1,432 research outputs found
Quantum Reverse Shannon Theorem
Dual to the usual noisy channel coding problem, where a noisy (classical or
quantum) channel is used to simulate a noiseless one, reverse Shannon theorems
concern the use of noiseless channels to simulate noisy ones, and more
generally the use of one noisy channel to simulate another. For channels of
nonzero capacity, this simulation is always possible, but for it to be
efficient, auxiliary resources of the proper kind and amount are generally
required. In the classical case, shared randomness between sender and receiver
is a sufficient auxiliary resource, regardless of the nature of the source, but
in the quantum case the requisite auxiliary resources for efficient simulation
depend on both the channel being simulated, and the source from which the
channel inputs are coming. For tensor power sources (the quantum generalization
of classical IID sources), entanglement in the form of standard ebits
(maximally entangled pairs of qubits) is sufficient, but for general sources,
which may be arbitrarily correlated or entangled across channel inputs,
additional resources, such as entanglement-embezzling states or backward
communication, are generally needed. Combining existing and new results, we
establish the amounts of communication and auxiliary resources needed in both
the classical and quantum cases, the tradeoffs among them, and the loss of
simulation efficiency when auxiliary resources are absent or insufficient. In
particular we find a new single-letter expression for the excess forward
communication cost of coherent feedback simulations of quantum channels (i.e.
simulations in which the sender retains what would escape into the environment
in an ordinary simulation), on non-tensor-power sources in the presence of
unlimited ebits but no other auxiliary resource. Our results on tensor power
sources establish a strong converse to the entanglement-assisted capacity
theorem.Comment: 35 pages, to appear in IEEE-IT. v2 has a fixed proof of the Clueless
Eve result, a new single-letter formula for the "spread deficit", better
error scaling, and an improved strong converse. v3 and v4 each make small
improvements to the presentation and add references. v5 fixes broken
reference
On converse bounds for classical communication over quantum channels
We explore several new converse bounds for classical communication over
quantum channels in both the one-shot and asymptotic regimes. First, we show
that the Matthews-Wehner meta-converse bound for entanglement-assisted
classical communication can be achieved by activated, no-signalling assisted
codes, suitably generalizing a result for classical channels. Second, we derive
a new efficiently computable meta-converse on the amount of classical
information unassisted codes can transmit over a single use of a quantum
channel. As applications, we provide a finite resource analysis of classical
communication over quantum erasure channels, including the second-order and
moderate deviation asymptotics. Third, we explore the asymptotic analogue of
our new meta-converse, the -information of the channel. We show that
its regularization is an upper bound on the classical capacity, which is
generally tighter than the entanglement-assisted capacity and other known
efficiently computable strong converse bounds. For covariant channels we show
that the -information is a strong converse bound.Comment: v3: published version; v2: 18 pages, presentation and results
improve
Quantum broadcast channels
We consider quantum channels with one sender and two receivers, used in
several different ways for the simultaneous transmission of independent
messages. We begin by extending the technique of superposition coding to
quantum channels with a classical input to give a general achievable region. We
also give outer bounds to the capacity regions for various special cases from
the classical literature and prove that superposition coding is optimal for a
class of channels. We then consider extensions of superposition coding for
channels with a quantum input, where some of the messages transmitted are
quantum instead of classical, in the sense that the parties establish bipartite
or tripartite GHZ entanglement. We conclude by using state merging to give
achievable rates for establishing bipartite entanglement between different
pairs of parties with the assistance of free classical communication.Comment: 15 pages; IEEE Trans. Inform. Theory, vol. 57, no. 10, October 201
Strong Converse and Second-Order Asymptotics of Channel Resolvability
We study the problem of channel resolvability for fixed i.i.d. input
distributions and discrete memoryless channels (DMCs), and derive the strong
converse theorem for any DMCs that are not necessarily full rank. We also
derive the optimal second-order rate under a condition. Furthermore, under the
condition that a DMC has the unique capacity achieving input distribution, we
derive the optimal second-order rate of channel resolvability for the worst
input distribution.Comment: 7 pages, a shorter version will appear in ISIT 2014, this version
includes the proofs of technical lemmas in appendice
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
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