137 research outputs found
Polar coding to achieve the Holevo capacity of a pure-loss optical channel
In the low-energy high-energy-efficiency regime of classical optical communications - relevant to deep-space optical channels - there is a big gap between reliable communication rates achievable via conventional optical receivers and the ultimate (Holevo) capacity. Achieving the Holevo capacity requires not only optimal codes but also receivers that make collective measurements on long (modulated) codeword waveforms, and it is impossible to implement these collective measurements via symbol-by-symbol detection along with classical postprocessing [1], [2]. Here, we apply our recent results on the classical-quantum polar code [3] - the first near-explicit, linear, symmetric-Holevo-rate achieving code - to the lossy optical channel, and we show that it almost closes the entire gap to the Holevo capacity in the low photon number regime. In contrast, Arikan\u27s original polar codes, applied to the DMC induced by the physical optical channel paired with any conceivable structured optical receiver (including optical homodyne, heterodyne, or direct-detection) fails to achieve the ultimate Holevo limit to channel capacity. However, our polar code construction (which uses the quantum fidelity as a channel parameter rather than the classical Bhattacharyya quantity to choose the good channels in the polar-code construction), paired with a quantum successive-cancellation receiver - which involves a sequence of collective non-destructive binary projective measurements on the joint quantum state of the received codeword waveform - can attain the Holevo limit, and can hence in principle achieve higher rates than Arikan\u27s polar code and decoder directly applied to the optical channel. However, even a theoretical recipe for construction of an optical realization of the quantum successive-cancellation receiver remains an open question. © 2012 IEEE
Superadditivity of Quantum Channel Coding Rate with Finite Blocklength Joint Measurements
The maximum rate at which classical information can be reliably transmitted
per use of a quantum channel strictly increases in general with , the number
of channel outputs that are detected jointly by the quantum joint-detection
receiver (JDR). This phenomenon is known as superadditivity of the maximum
achievable information rate over a quantum channel. We study this phenomenon
for a pure-state classical-quantum (cq) channel and provide a lower bound on
, the maximum information rate when the JDR is restricted to making
joint measurements over no more than quantum channel outputs, while
allowing arbitrary classical error correction. We also show the appearance of a
superadditivity phenomenon---of mathematical resemblance to the aforesaid
problem---in the channel capacity of a classical discrete memoryless channel
(DMC) when a concatenated coding scheme is employed, and the inner decoder is
forced to make hard decisions on -length inner codewords. Using this
correspondence, we develop a unifying framework for the above two notions of
superadditivity, and show that for our lower bound to to be equal to a
given fraction of the asymptotic capacity of the respective channel,
must be proportional to , where is the respective channel dispersion
quantity.Comment: To appear in IEEE Transactions on Information Theor
Towards efficient decoding of classical-quantum polar codes
Known strategies for sending bits at the capacity rate over a general channel
with classical input and quantum output (a cq channel) require the decoder to
implement impractically complicated collective measurements. Here, we show that
a fully collective strategy is not necessary in order to recover all of the
information bits. In fact, when coding for a large number N uses of a cq
channel W, N I(W_acc) of the bits can be recovered by a non-collective strategy
which amounts to coherent quantum processing of the results of product
measurements, where I(W_acc) is the accessible information of the channel W. In
order to decode the other N (I(W) - I(W_acc)) bits, where I(W) is the Holevo
rate, our conclusion is that the receiver should employ collective
measurements. We also present two other results: 1) collective Fuchs-Caves
measurements (quantum likelihood ratio measurements) can be used at the
receiver to achieve the Holevo rate and 2) we give an explicit form of the
Helstrom measurements used in small-size polar codes. The main approach used to
demonstrate these results is a quantum extension of Arikan's polar codes.Comment: 21 pages, 2 figures, submission to the 8th Conference on the Theory
of Quantum Computation, Communication, and Cryptograph
Sequential decoding of a general classical-quantum channel
Since a quantum measurement generally disturbs the state of a quantum system,
one might think that it should not be possible for a sender and receiver to
communicate reliably when the receiver performs a large number of sequential
measurements to determine the message of the sender. We show here that this
intuition is not true, by demonstrating that a sequential decoding strategy
works well even in the most general "one-shot" regime, where we are given a
single instance of a channel and wish to determine the maximal number of bits
that can be communicated up to a small failure probability. This result follows
by generalizing a non-commutative union bound to apply for a sequence of
