相关论文: Optimal Non-Universally Covariant Cloning
The paper is devoted to integral quantization, a procedure based on operator-valued measure and resolution of the identity. We insist on covariance properties in the important case where group representation theory is involved. We also…
We investigate the question of studying spectral clustering in a Hilbert space where the set of points to cluster are drawn i.i.d. according to an unknown probability distribution whose support is a union of compact connected components. We…
A scheme for optimal Gaussian cloning of optical coherent states is proposed and experimentally demonstrated. Its optical realization is based entirely on simple linear optical elements and homodyne detection. The optimality of the…
In this work, we revisit the problem of finding an admissible region of fidelities obtained after an application of an arbitrary $1 \rightarrow N$ universal quantum cloner which has been recently solved in [A. Kay et al., Quant. Inf. Comput…
We show that one can deterministically generate out of $N$ copies of an unknown unitary operation up to $N^2$ almost perfect copies. The result holds for all operations generated by a Hamiltonian with an unknown interaction strength. This…
We address the phase space formulation of a noncommutative extension of quantum mechanics in arbitrary dimension, displaying both spatial and momentum noncommutativity. By resorting to a covariant generalization of the Weyl-Wigner transform…
Unitary equivariance is a natural symmetry that occurs in many contexts in physics and mathematics. Optimization problems with such symmetry can often be formulated as semidefinite programs for a $d^{p+q}$-dimensional matrix variable that…
This is a review of concepts of noncommutative supergeometry - namely Hilbert superspace, C*-superalgebra, quantum supergroup - and corresponding results. In particular, we present applications of noncommutative supergeometry in harmonic…
An important topic in quantum information is the theory of error correction codes. Practical situations often involve quantum systems with states in an infinite dimensional Hilbert space, for example coherent states. Motivated by these…
Probabilistic quantum cloning and identifying machines can be constructed via unitary-reduction processes [Duan and Guo, Phys. Rev. Lett. 80, 4999 (1998)]. Given the cloning (identifying) probabilities, we derive an explicit representation…
The impossibility of superluminal communication is a fundamental principle of physics. Here we show that this principle underpins the performance of several fundamental tasks in quantum information processing and quantum metrology. In…
Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…
We analyze the geometry on the space of non-unital phase-covariant qubit maps. Using the corresponding Choi-Jamio{\l}kowski states, we derive the Hilbert-Schmidt line and volume elements using the channel eigenvalues together with the…
In this paper, we study the transformations that are obtained in one-way quantum computation on continuous-variable cluster states of various configurations. Of all possible cluster configurations, we choose those that are suitable for…
The fidelity of a quantum transformation is strongly linked with the prior partial information of the state to be transformed. We illustrate this interesting point by proposing and demonstrating the superior cloning of coherent states with…
Extending our previous work on time optimal quantum state evolution, we formulate a variational principle for the time optimal unitary operation, which has direct relevance to quantum computation. We demonstrate our method with three…
Quantum cloning of two identical mixed qubits $\rho \otimes \rho $ is studied. We propose the quantum cloning transformations not only for the triplet (symmetric) states but also for the singlet (antisymmetric) state. We can copy these two…
We propose a quantum algorithm that emulates the action of an unknown unitary transformation on a given input state, using multiple copies of some unknown sample input states of the unitary and their corresponding output states. The…
We give an algorithm allowing to construct bases of local unitary invariants of pure k-qubit states from the knowledge of polynomial covariants of the group of invertible local filtering operations. The simplest invariants obtained in this…
We describe a general framework to study covariant symmetric broadcasting maps for mixed qubit states. We explicitly derive the optimal N to M superbroadcasting maps, achieving optimal purification of the single-site output copy, in both…