79 research outputs found

### 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

### 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

### Quantum key distribution for d-level systems with generalized Bell states

Using the generalized Bell states and controlled not gates, we introduce an
enatanglement-based quantum key distribution (QKD) of d-level states (qudits).
In case of eavesdropping, Eve's information gain is zero and a quantum error
rate of (d-1)/d is introduced in Bob's received qudits, so that for large d,
comparison of only a tiny fraction of received qudits with the sent ones can
detect the presence of Eve.Comment: 8 pages, 3 figures, REVTEX, references added, extensive revision, to
appear in Phys. Rev.

### Reversibility of continuous-variable quantum cloning

We analyze a reversibility of optimal Gaussian $1\to 2$ quantum cloning of a
coherent state using only local operations on the clones and classical
communication between them and propose a feasible experimental test of this
feature. Performing Bell-type homodyne measurement on one clone and anti-clone,
an arbitrary unknown input state (not only a coherent state) can be restored in
the other clone by applying appropriate local unitary displacement operation.
We generalize this concept to a partial LOCC reversal of the cloning and we
show that this procedure converts the symmetric cloner to an asymmetric cloner.
Further, we discuss a distributed LOCC reversal in optimal $1\to M$ Gaussian
cloning of coherent states which transforms it to optimal $1\to M'$ cloning for
$M'<M$. Assuming the quantum cloning as a possible eavesdropping attack on
quantum communication link, the reversibility can be utilized to improve the
security of the link even after the attack.Comment: 7 pages, 5 figure

### What information theory can tell us about quantum reality

An investigation of Einstein's ``physical'' reality and the concept of
quantum reality in terms of information theory suggests a solution to quantum
paradoxes such as the Einstein-Podolsky-Rosen (EPR) and the Schroedinger-cat
paradoxes. Quantum reality, the picture based on unitarily evolving
wavefunctions, is complete, but appears incomplete from the observer's point of
view for fundamental reasons arising from the quantum information theory of
measurement. Physical reality, the picture based on classically accessible
observables is, in the worst case of EPR experiments, unrelated to the quantum
reality it purports to reflect. Thus, quantum information theory implies that
only correlations, not the correlata, are physically accessible: the mantra of
the Ithaca interpretation of quantum mechanics.Comment: LaTeX with llncs.cls, 11 pages, 6 postscript figures, Proc. of 1st
NASA Workshop on Quantum Computation and Quantum Communication (QCQC 98

### Multipartite Classical and Quantum Secrecy Monotones

In order to study multipartite quantum cryptography, we introduce quantities
which vanish on product probability distributions, and which can only decrease
if the parties carry out local operations or carry out public classical
communication. These ``secrecy monotones'' therefore measure how much secret
correlations are shared by the parties. In the bipartite case we show that the
mutual information is a secrecy monotone. In the multipartite case we describe
two different generalisations of the mutual information, both of which are
secrecy monotones. The existence of two distinct secrecy monotones allows us to
show that in multipartite quantum cryptography the parties must make
irreversible choices about which multipartite correlations they want to obtain.
Secrecy monotones can be extended to the quantum domain and are then defined on
density matrices. We illustrate this generalisation by considering tri-partite
quantum cryptography based on the Greenberger-Horne-Zeilinger (GHZ) state. We
show that before carrying out measurements on the state, the parties must make
an irreversible decision about what probability distribution they want to
obtain

### Information-theoretic interpretation of quantum error-correcting codes

Quantum error-correcting codes are analyzed from an information-theoretic
perspective centered on quantum conditional and mutual entropies. This approach
parallels the description of classical error correction in Shannon theory,
while clarifying the differences between classical and quantum codes. More
specifically, it is shown how quantum information theory accounts for the fact
that "redundant" information can be distributed over quantum bits even though
this does not violate the quantum "no-cloning" theorem. Such a remarkable
feature, which has no counterpart for classical codes, is related to the
property that the ternary mutual entropy vanishes for a tripartite system in a
pure state. This information-theoretic description of quantum coding is used to
derive the quantum analogue of the Singleton bound on the number of logical
bits that can be preserved by a code of fixed length which can recover a given
number of errors.Comment: 14 pages RevTeX, 8 Postscript figures. Added appendix. To appear in
Phys. Rev.

### Optimal estimation of multiple phases

We study the issue of simultaneous estimation of several phase shifts induced
by commuting operators on a quantum state. We derive the optimal positive
operator-valued measure corresponding to the multiple-phase estimation. In
particular, we discuss the explicit case of the optimal detection of double
phase for a system of identical qutrits and generalise these results to optimal
multiple phase detection for d-dimensional quantum states.Comment: 6 page

### Cloning of spin-coherent states

We consider optimal cloning of the spin coherent states in Hilbert spaces of
different dimensionality d. We give explicit form of optimal cloning
transformation for spin coherent states in the three-dimensional space,
analytical results for the fidelity of the optimal cloning in d=3 and d=4 as
well as numerical results for higher dimensions. In the low-dimensional case we
construct the corresponding completely positive maps and exhibit their
structure with the help of Jamiolkowski isomorphism. This allows us to
formulate some conjectures about the form of optimal coherent cloning CP maps
in arbitrary dimension.Comment: LateX, 9 pages, 1 figur

### Asymmetric quantum telecloning of d-level systems and broadcasting of entanglement to different locations using the "many-to-many" communication protocol

We propose a generalization of quantum teleportation: the so-called
many-to-many quantum communication of the information of a d-level system from
N spatially separated senders to M>N receivers situated at different locations.
We extend the concept of asymmetric telecloning from qubits to d-dimensional
systems. We investigate the broadcasting of entanglement by using local 1->2
optimal universal asymmetric Pauli machines and show that the maximal
fidelities of the two final entangled states are obtained when symmetric
machines are applied. Cloning of entanglement is studied using a nonlocal
optimal universal asymmetric cloning machine and we show that the symmetric
machine optimally copies the entanglement. The "many-to-many" teleportation
scheme is applied in order to distribute entanglement shared between two
observers to two pairs of spatially separated observers.Comment: 17 pages, 1 figur

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