77,366 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
Strong Converse for Identification via Quantum Channels
In this paper we present a simple proof of the strong converse for
identification via discrete memoryless quantum channels, based on a novel
covering lemma. The new method is a generalization to quantum communication
channels of Ahlswede's recently discovered appoach to classical channels. It
involves a development of explicit large deviation estimates to the case of
random variables taking values in selfadjoint operators on a Hilbert space.
This theory is presented separately in an appendix, and we illustrate it by
showing its application to quantum generalizations of classical hypergraph
covering problems.Comment: 11 pages, LaTeX2e, requires IEEEtran2e.cls. Some errors and omissions
corrected, references update
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
Quantum soft-covering lemma with applications to rate-distortion coding, resolvability and identification via quantum channels
We propose a quantum soft-covering problem for a given general quantum
channel and one of its output states, which consists in finding the minimum
rank of an input state needed to approximate the given channel output. We then
prove a one-shot quantum covering lemma in terms of smooth min-entropies by
leveraging decoupling techniques from quantum Shannon theory. This covering
result is shown to be equivalent to a coding theorem for rate distortion under
a posterior (reverse) channel distortion criterion [Atif, Sohail, Pradhan,
arXiv:2302.00625]. Both one-shot results directly yield corollaries about the
i.i.d. asymptotics, in terms of the coherent information of the channel.
The power of our quantum covering lemma is demonstrated by two additional
applications: first, we formulate a quantum channel resolvability problem, and
provide one-shot as well as asymptotic upper and lower bounds. Secondly, we
provide new upper bounds on the unrestricted and simultaneous identification
capacities of quantum channels, in particular separating for the first time the
simultaneous identification capacity from the unrestricted one, proving a
long-standing conjecture of the last author.Comment: 29 pages, 3 figures; v2 fixes an error in Definition 6.1 and various
typos and minor issues throughou
Quantum Process Estimation via Generic Two-Body Correlations
Performance of quantum process estimation is naturally limited to
fundamental, random, and systematic imperfections in preparations and
measurements. These imperfections may lead to considerable errors in the
process reconstruction due to the fact that standard data analysis techniques
presume ideal devices. Here, by utilizing generic auxiliary quantum or
classical correlations, we provide a framework for estimation of quantum
dynamics via a single measurement apparatus. By construction, this approach can
be applied to quantum tomography schemes with calibrated faulty state
generators and analyzers. Specifically, we present a generalization of "Direct
Characterization of Quantum Dynamics" [M. Mohseni and D. A. Lidar, Phys. Rev.
Lett. 97, 170501 (2006)] with an imperfect Bell-state analyzer. We demonstrate
that, for several physically relevant noisy preparations and measurements, only
classical correlations and small data processing overhead are sufficient to
accomplish the full system identification. Furthermore, we provide the optimal
input states for which the error amplification due to inversion on the
measurement data is minimal.Comment: 7 pages, 2 figure
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