相关论文: How many orthonormal bases are needed to distingui…
A long standing problem in quantum mechanics is the minimum number of observables required for the characterisation of unknown pure quantum states. The solution to this problem is specially important for the developing field of…
The question of determining the maximal number of mutually unbiased bases in dimension six has received much attention since their introduction to quantum information theory, but a definitive answer has still not been found. In this paper…
We present an analytical method to estimate pure quantum states using a minimum of three measurement bases in any finite-dimensional Hilbert space. This is optimal as two bases are insufficient to construct an informationally complete…
A long-standing problem in quantum physics is to determine the minimal number of measurement bases required for the complete characterization of unknown quantum states, a question of particular relevance to high-dimensional quantum…
For any finite dimensional Hilbert space, we construct explicitly five orthonormal bases such that the corresponding measurements allow for efficient tomography of an arbitrary pure quantum state. This means that such measurements can be…
Given a finite set of linearly independent quantum states, an observer who examines a single quantum system may sometimes identify its state with certainty. However, unless these quantum states are orthogonal, there is a finite probability…
We introduce a new method to estimate unknown pure $d$-dimensional quantum states using the probability distributions associated with only three measurement bases. Measurement results of $2d$ projectors are employed to generate a set of…
Finding the least measurement settings to determine an arbitrary pure state has been long known as the Pauli problem. In the fixed measurement scheme four orthonormal bases are required even though there are far less parameters in a pure…
Efficiently extracting information from pure quantum states using minimal observables on the main system is a longstanding and fundamental issue in quantum information theory. Despite the inability of probability distributions of position…
We tabulate bounds on the optimal number of mutually unbiased bases in R^d. For most dimensions d, it can be shown with relatively simple methods that either there are no real orthonormal bases that are mutually unbiased or the optimal…
We present a tomographic method which requires only $4d-3$ measurement outcomes to reconstruct \emph{any} pure quantum state of arbitrary dimension $d$. Using the proposed scheme we have experimentally reconstructed a large number of pure…
What is the minimal number of elements in a rank-1 positive-operator-valued measure (POVM) which can uniquely determine any pure state in $d$-dimensional Hilbert space $\mathcal{H}_d$? The known result is that the number is no less than…
One of the fundamental questions in quantum information theory is to find how many measurement bases are required to obtain the full information of a quantum state. While a minimum of four measurement bases is typically required to…
We introduce the problem of constructing weighted complex projective 2-designs from the union of a family of orthonormal bases. If the weight remains constant across elements of the same basis, then such designs can be interpreted as…
We present Schmidt decomposition formulas for mutually orthogonal two-qubit pure states and classify orthonormal sets based on their entanglement structure. First, we derive explicit Schmidt decomposition formulas for any pure state and…
We characterize minimal measurement setups for validating the quantum coherence of an unknown quantum state. We show that for a $d$-level system, the optimal strategy consists of measuring $d$ orthonormal bases such that each measured basis…
We discuss possibility of upper-bounding dimension of quantum states device-independently. Provided that the states are pure, it is possible to generate certain four states whose dimension is bounded by two.
It has been recently shown that an observable that identifies all pure states of a d-dimensional quantum system has minimally 4d-4 outcomes or slightly less (the exact number depending on the dimension d). However, no simple construction of…
We consider the average distance between four bases in dimension six. The distance between two orthonormal bases vanishes when the bases are the same, and the distance reaches its maximal value of unity when the bases are unbiased. We…
There has been great interest in finding sets of $m$ mutually unbiased bases which are compatible with a given space $\mathbb{C}^d$, specially in physics due to their interesting applications in quantum information theory. Several general…