Related papers: Quantum Cloning in $d$ dimensions
A scalable, high-performance quantum processor can be implemented using near-resonant dipole-dipole interacting dopants in a solid state host. In this scheme, the qubits are represented by ground and subradiant states of effective dimers…
Using angular position-orbital angular momentum entangled photons, we propose an experiment to generate maximally entangled states of $D$-dimensional quantum systems, the so called qudits, by exploiting correlations of parametric…
The tomographic description of a quantum state is formulated in an abstract infinite dimensional Hilbert space framework, the space of the Hilbert-Schmidt linear operators, with trace formula as scalar product. Resolutions of the unity,…
We generalize the formulation of non-commutative quantum mechanics to three dimensional non-commutative space. Particular attention is paid to the identification of the quantum Hilbert space in which the physical states of the system are to…
A particle which lives in a d-dimensional ordinary and a d-dimensional Grassmann space manifests itself in an ordinary four-dimensional subspace as a spinor, a scalar or a vector with charges. Operators of the Lorentz transformations and…
The optimal phase covariant cloning machine (PQCM) broadcasts the information associated to an input qubit into a multi-qubit systems, exploiting a partial a-priori knowledge of the input state. This additional a priori information leads to…
An array of $N$ closely spaced dipole coupled quantum emitters exhibits super- and subradiance with characteristic tailorable spatial radiation patterns. Optimizing their geometry and distance with respect to the spatial profile of a near…
We propose a quantum cloning machine, which clones a qubit into two clones assuming known modulus of expectation value of Pauli Z-matrix. The process is referred to as the mirror phase-covariant cloning, for which the input state is a…
After the appearance of the no-cloning theorem, approximate quantum cloning machines (QCMs) have become one of the most well-studied subject in quantum information theory. Among several measures to quantify the performance of a QCM,…
The cloning of quantum variables with continuous spectra is analyzed. A universal - or Gaussian - quantum cloning machine is exhibited that copies equally well the states of two conjugate variables such as position and momentum. It also…
We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed…
Quantum Fourier transform (QFT) is a key ingredient of many quantum algorithms where a considerable amount of ancilla qubits and gates are often needed to form a Hilbert space large enough for high-precision results. Qubit recycling reduces…
We introduce a high-dimensional quantum encoding based on coherent mode-dependent single-photon subtraction from multimode squeezed states. This encoding can be seen as a generalization to the case of non-zero squeezing of the standard…
We find an optimal quantum cloning machine, which clones qubits of arbitrary symmetrical distribution around the Bloch vector with the highest fidelity. The process is referred to as phase-independent cloning in contrast to the standard…
Encoding in a high-dimensional Hilbert space improves noise resilience in quantum information processing. This approach, however, may result in cross-mode coupling and detection complexities, thereby reducing quantum cryptography…
We describe three ways of modifying the relativistic Heisenberg algebra - first one not linked with quantum symmetries, second and third related with the formalism of quantum groups. The third way is based on the identification of…
Quantum computation can be achieved by preparing an appropriate initial product state of qudits and then letting it evolve under a fixed Hamiltonian. The readout is made by measurement on individual qudits at some later time. This approach…
We explore the conceptual usefulness of Riemannian geometric tools induced by the statistical concept of distinguishability in quantifying the effect of a depolarizing channel on quantum states. Specifically, we compare the geometries of…
The $D$-dimensional two-parameter deformed algebra with minimal length introduced by Kempf is generalized to a Lorentz-covariant algebra describing a ($D+1$)-dimensional quantized space-time. For D=3, it includes Snyder algebra as a special…
The state of a finite-dimensional quantum system is described by a density matrix that can be decomposed into a real diagonal, a real off-diagonal and and an imaginary off-diagonal part. The latter plays a peculiar role. While it is…