Related papers: Physical accessible transformations on a finite nu…
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 solve the problem of achieving the optimal physical approximation of the transposition for pure states of arbitrary quantum systems for finite and infinite dimensions. A unitary realization is also given for any finite dimension, which…
Any evolution described by a completely positive trace-preserving linear map can be imagined as arising from the interaction of the evolving system with an initially uncorrelated ancilla. The interaction is given by a joint unitary…
We derive a necessary condition for the existence of a completely-positive, linear, trace-preserving map which deterministically transforms one finite set of pure quantum states into another. This condition is also sufficient for…
Given two sets of quantum states {A_1, ..., A_k} and {B_1, ..., B_k}, represented as sets of density matrices, necessary and sufficient conditions are obtained for the existence of a physical transformation T, represented as a…
We analyze to what extent it is possible to copy arbitrary states of a two-level quantum system. We show that there exists a "universal quantum copying machine", which approximately copies quantum mechanical states in such a way that the…
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 propose a general description on the unambiguous discrimination of mixed states according to the system-environment coupling, and present a procedure to reduce this to a standard semidefinite programming problem. In the two states case,…
In this note, we characterize the form of an invertible quantum operation, i.e., a completely positive trace preserving linear transformation (a CPTP map) whose inverse is also a CPTP map. The precise form of such maps becomes important in…
In this work, we introduce a novel state-dependent quantum cloning (copying) process by introducing a new class of ancillary system -- an adaptive ancilla -- modifying the conventional state-dependent quantum copying process. This…
Valid transformations between quantum states are necessarily described by completely positive maps, instead of just positive maps. Positive but not completely positive maps such as the transposition map cannot be implemented due to the…
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…
We investigate probabilistic transformations of quantum states from a `source' set to a `target' set of states. Such transforms have many applications. They can be used for tasks which include state-dependent cloning or quantum state…
We present a unified universal quantum cloning machine, which combines several different existing universal cloning machines together including the asymmetric case. In this unified framework, the identical pure states are projected equally…
Quantum states that remain separable (i.e., not entangled) under any global unitary transformation are known as absolutely separable and form a convex set. Despite extensive efforts, the complete characterization of this set remains largely…
For a given set of input-output pairs of quantum states or observables, we ask the question whether there exists a physically implementable transformation that maps each of the inputs to the corresponding output. The physical maps on…
We realize the probabilistic cloning and identifying linear independent quantum states of multi-particles system, given prior probability, with universal quantum logic gates using the method of unitary representation. Our result is…
In quantum information processing it may be possible to have efficient computation and secure communication beyond the limitations of classical systems. In a fundamental point of view, however, evolution of quantum systems by the laws of…
It is well-known that any two pure quantum states (in the same Hilbert space) can be mapped to any other using unitary transformations. However, previous approaches to this problem required two explicit bases for the Hilbert space, one each…
We consider N quantum systems initially prepared in pure states and address the problem of unambiguously comparing them. One may ask whether or not all $N$ systems are in the same state. Alternatively, one may ask whether or not the states…