50 research outputs found
Quantum enigma machines and the locking capacity of a quantum channel
The locking effect is a phenomenon which is unique to quantum information
theory and represents one of the strongest separations between the classical
and quantum theories of information. The Fawzi-Hayden-Sen (FHS) locking
protocol harnesses this effect in a cryptographic context, whereby one party
can encode n bits into n qubits while using only a constant-size secret key.
The encoded message is then secure against any measurement that an eavesdropper
could perform in an attempt to recover the message, but the protocol does not
necessarily meet the composability requirements needed in quantum key
distribution applications. In any case, the locking effect represents an
extreme violation of Shannon's classical theorem, which states that
information-theoretic security holds in the classical case if and only if the
secret key is the same size as the message. Given this intriguing phenomenon,
it is of practical interest to study the effect in the presence of noise, which
can occur in the systems of both the legitimate receiver and the eavesdropper.
This paper formally defines the locking capacity of a quantum channel as the
maximum amount of locked information that can be reliably transmitted to a
legitimate receiver by exploiting many independent uses of a quantum channel
and an amount of secret key sublinear in the number of channel uses. We provide
general operational bounds on the locking capacity in terms of other well-known
capacities from quantum Shannon theory. We also study the important case of
bosonic channels, finding limitations on these channels' locking capacity when
coherent-state encodings are employed and particular locking protocols for
these channels that might be physically implementable.Comment: 37 page
Converse bounds for private communication over quantum channels
This paper establishes several converse bounds on the private transmission
capabilities of a quantum channel. The main conceptual development builds
firmly on the notion of a private state, which is a powerful, uniquely quantum
method for simplifying the tripartite picture of privacy involving local
operations and public classical communication to a bipartite picture of quantum
privacy involving local operations and classical communication. This approach
has previously led to some of the strongest upper bounds on secret key rates,
including the squashed entanglement and the relative entropy of entanglement.
Here we use this approach along with a "privacy test" to establish a general
meta-converse bound for private communication, which has a number of
applications. The meta-converse allows for proving that any quantum channel's
relative entropy of entanglement is a strong converse rate for private
communication. For covariant channels, the meta-converse also leads to
second-order expansions of relative entropy of entanglement bounds for private
communication rates. For such channels, the bounds also apply to the private
communication setting in which the sender and receiver are assisted by
unlimited public classical communication, and as such, they are relevant for
establishing various converse bounds for quantum key distribution protocols
conducted over these channels. We find precise characterizations for several
channels of interest and apply the methods to establish several converse bounds
on the private transmission capabilities of all phase-insensitive bosonic
channels.Comment: v3: 53 pages, 3 figures, final version accepted for publication in
IEEE Transactions on Information Theor
Quantum channels and their entropic characteristics
One of the major achievements of the recently emerged quantum information
theory is the introduction and thorough investigation of the notion of quantum
channel which is a basic building block of any data-transmitting or
data-processing system. This development resulted in an elaborated structural
theory and was accompanied by the discovery of a whole spectrum of entropic
quantities, notably the channel capacities, characterizing
information-processing performance of the channels. This paper gives a survey
of the main properties of quantum channels and of their entropic
characterization, with a variety of examples for finite dimensional quantum
systems. We also touch upon the "continuous-variables" case, which provides an
arena for quantum Gaussian systems. Most of the practical realizations of
quantum information processing were implemented in such systems, in particular
based on principles of quantum optics. Several important entropic quantities
are introduced and used to describe the basic channel capacity formulas. The
remarkable role of the specific quantum correlations - entanglement - as a
novel communication resource, is stressed.Comment: review article, 60 pages, 5 figures, 194 references; Rep. Prog. Phys.
(in press
Quantum Channel Capacities Per Unit Cost
Communication over a noisy channel is often conducted in a setting in which
different input symbols to the channel incur a certain cost. For example, for
bosonic quantum channels, the cost associated with an input state is the number
of photons, which is proportional to the energy consumed. In such a setting, it
is often useful to know the maximum amount of information that can be reliably
transmitted per cost incurred. This is known as the capacity per unit cost. In
this paper, we generalize the capacity per unit cost to various communication
tasks involving a quantum channel such as classical communication,
entanglement-assisted classical communication, private communication, and
quantum communication. For each task, we define the corresponding capacity per
unit cost and derive a formula for it analogous to that of the usual capacity.
Furthermore, for the special and natural case in which there is a zero-cost
state, we obtain expressions in terms of an optimized relative entropy
involving the zero-cost state. For each communication task, we construct an
explicit pulse-position-modulation coding scheme that achieves the capacity per
unit cost. Finally, we compute capacities per unit cost for various bosonic
Gaussian channels and introduce the notion of a blocklength constraint as a
proposed solution to the long-standing issue of infinite capacities per unit
cost. This motivates the idea of a blocklength-cost duality, on which we
elaborate in depth.Comment: v3: 18 pages, 2 figure
A generalization of the Entropy Power Inequality to Bosonic Quantum Systems
In most communication schemes information is transmitted via travelling modes
of electromagnetic radiation. These modes are unavoidably subject to
environmental noise along any physical transmission medium and the quality of
the communication channel strongly depends on the minimum noise achievable at
the output. For classical signals such noise can be rigorously quantified in
terms of the associated Shannon entropy and it is subject to a fundamental
lower bound called entropy power inequality. Electromagnetic fields are however
quantum mechanical systems and then, especially in low intensity signals, the
quantum nature of the information carrier cannot be neglected and many
important results derived within classical information theory require
non-trivial extensions to the quantum regime. Here we prove one possible
generalization of the Entropy Power Inequality to quantum bosonic systems. The
impact of this inequality in quantum information theory is potentially large
and some relevant implications are considered in this work
Noisy Feedback and Loss Unlimited Private Communication
Alice is transmitting a private message to Bob across a bosonic wiretap
channel with the help of a public feedback channel to which all parties,
including the fully-quantum equipped Eve, have completely noiseless access. We
find that by altering the model such that Eve's copy of the initial round of
feedback is corrupted by an iota of noise, one step towards physical relevance,
the capacity can be increased dramatically. It is known that the private
capacity with respect to the original model for a pure-loss bosonic channel is
at most bits per mode, where is the transmissivity, in
the limit of infinite input photon number. This is a very pessimistic result as
there is a finite rate limit even with an arbitrarily large number of input
photons. We refer to this as a loss limited rate. However, in our altered model
we find that we can achieve a rate of bits per
mode, where is the input photon number. This rate diverges with , in
sharp contrast to the result for the original model. This suggests that
physical considerations behind the eavesdropping model should be taken more
seriously, as they can create strong dependencies of the achievable rates on
the model. For by a seemingly inconsequential weakening of Eve, we obtain a
loss-unlimited rate. Our protocol also works verbatim for arbitrary i.i.d.
noise (not even necessarily Gaussian) injected by Eve in every round, and even
if Eve is given access to copies of the initial transmission and noise. The
error probability of the protocol decays super-exponentially with the
blocklength.Comment: 7 pages, 2 figure