\}$ is a set of quantum states each occurring randomly with a given probability. Quantum ensembles are necessary to describe situations with incomplete a priori information, such as the output of a…

In the theory of classical statistical inference one can derive a simple rule by which two or more observers may combine {\em independently} obtained states of knowledge together to form a new state of knowledge, which is the state which…

Given a finite number of copies of an unknown qubit state that have already been measured optimally, can one still extract any information about the original unknown state? We give a positive answer to this question and quantify the…

We analyze the average of weak values over statistical ensembles of pre- and post-selected states. The protocol of weak values, proposed by Aharonov et al., is the result of a weak measurement conditional on the outcome of a subsequent…

We address the problem of distinguishing among a finite collection of quantum states, when the states are not entirely known. For completely specified states, necessary and sufficient conditions on a quantum measurement minimizing the…

We demonstrate that quantum instruments can provide a unified operational foundation for quantum theory. Since these instruments directly correspond to laboratory devices, this foundation provides an alternate, more experimentally grounded,…

We present a new procedure for quantum state reconstruction based on weak continuous measurement of an ensemble average. By applying controlled evolution to the initial state new information is continually mapped onto the measured…

Ensemble Kalman methods constitute an increasingly important tool in both state and parameter estimation problems. Their popularity stems from the derivative-free nature of the methodology which may be readily applied when computer code is…