Related papers: Optimal purification of single qubits

We investigate the problem of copying pure two-qubit states of a given degree of entanglement in an optimal way. Completely positive covariant quantum operations are constructed which maximize the fidelity of the output states with respect…

We consider cloning transformations of equatorial qubits and qutrits, with the transformation covariant for rotation of the phases. The optimal cloning maps are derived without simplifying assumptions from first principles, for any number…

We establish the ultimate limits to the compression of sequences of identically prepared qubits. The limits are determined by Holevo's information quantity and are attained through use of the optimal universal cloning machine, which finds…

We investigate optimal separable approximations (decompositions) of states rho of bipartite quantum systems A and B of arbitrary dimensions MxN following the lines of Ref. [M. Lewenstein and A. Sanpera, Phys. Rev. Lett. 80, 2261 (1998)].…

We discuss the "partial" quantum cloning of the pure two-partite states, when the "part" of initial state related to the one qubit is copied only. The same approach gives the possibility to design the quantum copying machine for the mixed…

We review our recent work on the universal (i.e. input state independent) optimal quantum copying (cloning) of qubits. We present unitary transformations which describe the optimal cloning of a qubit and we present the corresponding quantum…

In this note we consider the problem of preparing a {\em single} copy of an arbitrary two-qubit mixed state $\rho$ starting from an entangled pure state $\psi$ and using only local operations assisted with classical communication. We…

We present one-shot compression protocols that optimally encode ensembles of $N$ identically prepared mixed states into $O(\log N)$ qubits. In contrast to the case of pure-state ensembles, we find that the number of encoding qubits drops…

We present a mapping which associates pure N-qubit states with a polynomial. The roots of the polynomial characterize the state completely. Using the properties of the polynomial we construct a way to determine the separability and the…

We provide a general method to calculate and maximize the purity of a qubit interacting with an anisotropic non-Markovian environment. Counter to intuition, we find that the purity is often maximized by preparing and storing the qubit in a…

We present optimal measuring strategies for the estimation of the entanglement of unknown two-qubit pure states and of the degree of mixing of unknown single-qubit mixed states, of which N identical copies are available. The most general…

We study the phase-covariant quantum cloning machine for qudits, i.e. the input states in d-level quantum system have complex coefficients with arbitrary phase but constant module. A cloning unitary transformation is proposed. After…

The goal of qubit purification is to combine multiple noisy copies of an unknown pure quantum state to obtain one or more copies that are closer to the pure state. We show that a simple protocol based solely on random SWAP tests achieves…

This work provides a parametrization of the set of purifications of a 2x2 mixed state, and joint purifications (if any) of a given pair of mixed 2x2 states. The former is parametrized by SO(3, R), while the latter is parametrized by…

We consider quantum devices for turning a finite number N of d-level quantum systems in the same unknown pure state \sigma into M>N systems of the same kind, in an approximation of the M-fold tensor product of the state \sigma. In a…

Entanglement purification describes a primitive in quantum information processing, where several copies of noisy quantum states are distilled into few copies of nearly-pure states of high quality via local operations and classical…

We address the problem of optimal estimation of the relative phase for two-dimensional quantum systems in mixed states. In particular, we derive the optimal measurement procedures for an arbitrary number of qubits prepared in the same mixed…

In this paper we consider the purification of a quantum state using the information obtained from a continuous measurement record, where the classical measurement record is digitized to a single bit per measurement after the measurements…

Known entanglement purification protocols for mixed states use collective measurements on several copies of the state in order to increase the entanglement of some of them. We address the question of whether it is possible to purify the…

We present a family of 3--qubit states to which any arbitrary state can be depolarized. We fully classify those states with respect to their separability and distillability properties. This provides a sufficient condition for…