Related papers: Random unitary maps for quantum state reconstructi…
The purpose of this paper is to introduce techniques of obtaining optimal ways to determine a d-level quantum state or distinguish such states. It entails designing constrained elementary measurements extracted from maximal abelian subsets…
The reconstruction of quantum states from a sufficient set of experimental data can be achieved with arbitrarily weak measurement interactions. Since such weak measurements have negligible back-action, the quantum state reconstruction is…
The exponential growth in Hilbert space with increasing size of a quantum system means that accurately characterising the system becomes significantly harder with system dimension d. We show that self-guided tomography is a practical,…
The knowledge of the density matrix of a quantum state plays a fundamental role in several fields ranging from quantum information processing to experiments on foundations of quantum mechanics and quantum optics. Recently, a method has been…
Standard quantum state reconstruction techniques indicate that a detection efficiency of $0.5$ is an absolute threshold below which quantum interferences cannot be measured. However, alternative statistical techniques suggest that this…
Alternatively to the full reconstruction of an unknown quantum process, the so-called selective and efficient quantum process tomography (SEQPT) allows estimating, individually and up to the required accuracy, a given element of the matrix…
Consider the $n!$ different unitary matrices that permute $n$ $d$-dimensional quantum systems. If $d\geq n$ then they are linearly independent. This paper discusses a sense in which they are approximately orthogonal (with respect to the…
Reconstructing the density matrix of the quantum state of photons through a tomographically complete set of measurements, known as quantum state tomography, is an essential task in nearly all applications of quantum science and technology,…
We derive a new bound on the effectiveness of the Petz map as a universal recovery channel in approximate quantum error correction using the second sandwiched R\'{e}nyi relative entropy $\tilde{D}_{2}$. For large Hilbert spaces, our bound…
The ability of fully reconstructing quantum maps is a fundamental task of quantum information, in particular when coupling with the environment and experimental imperfections of devices are taken into account. In this context we carry out a…
We propose and experimentally demonstrate a quantum state tomography protocol that generalizes the Wallentowitz-Vogel-Banaszek-W\'odkiewicz point-by-point Wigner function reconstruction. The full density operator of an arbitrary quantum…
We consider the problem of certification of arbitrary ensembles of pure states and projective measurements solely from the experimental statistics in the prepare-and-measure scenario assuming the upper bound on the dimension of the Hilbert…
The problem of recovering a matrix of low rank from an incomplete and possibly noisy set of linear measurements arises in a number of areas. In order to derive rigorous recovery results, the measurement map is usually modeled…
The optimal quantum measurements for estimating different unknown parameters in a parameterized quantum state are usually incompatible with each other. Traditional approaches to addressing the measurement incompatibility issue, such as the…
Characterizing complex quantum systems is a vital task in quantum information science. Quantum tomography, the standard tool used for this purpose, uses a well-designed measurement record to reconstruct quantum states and processes. It is,…
We analyze how an action of a qubit channel (map) can be estimated from the measured data that are incomplete or even inconsistent. That is, we consider situations when measurement statistics is insufficient to determine consistent…
We demonstrate that the task of determining an unknown quantum state can be accomplished efficiently by making a sequential measurement of two observables $\hat{A}$ and $\hat{B}$, provided that the two observables are chosen in such a way…
We significantly extend recently developed methods to faithfully reconstruct unknown quantum states that are approximately low-rank, using only a few measurement settings. Our new method is general enough to allow for measurements from a…
Quantum computation and quantum control operate by building unitary transformations out of sequences of elementary quantum logic operations or applications of control fields. This paper puts upper bounds on the minimum time required to…
As one of the most intriguing intrinsic properties of quantum world, quantum superposition provokes great interests in its own generation. Oszmaniec [Phys. Rev. Lett. 116, 110403 (2016)] have proven that though a universal quantum machine…