Related papers: Universal and Efficient Quantum State Verification…
The well-known Schmidt decomposition, or equivalently, the complex singular value decomposition, states that a pure quantum state of a bipartite system can always be brought into a "diagonal" form using local unitary transformations. In…
Verifying prepared quantum states is crucial for hybrid systems whose subsystems may have different local dimensions. We present a generalized stabilizer framework and associated test that apply to general multi-qudit states, including…
Recently, a technique known as quantum symmetry test has gained increasing attention for detecting bipartite entanglement in pure quantum states. In this work we show that, beyond qualitative detection, a family of well-defined measures of…
In this paper, we give out some effective criterions which can be used to judge the separability of multipartite pure states. We obtain the relationship between separability and Schmidt decomposable of multipartite pure states in Theorem1.…
Estimation of quantum states and measurements is crucial for the implementation of quantum information protocols. The standard method for each is quantum tomography. However, quantum tomography suffers from systematic errors caused by…
Characterizing large quantum systems with minimal assumptions is a central challenge in quantum information science. Self-testing provides the strongest form of certification by identifying the underlying quantum state solely from observed…
Quantum self-testing addresses the following question: is it possible to verify the existence of a multipartite state even when one's measurement devices are completely untrusted? This problem has seen abundant activity in the last few…
Quantum state tomography, the ability to deduce the state of a quantum system from measured data, is the gold standard for verification and benchmarking of quantum devices. It has been realized in systems with few components, but for larger…
We find a canonical form for pure states of a general multipartite system, in which the constraints on the coordinates (with respect to a factorisable orthonormal basis) are simply that certain ones vanish and certain others are real. For…
Characterizing increasingly complex quantum systems is a central task in quantum information science, yet experimental costs often scale prohibitively with system size. Certifying key properties using simple local measurements is highly…
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…
In the realm of quantum information processing, the efficient characterization of entangled states poses an overwhelming challenge, rendering the traditional methods including quantum tomography unfeasible and impractical. To tackle this…
A general framework is developed for separating classical and quantum correlations in a multipartite system. Entanglement is defined as the difference in the correlation information encoded by the state of a system and a suitably defined…
We present a generalized Schmidt decomposition for a pure system with any number of two-level subsystems. The basis is symmetric under the permutation of the parties and is derived from the product state defining the injective tensor norm…
The rapid development of quantum computing technologies already made it possible to manipulate a collective state of several dozen of qubits. This success poses a strong demand on efficient and reliable methods for characterization and…
Detecting entanglement in multipartite quantum states is an inherently probabilistic process, typically with a few measured samples. The level of confidence in entanglement detection quantifies the scheme's validity via the probability that…
Mutually unbiased bases determine an optimal set of measurements to extract complete information about the quantum state of a system. However, quite often a priori information about the state exist, making some of the measurement bases…
Quantum state tomography (QST) aims at estimating a quantum state from averaged quantum measurements made on copies of the state. Most quantum algorithms rely on QST at some point and it is a well explored topic in the literature, mostly…
In this article we propose a method to estimate with high accuracy pure quantum states of a single qudit. Our method is based on the minimization of the squared error between the complex probability amplitudes of the unknown state and its…
We investigate the dimensionality of bipartite quantum systems by construction of a device-independent null witness test. This test assesses whether a given bipartite state conforms with the expected quantum dimension, Schmidt number, and…