1,605 research outputs found
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
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
The Capacity of the Quantum Multiple Access Channel
We define classical-quantum multiway channels for transmission of classical
information, after recent work by Allahverdyan and Saakian. Bounds on the
capacity region are derived in a uniform way, which are analogous to the
classically known ones, simply replacing Shannon entropy with von Neumann
entropy. For the single receiver case (multiple access channel) the exact
capacity region is determined. These results are applied to the case of noisy
channels, with arbitrary input signal states. A second issue of this work is
the presentation of a calculus of quantum information quantities, based on the
algebraic formulation of quantum theory.Comment: 7 pages, requires IEEEtran2e.cl
Languages of Quantum Information Theory
This note will introduce some notation and definitions for information
theoretic quantities in the context of quantum systems, such as (conditional)
entropy and (conditional) mutual information. We will employ the natural
C*-algebra formalism, and it turns out that one has an allover dualism of
language: we can define everything for (compatible) observables, but also for
(compatible) C*-subalgebras. The two approaches are unified in the formalism of
quantum operations, and they are connected by a very satisfying inequality,
generalizing the well known Holevo bound. Then we turn to communication via
(discrete memoryless) quantum channels: we formulate the Fano inequality, bound
the capacity region of quantum multiway channels, and comment on the quantum
broadcast channel.Comment: 16 pages, REVTEX, typos corrected, references added and extende
Scalable programmable quantum gates and a new aspect of the additivity problem for the classical capacity of quantum channels
We consider two apparently separated problems: in the first part of the paper
we study the concept of a scalable (approximate) programmable quantum gate
(SPQG). These are special (approximate) programmable quantum gates, with nice
properties that could have implications on the theory of universal computation.
Unfortunately, as we prove, such objects do not exist in the domain of usual
quantum theory. In the second part the problem of noisy dense coding (and
generalizations) is addressed. We observe that the additivity problem for the
classical capacity obtained is of apparently greater generality than for the
usual quantum channel (completely positive maps): i.e., the latter occurs as a
special case of the former, but, as we shall argue with the help of the
non-existence result of the first part, the former cannot be reduced to an
instance of the latter. We conclude by suggesting that the additivity problem
for the classical capacity of quantum channels, as posed until now, may
conceptually not be in its appropriate generality.Comment: 9 pages, revtex4. Added a few references and updated others. Extended
discussion a bi
"Pretty strong" converse for the private capacity of degraded quantum wiretap channels
In the vein of the recent "pretty strong" converse for the quantum and
private capacity of degradable quantum channels [Morgan/Winter, IEEE Trans.
Inf. Theory 60(1):317-333, 2014], we use the same techniques, in particular the
calculus of min-entropies, to show a pretty strong converse for the private
capacity of degraded classical-quantum-quantum (cqq-)wiretap channels, which
generalize Wyner's model of the degraded classical wiretap channel.
While the result is not completely tight, leaving some gap between the region
of error and privacy parameters for which the converse bound holds, and a
larger no-go region, it represents a further step towards an understanding of
strong converses of wiretap channels [cf. Hayashi/Tyagi/Watanabe,
arXiv:1410.0443 for the classical case].Comment: 5 pages, 1 figure, IEEEtran.cls. V2 final (conference) version,
accepted for ISIT 2016 (Barcelona, 10-15 July 2016
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