308 research outputs found
Optimal universal quantum cloning and state estimation
We derive a tight upper bound for the fidelity of a universal N to M qubit
cloner, valid for any M \geq N, where the output of the cloner is required to
be supported on the symmetric subspace. Our proof is based on the concatenation
of two cloners and the connection between quantum cloning and quantum state
estimation. We generalise the operation of a quantum cloner to mixed and/or
entangled input qubits described by a density matrix supported on the symmetric
subspace of the constituent qubits. We also extend the validity of optimal
state estimation methods to inputs of this kind.Comment: 4 pages (RevTeX
Quantum Cloning of Mixed States in Symmetric Subspace
Quantum cloning machine for arbitrary mixed states in symmetric subspace is
proposed. This quantum cloning machine can be used to copy part of the output
state of another quantum cloning machine and is useful in quantum computation
and quantum information. The shrinking factor of this quantum cloning achieves
the well-known upper bound. When the input is identical pure states, two
different fidelities of this cloning machine are optimal.Comment: Revtex, 4 page
Bounds for state-dependent quantum cloning
Due to the no-cloning theorem, the unknown quantum state can only be cloned
approximately or exactly with some probability. There are two types of cloners:
universal and state-dependent cloner. The optimal universal cloner has been
found and could be viewed as a special state-dependent quantum cloner which has
no information about the states. In this paper, we investigate the
state-dependent cloning when the state-set contains more than two states. We
get some bounds of the global fidelity for these processes. This method is not
dependent on the number of the states contained in the state-set. It is also
independent of the numbers of copying.Comment: 13 pages, 1 figure, to appear in Phys. Rev.
Cloning a real d-dimensional quantum state on the edge of the no-signaling condition
We investigate a new class of quantum cloning machines that equally duplicate
all real states in a Hilbert space of arbitrary dimension. By using the
no-signaling condition, namely that cloning cannot make superluminal
communication possible, we derive an upper bound on the fidelity of this class
of quantum cloning machines. Then, for each dimension d, we construct an
optimal symmetric cloner whose fidelity saturates this bound. Similar
calculations can also be performed in order to recover the fidelity of the
optimal universal cloner in d dimensions.Comment: 6 pages RevTex, 1 encapuslated Postscript figur
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
Optimal N-to-M Cloning of Quantum Coherent States
The cloning of continuous quantum variables is analyzed based on the concept
of Gaussian cloning machines, i.e., transformations that yield copies that are
Gaussian mixtures centered on the state to be copied. The optimality of
Gaussian cloning machines that transform N identical input states into M output
states is investigated, and bounds on the fidelity of the process are derived
via a connection with quantum estimation theory. In particular, the optimal
N-to-M cloning fidelity for coherent states is found to be equal to
MN/(MN+M-N).Comment: 3 pages, RevTe
Universal Quantum Cloning in Cavity QED
We propose an implementation of an universal quantum cloning machine [UQCM,
Hillery and Buzek, Phys. Rev. A {\bf 56}, 3446 (1997)] in a Cavity Quantum
Electrodynamics (CQED) experiment. This UQCM acts on the electronic states of
atoms that interact with the electromagnetic field of a high cavity. We
discuss here the specific case of the cloning process using either a
one- or a two-cavity configuration
Quantum cloning and the capacity of the Pauli channel
A family of quantum cloning machines is introduced that produce two
approximate copies from a single quantum bit, while the overall input-to-output
operation for each copy is a Pauli channel. A no-cloning inequality is derived,
describing the balance between the quality of the two copies. This also
provides an upper bound on the quantum capacity of the Pauli channel with
probabilities , and . The capacity is shown to be vanishing if
lies outside an ellipsoid whose pole
coincides with the depolarizing channel that underlies the universal cloning
machine.Comment: 5 pages RevTeX, 3 Postscript figure
Approximate quantum cloning and the impossibility of superluminal information transfer
We show that nonlocality of quantum mechanics cannot lead to superluminal
transmission of information, even if most general local operations are allowed,
as long as they are linear and trace preserving. In particular, any quantum
mechanical approximate cloning transformation does not allow signalling. On the
other hand, the no-signalling constraint on its own is not sufficient to
prevent a transformation from surpassing the known cloning bounds. We
illustrate these concepts on the basis of some examples.Comment: 4 pages, 1eps figur
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