125 research outputs found
Trade-off coding for universal qudit cloners motivated by the Unruh effect
A "triple trade-off" capacity region of a noisy quantum channel provides a
more complete description of its capabilities than does a single capacity
formula. However, few full descriptions of a channel's ability have been given
due to the difficult nature of the calculation of such regions---it may demand
an optimization of information-theoretic quantities over an infinite number of
channel uses. This work analyzes the d-dimensional Unruh channel, a noisy
quantum channel which emerges in relativistic quantum information theory. We
show that this channel belongs to the class of quantum channels whose capacity
region requires an optimization over a single channel use, and as such is
tractable. We determine two triple-trade off regions, the quantum dynamic
capacity region and the private dynamic capacity region, of the d-dimensional
Unruh channel. Our results show that the set of achievable rate triples using
this coding strategy is larger than the set achieved using a time-sharing
strategy. Furthermore, we prove that the Unruh channel has a distinct structure
made up of universal qudit cloning channels, thus providing a clear
relationship between this relativistic channel and the process of stimulated
emission present in quantum optical amplifiers.Comment: 26 pages, 4 figures; v2 has minor corrections to Definition 2.
Definition 4 and Remark 5 have been adde
Remote information concentration and multipartite entanglement in multilevel systems
Remote information concentration (RIC) in -level systems (qudits) is
studied. It is shown that the quantum information initially distributed in
three spatially separated qudits can be remotely and deterministically
concentrated to a single qudit via an entangled channel without performing any
global operations. The entangled channel can be different types of genuine
multipartite pure entangled states which are inequivalent under local
operations and classical communication. The entangled channel can also be a
mixed entangled state, even a bound entangled state which has a similar form to
the Smolin state, but has different features from the Smolin state. A common
feature of all these pure and mixed entangled states is found, i.e., they have
common commuting stabilizers. The differences of qudit-RIC and qubit-RIC
() are also analyzed.Comment: 10 pages, 3 figure
Quantum Cloning Machines and the Applications
No-cloning theorem is fundamental for quantum mechanics and for quantum
information science that states an unknown quantum state cannot be cloned
perfectly. However, we can try to clone a quantum state approximately with the
optimal fidelity, or instead, we can try to clone it perfectly with the largest
probability. Thus various quantum cloning machines have been designed for
different quantum information protocols. Specifically, quantum cloning machines
can be designed to analyze the security of quantum key distribution protocols
such as BB84 protocol, six-state protocol, B92 protocol and their
generalizations. Some well-known quantum cloning machines include universal
quantum cloning machine, phase-covariant cloning machine, the asymmetric
quantum cloning machine and the probabilistic quantum cloning machine etc. In
the past years, much progress has been made in studying quantum cloning
machines and their applications and implementations, both theoretically and
experimentally. In this review, we will give a complete description of those
important developments about quantum cloning and some related topics. On the
other hand, this review is self-consistent, and in particular, we try to
present some detailed formulations so that further study can be taken based on
those results.Comment: 98 pages, 12 figures, 400+ references. Physics Reports (published
online
Quantum Communication in Rindler Spacetime
A state that an inertial observer in Minkowski space perceives to be the
vacuum will appear to an accelerating observer to be a thermal bath of
radiation. We study the impact of this Davies-Fulling-Unruh noise on
communication, particularly quantum communication from an inertial sender to an
accelerating observer and private communication between two inertial observers
in the presence of an accelerating eavesdropper. In both cases, we establish
compact, tractable formulas for the associated communication capacities
assuming encodings that allow a single excitation in one of a fixed number of
modes per use of the communications channel. Our contributions include a
rigorous presentation of the general theory of the private quantum capacity as
well as a detailed analysis of the structure of these channels, including their
group-theoretic properties and a proof that they are conjugate degradable.
Connections between the Unruh channel and optical amplifiers are also
discussed.Comment: v3: 44 pages, accepted in Communications in Mathematical Physic
Universal Quantum Cloning
After introducing the no-cloning theorem and the most common forms of approximate quantum cloning, universal quantum cloning is considered in detail. The connections it has with universal NOT-gate, quantum cryptography and state estimation are presented and briefly discussed. The state estimation connection is used to show that the amount of extractable classical information and total Bloch vector length are conserved in universal quantum cloning. The 1 2 qubit cloner is also shown to obey a complementarity relation between local and nonlocal information. These are interpreted to be a consequence of the conservation of total information in cloning. Finally, the performance of the 1 M cloning network discovered by Bužek, Hillery and Knight is studied in the presence of decoherence using the Barenco et al. approach where random phase fluctuations are attached to 2-qubit gates. The expression for average fidelity is calculated for three cases and it is found to depend on the optimal fidelity and the average of the phase fluctuations in a specific way. It is conjectured to be the form of the average fidelity in the general case. While the cloning network is found to be rather robust, it is nevertheless argued that the scalability of the quantum network implementation is poor by studying the effect of decoherence during the preparation of the initial state of the cloning machine in the 1 ! 2 case and observing that the loss in average fidelity can be large. This affirms the result by Maruyama and Knight, who reached the same conclusion in a slightly different manner.Siirretty Doriast
The superadditivity effects of quantum capacity decrease with the dimension for qudit depolarizing channels
Quantum channel capacity is a fundamental quantity in order to understand how
good can quantum information be transmitted or corrected when subjected to
noise. However, it is generally not known how to compute such quantities, since
the quantum channel coherent information is not additive for all channels,
implying that it must be maximized over an unbounded number of channel uses.
This leads to the phenomenon known as superadditivity, which refers to the fact
that the regularized coherent information of channel uses exceeds one-shot
coherent information. In this article, we study how the gain in quantum
capacity of qudit depolarizing channels relates to the dimension of the systems
considered. We make use of an argument based on the no-cloning bound in order
to proof that the possible superadditive effects decrease as a function of the
dimension for such family of channels. In addition, we prove that the capacity
of the qudit depolarizing channel coincides with the coherent information when
. We conclude that when high dimensional qudits
experiencing depolarizing noise are considered, the coherent information of the
channel is not only an achievable rate but essentially the maximum possible
rate for any quantum block code.Comment: 7 pages, 2 figure
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