15,232 research outputs found
Codes for Simultaneous Transmission of Quantum and Classical Information
We consider the characterization as well as the construction of quantum codes
that allow to transmit both quantum and classical information, which we refer
to as `hybrid codes'. We construct hybrid codes with
length and distance , that simultaneously transmit qudits and
symbols from a classical alphabet of size . Many good codes such as
, , ,
, , ,
, , ,
, , ,
have been found. All these codes have better parameters
than hybrid codes obtained from the best known stabilizer quantum codes.Comment: 6 page
Quantum and Classical Message Identification via Quantum Channels
We discuss concepts of message identification in the sense of Ahlswede and
Dueck via general quantum channels, extending investigations for classical
channels, initial work for classical-quantum (cq) channels and "quantum
fingerprinting".
We show that the identification capacity of a discrete memoryless quantum
channel for classical information can be larger than that for transmission;
this is in contrast to all previously considered models, where it turns out to
equal the common randomness capacity (equals transmission capacity in our
case): in particular, for a noiseless qubit, we show the identification
capacity to be 2, while transmission and common randomness capacity are 1.
Then we turn to a natural concept of identification of quantum messages (i.e.
a notion of "fingerprint" for quantum states). This is much closer to quantum
information transmission than its classical counterpart (for one thing, the
code length grows only exponentially, compared to double exponentially for
classical identification). Indeed, we show how the problem exhibits a nice
connection to visible quantum coding. Astonishingly, for the noiseless qubit
channel this capacity turns out to be 2: in other words, one can compress two
qubits into one and this is optimal. In general however, we conjecture quantum
identification capacity to be different from classical identification capacity.Comment: 18 pages, requires Rinton-P9x6.cls. On the occasion of Alexander
Holevo's 60th birthday. Version 2 has a few theorems knocked off: Y Steinberg
has pointed out a crucial error in my statements on simultaneous ID codes.
They are all gone and replaced by a speculative remark. The central results
of the paper are all unharmed. In v3: proof of Proposition 17 corrected,
without change of its statemen
Quantum linear network coding as one-way quantum computation
Network coding is a technique to maximize communication rates within a
network, in communication protocols for simultaneous multi-party transmission
of information. Linear network codes are examples of such protocols in which
the local computations performed at the nodes in the network are limited to
linear transformations of their input data (represented as elements of a ring,
such as the integers modulo 2). The quantum linear network coding protocols of
Kobayashi et al [arXiv:0908.1457 and arXiv:1012.4583] coherently simulate
classical linear network codes, using supplemental classical communication. We
demonstrate that these protocols correspond in a natural way to
measurement-based quantum computations with graph states over over qudits
[arXiv:quant-ph/0301052, arXiv:quant-ph/0603226, and arXiv:0704.1263] having a
structure directly related to the network.Comment: 17 pages, 6 figures. Updated to correct an incorrect (albeit
hilarious) reference in the arXiv version of the abstrac
Hybrid Codes
A hybrid code can simultaneously encode classical and quantum information
into quantum digits such that the information is protected against errors when
transmitted through a quantum channel. It is shown that a hybrid code has the
remarkable feature that it can detect more errors than a comparable quantum
code that is able to encode the classical and quantum information. Weight
enumerators are introduced for hybrid codes that allow to characterize the
minimum distance of hybrid codes. Surprisingly, the weight enumerators for
hybrid codes do not obey the usual MacWilliams identity.Comment: 5 page
Capacity Theorems for Quantum Multiple Access Channels
We consider quantum channels with two senders and one receiver. For an
arbitrary such channel, we give multi-letter characterizations of two different
two-dimensional capacity regions. The first region characterizes the rates at
which it is possible for one sender to send classical information while the
other sends quantum information. The second region gives the rates at which
each sender can send quantum information. We give an example of a channel for
which each region has a single-letter description, concluding with a
characterization of the rates at which each user can simultaneously send
classical and quantum information.Comment: 5 pages. Conference version of quant-ph/0501045, to appear in the
proceedings of the IEEE International Symposium on Information Theory,
Adelaide, Australia, 200
Identification via Quantum Channels in the Presence of Prior Correlation and Feedback
Continuing our earlier work (quant-ph/0401060), we give two alternative
proofs of the result that a noiseless qubit channel has identification capacity
2: the first is direct by a "maximal code with random extension" argument, the
second is by showing that 1 bit of entanglement (which can be generated by
transmitting 1 qubit) and negligible (quantum) communication has identification
capacity 2.
This generalises a random hashing construction of Ahlswede and Dueck: that 1
shared random bit together with negligible communication has identification
capacity 1.
We then apply these results to prove capacity formulas for various quantum
feedback channels: passive classical feedback for quantum-classical channels, a
feedback model for classical-quantum channels, and "coherent feedback" for
general channels.Comment: 19 pages. Requires Rinton-P9x6.cls. v2 has some minor errors/typoes
corrected and the claims of remark 22 toned down (proofs are not so easy
after all). v3 has references to simultaneous ID coding removed: there were
necessary changes in quant-ph/0401060. v4 (final form) has minor correction
- …