Related papers: Optimal realization of the transposition maps
We derive an extremal equation for optimal completely-positive map which most closely approximates a given transformation between pure quantum states. Moreover, we also obtain an upper bound on the maximal mean fidelity that can be attained…
We consider to treat the usual probabilistic cloning, state separation, unambiguous state discrimination, \emph{etc} in a uniform framework. All these transformations can be regarded as special examples of generalized completely positive…
We consider the transformations of quantum states obtainable by a process of the following sort. Combine the given input state with a specially prepared initial state of an auxiliary system. Apply a unitary transformation to the combined…
We establish a connection between optimal quantum cloning and optimal state estimation for d-dimensional quantum systems. In this way we derive an upper limit on the fidelity of state estimation for d-dimensional pure quantum states and,…
We show that quantum designs characterize the general structure of the optimal approximation of the transpose map on quantum states. Based on this characterization, we propose an implementation of the approximate transpose map by a…
The universal transpose of quantum states is an anti-unitary transformation that is not allowed in quantum theory. In this work, we investigate approximating the universal transpose of quantum states of two-level systems (qubits) using the…
We study the optimal cloning transformation for two pairs of orthogonal states of two-dimensional quantum systems, and derive the corresponding optimal fidelities.
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,…
We review some partial results for two strictly related problems. The first problem consists in finding the optimal joint unitary transformation on system and ancilla which is the most efficient in programming any desired channel on the…
We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and…
The relative error of cloning of quantum states with arbitrary prior probabilities is considered. It is assumed that the ancilla may contain some a priori information about the input state to be cloned. The lower bound on the relative error…
After proving a general no-cloning theorem for black boxes, we derive the optimal universal cloning of unitary transformations, from one to two copies. The optimal cloner is realized by quantum channels with memory, and greately outperforms…
Optimal quantum cloning is the process of making one or more copies of an arbitrary unknown input quantum state with the highest possible fidelity. All reported demonstrations of quantum cloning have so far been limited to copying…
State cloning and state transposition are fundamental transformations which, despite being desirable, cannot be perfectly realised due to two conceptually distinct constraints of quantum theory: cloning is forbidden by linearity, while…
We study quantum cloning machines (QCM) that act on an unknown N-level quantum state and make M copies. We give a formula for the maximum of the fidelity of cloning and exhibit the unitary transformations that realize this optimal fidelity.…
We have found a quantum cloning machine that optimally duplicates the entanglement of a pair of $d$-dimensional quantum systems. It maximizes the entanglement of formation contained in the two copies of any maximally-entangled input state,…
The impossibility of perfectly copying (or cloning) an arbitrary quantum state is one of the basic rules governing the physics of quantum systems. The processes that perform the optimal approximate cloning have been found in many cases.…
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 best possible approximation to a perfect quantum cloning machine which produces two clones out of a single input. We analyze both universal and state-dependent cloners. The maximal fidelity of cloning is shown to be 5/6 for…
Optimal quantum machines can be implemented by linear projective operations. In the present work a general qubit symmetrization theory is presented by investigating the close links to the qubit purification process and to the programmable…