2,005 research outputs found
Explicit capacity-achieving receivers for optical communication and quantum reading
An important practical open question has been to design explicit, structured optical receivers that achieve the Holevo limit in the contexts of optical communication and “quantum reading.” The Holevo limit is an achievable rate that is higher than the Shannon limit of any known optical receiver. We demonstrate how a sequential decoding approach can achieve the Holevo limit for both of these settings. A crucial part of our scheme for both settings is a non-destructive “vacuum-or-not” measurement that projects an n-symbol modulated codeword onto the n-fold vacuum state or its orthogonal complement, such that the post-measurement state is either the n-fold vacuum or has the vacuum removed from the support of the n symbols' joint quantum state. The sequential decoder for optical communication requires the additional ability to perform multimode optical phase-space displacements - realizable using a beamsplitter and a laser, while the sequential decoder for quantum reading also requires the ability to perform phase-shifting (realizable using a phase plate) and online squeezing (a phase-sensitive amplifier)
Explicit receivers for pure-interference bosonic multiple access channels
The pure-interference bosonic multiple access channel has two senders and one
receiver, such that the senders each communicate with multiple temporal modes
of a single spatial mode of light. The channel mixes the input modes from the
two users pairwise on a lossless beamsplitter, and the receiver has access to
one of the two output ports. In prior work, Yen and Shapiro found the capacity
region of this channel if encodings consist of coherent-state preparations.
Here, we demonstrate how to achieve the coherent-state Yen-Shapiro region (for
a range of parameters) using a sequential decoding strategy, and we show that
our strategy outperforms the rate regions achievable using conventional
receivers. Our receiver performs binary-outcome quantum measurements for every
codeword pair in the senders' codebooks. A crucial component of this scheme is
a non-destructive "vacuum-or-not" measurement that projects an n-symbol
modulated codeword onto the n-fold vacuum state or its orthogonal complement,
such that the post-measurement state is either the n-fold vacuum or has the
vacuum removed from the support of the n symbols' joint quantum state. This
receiver requires the additional ability to perform multimode optical
phase-space displacements which are realizable using a beamsplitter and a
laser.Comment: v1: 9 pages, 2 figures, submission to the 2012 International
Symposium on Information Theory and its Applications (ISITA 2012), Honolulu,
Hawaii, USA; v2: minor change
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
The capacity of coherent-state adaptive decoders with interferometry and single-mode detectors
A class of Adaptive Decoders (AD's) for coherent-state sequences is studied,
including in particular the most common technology for optical-signal
processing, e.g., interferometers, coherent displacements and photon-counting
detectors. More generally we consider AD's comprising adaptive procedures based
on passive multi-mode Gaussian unitaries and arbitrary single-mode destructive
measurements. For classical communication on quantum phase-insensitive Gaussian
channels with a coherent-state encoding, we show that the AD's optimal
information transmission rate is not greater than that of a single-mode
decoder. Our result also implies that the ultimate classical capacity of
quantum phase-insensitive Gaussian channels is unlikely to be achieved with the
considered class of AD's.Comment: v3: final version; 6 pages; 2 figure
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
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
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
Second-order coding rates for pure-loss bosonic channels
A pure-loss bosonic channel is a simple model for communication over
free-space or fiber-optic links. More generally, phase-insensitive bosonic
channels model other kinds of noise, such as thermalizing or amplifying
processes. Recent work has established the classical capacity of all of these
channels, and furthermore, it is now known that a strong converse theorem holds
for the classical capacity of these channels under a particular photon number
constraint. The goal of the present paper is to initiate the study of
second-order coding rates for these channels, by beginning with the simplest
one, the pure-loss bosonic channel. In a second-order analysis of
communication, one fixes the tolerable error probability and seeks to
understand the back-off from capacity for a sufficiently large yet finite
number of channel uses. We find a lower bound on the maximum achievable code
size for the pure-loss bosonic channel, in terms of the known expression for
its capacity and a quantity called channel dispersion. We accomplish this by
proving a general "one-shot" coding theorem for channels with classical inputs
and pure-state quantum outputs which reside in a separable Hilbert space. The
theorem leads to an optimal second-order characterization when the channel
output is finite-dimensional, and it remains an open question to determine
whether the characterization is optimal for the pure-loss bosonic channel.Comment: 18 pages, 3 figures; v3: final version accepted for publication in
Quantum Information Processin
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