general measurements. We also demonstrate two ways in which a receiver can
recover a state close to the original state after it has been decoded by a
sequence of measurements that each succeed with high probability. The second of
these methods will be useful in realizing an efficient decoder for fully
quantum polar codes, should a method ever be found to realize an efficient
decoder for classical-quantum polar codes.Comment: 12 pages; accepted for publication in the Proceedings of the Royal
Society
An improved rate region for the classical-quantum broadcast channel
We present a new achievable rate region for the two-user binary-input
classical-quantum broadcast channel. The result is a generalization of the
classical Marton-Gelfand-Pinsker region and is provably larger than the best
previously known rate region for classical-quantum broadcast channels. The
proof of achievability is based on the recently introduced polar coding scheme
and its generalization to quantum network information theory.Comment: 5 pages, double column, 1 figure, based on a result presented in the
Master's thesis arXiv:1501.0373
Capacity of optical reading, Part 1: Reading boundless error-free bits using a single photon
We show that nature imposes no fundamental upper limit to the number of
information bits per expended photon that can, in principle, be read reliably
when classical data is encoded in a medium that can only passively modulate the
amplitude and phase of the probe light. We show that with a coherent-state
(laser) source, an on-off (amplitude-modulation) pixel encoding, and
shot-noise-limited direct detection (an overly-optimistic model for commercial
CD/DVD drives), the highest photon information efficiency achievable in
principle is about 0.5 bit per transmitted photon. We then show that a
coherent-state probe can read unlimited bits per photon when the receiver is
allowed to make joint (inseparable) measurements on the reflected light from a
large block of phase-modulated memory pixels. Finally, we show an example of a
spatially-entangled non-classical light probe and a receiver
design---constructable using a single-photon source, beam splitters, and
single-photon detectors---that can in principle read any number of error-free
bits of information. The probe is a single photon prepared in a uniform
coherent superposition of multiple orthogonal spatial modes, i.e., a W-state.
The code, target, and joint-detection receiver complexity required by a
coherent-state transmitter to achieve comparable photon efficiency performance
is shown to be much higher in comparison to that required by the W-state
transceiver.Comment: 11 pages, 12 figures, v3 includes a new plot characterizing the
photon efficiency vs. encoding efficiency tradeoff for optical reading. The
main technical body of the paper remains unaltere
Polar codes for classical-quantum channels
Holevo, Schumacher, and Westmoreland's coding theorem guarantees the
existence of codes that are capacity-achieving for the task of sending
classical data over a channel with classical inputs and quantum outputs.
Although they demonstrated the existence of such codes, their proof does not
provide an explicit construction of codes for this task. The aim of the present
paper is to fill this gap by constructing near-explicit "polar" codes that are
capacity-achieving. The codes exploit the channel polarization phenomenon
observed by Arikan for the case of classical channels. Channel polarization is
an effect in which one can synthesize a set of channels, by "channel combining"
and "channel splitting," in which a fraction of the synthesized channels are
perfect for data transmission while the other fraction are completely useless
for data transmission, with the good fraction equal to the capacity of the
channel. The channel polarization effect then leads to a simple scheme for data
transmission: send the information bits through the perfect channels and
"frozen" bits through the useless ones. The main technical contributions of the
present paper are threefold. First, we leverage several known results from the
quantum information literature to demonstrate that the channel polarization
effect occurs for channels with classical inputs and quantum outputs. We then
construct linear polar codes based on this effect, and the encoding complexity
is O(N log N), where N is the blocklength of the code. We also demonstrate that
a quantum successive cancellation decoder works well, in the sense that the
word error rate decays exponentially with the blocklength of the code. For this
last result, we exploit Sen's recent "non-commutative union bound" that holds
for a sequence of projectors applied to a quantum state.Comment: 12 pages, 3 figures; v2 in IEEE format with minor changes; v3 final
version accepted for publication in the IEEE Transactions on Information
Theor
Multiple-Access Bosonic Communications
The maximum rates for reliably transmitting classical information over
Bosonic multiple-access channels (MACs) are derived when the transmitters are
restricted to coherent-state encodings. Inner and outer bounds for the ultimate
capacity region of the Bosonic MAC are also presented. It is shown that the
sum-rate upper bound is achievable with a coherent-state encoding and that the
entire region is asymptotically achievable in the limit of large mean input
photon numbers.Comment: 11 pages, 5 figures, corrected two figures, accepted for publication
in Phys. Rev.
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