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Quantum State Tomography (QST) is a fundamental technique in Quantum Information Processing (QIP) for reconstructing unknown quantum states. However, the conventional QST methods are limited by the number of measurements required, which…
Quantum state tomography is the fundamental physical task of learning a complete classical description of an unknown state of a quantum system given coherent access to many identical samples of it. The complexity of this task is commonly…
Comparison of statistical models (experiments) is an important branch of mathematical statistics, which gives deep insights in many aspects of foundation of statistics. So far, there are two quantum versions of the concept: Comparison with…
We propose an iterative algorithm for incomplete quantum process tomography, with the help of quantum state estimation, based on the combined principles of maximum-likelihood and maximum-entropy. The algorithm yields a unique estimator for…
The engine that powers quantum cryptography is the principle that there are no physical means for gathering information about the identity of a quantum system's state (when it is known to be prepared in one of a set of nonorthogonal states)…
We show that combining randomized measurement protocols with importance sampling allows for characterizing entanglement in significantly larger quantum systems and in a more efficient way than in previous work. A drastic reduction of…
Quantum state discrimination depicts the general progress of extracting classical information from quantum systems. We show that quantum state discrimination can be realized in a device-independent scenario using tools of self-testing…
Quantum process tomography, the standard procedure to characterize any quantum channel in nature, is affected by a circular argument: in order to characterize the channel, the tomographic preparation and measurement need in turn to be…
A minimal set of measurement operators for quantum state tomography has in the non-degenerate case ideally eigenbases which are mutually unbiased. This is different for the degenerate case. Here, we consider the situation where the…
We consider quantum state tomography with measurement procedures of the following type: First, we subject the quantum state we aim to identify to a know time evolution for a desired period of time. Afterwards we perform a measurement with a…
In quantum information theory, the reliable and effective detection of entanglement is of paramount importance. However, given an unknown state, assessing its entanglement is a challenging task. To attack this problem, we investigate the…
We report on an intrinsic relationship between the maximum-likelihood quantum-state estimation and the representation of the signal. A quantum analogy of the transfer function determines the space where the reconstruction should be done…
Indistinguishable quantum states interfere, but the mere possibility of obtaining information that could distinguish between overlapping states inhibits quantum interference. Quantum interference imaging can outperform classical imaging or…
Quantum tomography makes it possible to obtain comprehensive information about certain logical elements of a quantum computer. In this regard, it is a promising tool for debugging quantum computers. The practical application of tomography,…
Several methods, known as Quantum Process Tomography, are available to characterize the evolution of quantum systems, a task of crucial importance. However, their complexity dramatically increases with the size of the system. Here we…
Quantum information technologies provide promising applications in communication and computation, while machine learning has become a powerful technique for extracting meaningful structures in 'big data'. A crossover between quantum…
Amongst the multitude of state reconstruction techniques, the so-called "quantum tomography" seems to be the most fruitful. In this letter, I will start by developing the mathematical apparatus of quantum tomography and, later, I will…
We train convolutional neural networks to predict whether or not a set of measurements is informationally complete to uniquely reconstruct any given quantum state with no prior information. In addition, we perform fidelity benchmarking…
Entanglement is at the heart of most quantum information tasks, and therefore considerable effort has been made to find methods of deciding the entanglement content of a given bipartite quantum state. Here, we prove a fundamental limitation…
In quantum state tomography, the estimated frequencies do not correspond directly to a physical quantum state, due to statistical fluctuations. Thus, one resorts to point estimators that return the state that matches observations the best,…