Related papers: Direct Schmidt number measurement of high-gain par…
We study the spatial properties of high-gain parametric down-conversion (PDC). From the Hamiltonian we find the Schmidt modes, apply the Bloch-Messiah reduction, and calculate analytically the measurable quantities, such as the angular…
The amount of entanglement that exists in a parametric down-converted state is investigated in terms of all the degrees of freedom of the state. We quantify the amount of entanglement by the Schmidt number of the state, represented as a…
An entanglement measure for pure-state continuous-variable bi-partite problem, the Schmidt number, is analytically calculated for one simple model of atom-field scattering.
We measure the transverse entanglement of photon pairs on their propagation from the near to the far field of spontaneous parametric downconversion (SPDC). The Fedorov ratio, depending on the widths of conditional and unconditional…
We put forward an approach to estimate the amount of bipartite spatial entanglement of down-converted photon states correlated in orbital angular momentum and the magnitude of the transverse (radial) wave vectors. Both degrees of freedom…
The Schmidt number represents the genuine entanglement dimension of a bipartite quantum state. We derive simple criteria for the Schmidt number of a density matrix in arbitrary local dimensions. They are based on the trace norm of…
The Schmidt number is a fundamental parameter characterizing the properties of quantum states, and the local projections are a fundamental operation in quantum physics. We investigate the relation between the Schmidt numbers of bipartite…
The Schmidt number characterizes the quantum entanglement of a bipartite mixed state and plays a significant role in certifying entanglement of quantum states. We derive a Schmidt number criterion based on the trace norm of the correlation…
Quantum entanglement is a fascinating phenomenon, especially if it is observed at the macroscopic scale. Importantly, macroscopic quantum correlations can be revealed only by accurate measurement outcomes and strategies. Here, we formulate…
The ability to efficiently characterize the spatial correlations of entangled states of light is critical for applications of many quantum technologies such as quantum imaging. Here, we demonstrate highly efficient theoretical and…
The Schmidt number is of crucial importance in characterizing the bipartite pure states. We explore and propose here a generalization of Schmidt number for states in multipartite systems. It is shown to be entanglement monotonic and valid…
Quantum entanglement associated with transverse wave vectors of down conversion photons is investigated based on the Schmidt decomposition method. We show that transverse entanglement involves two variables: orbital angular momentum and…
The Schmidt numbers quantify the entanglement degree of quantum states. Quantum states with high Schmidt numbers provide a larger advantage in various quantum information processing tasks compared to quantum states with low Schmidt numbers.…
Higher dimensional entangled states demonstrate significant advantages in quantum information processing tasks. Schmidt number is a quantity on the entanglement dimension of a bipartite state. Here we build families of k-positive maps from…
Spontaneous parametric down-conversion (SPDC) is the most widely-used source of high-dimensional entangled two-photon states, and the entanglement in the spatial degree of freedom is considered best suited for harnessing high-dimensional…
The direct measurement of a complex wavefunction has been recently realized by using weak-values. In this paper, we introduce a method that exploits sparsity for compressive measurement of the transverse spatial wavefunction of photons. The…
We explore, both experimentally and theoretically, the propagation dynamics of spatially entangled photon pairs (biphotons). Characterization of entanglement is done via the Schmidt number, which is a universal measurement of the degree of…
Quantum entanglement is an important resource in many modern technologies, like quantum computation or quantum communication and information processing. Therefore, most interest is given to detect and quantify entangled states. Entanglement…
A deep understanding of quantum entanglement is vital for advancing quantum technologies. The strength of entanglement can be quantified by counting the degrees of freedom that are entangled, which results in a quantity called Schmidt…
We analytically calculate the average value of i-th largest Schmidt coefficient for random pure quantum states. Schmidt coefficients, i.e., eigenvalues of the reduced density matrix, are expressed in the limit of large Hilbert space size…