410 research outputs found
Conditional implementation of asymmetrical universal quantum cloning machine
We propose two feasible experimental implementations of an optimal asymmetric
1->2 quantum cloning of a polarization state of photon. Both implementations
are based on a partial and optimal reverse of recent conditional symmetrical
quantum cloning experiments. The reversion procedure is performed only by a
local measurement of one from the clones and ancilla followed by a local
operation on the other clone. The local measurement consists only of a single
unbalanced beam splitter followed in one output by a single photon detector and
the asymmetry of fidelities in the cloning is controlled by a reflectivity of
the beam splitter.Comment: 5 pages, 3 figures, accepted for pulication in PR
Quantum Cloning in dimensions
The quantum state space over a -dimensional Hilbert space is
represented as a convex subset of a -dimensional sphere , where Quantum tranformations (CP-maps) are then
associated with the affine transformations of and
{\it cloners} induce polynomial mappings. In this geometrical setting it is
shown that an optimal cloner can be chosen covariant and induces a map between
reduced density matrices given by a simple contraction of the associated
-dimensional Bloch vectors.Comment: 8 pages LaTeX, no figure
Optimal Cloning and No Signaling
It is shown that no signaling constraint generates the whole class of 1
2 optimal quantum cloning machines of single qubits.Comment: 6 pages, late
Quantum copying: A network
We present a network consisting of quantum gates which produces two imperfect
copies of an arbitrary qubit. The quality of the copies does not depend on the
input qubit. We also show that for a restricted class of inputs it is possible
to use a very similar network to produce three copies instead of two. For
qubits in this class, the copy quality is again independent of the input and is
the same as the quality of the copies produced by the two-copy network.Comment: 10 pages LaTeX, with 1 figure, submitted to the Physical Review
Nonlinear Qubit Transformations
We generalise our previous results of universal linear manipulations [Phys.
Rev. A63, 032304 (2001)] to investigate three types of nonlinear qubit
transformations using measurement and quantum based schemes. Firstly, nonlinear
rotations are studied. We rotate different parts of a Bloch sphere in opposite
directions about the z-axis. The second transformation is a map which sends a
qubit to its orthogonal state (which we define as ORTHOG). We consider the case
when the ORTHOG is applied to only a partial area of a Bloch sphere. We also
study nonlinear general transformation, i.e. (theta,phi)->(theta-alpha,phi),
again, applied only to part of the Bloch sphere. In order to achieve these
three operations, we consider different measurement preparations and derive the
optimal average (instead of universal) quantum unitary transformations. We also
introduce a simple method for a qubit measurement and its application to other
cases.Comment: minor corrections. To appear in PR
Extremal equation for optimal completely-positive 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 by the optimal approximate transformation. The developed formalism
is applied to universal-NOT gate, quantum cloning machines, quantum entanglers,
and qubit theta-shifter.Comment: REVTeX, 7 pages, 2 figures, important reference adde
Dynamics of open quantum systems initially entangled with environment: Beyond the Kraus representation
We present a general analysis of the role of initial correlations between the
open system and an environment on quantum dynamics of the open system.Comment: 5 revtex pages, no figures, accepted for publication in Phys. Rev.
Quantum copying: Fundamental inequalities
How well one can copy an arbitrary qubit? To answer this question we consider
two arbitrary vectors in a two-dimensional state space and an abstract copying
transformation which will copy these two vectors. If the vectors are
orthogonal, then perfect copies can be made. If they are not, then errors will
be introduced. The size of the error depends on the inner product of the two
original vectors. We derive a lower bound for the amount of noise induced by
quantum copying. We examine both copying transformations which produce one copy
and transformations which produce many, and show that the quality of each copy
decreases as the number of copies increases.Comment: 5 pages + 1 figure, LaTeX with revtex, epsfig submitted to Phys. Rev.
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