Quantum
communication
channels
Classical communication
systems based on optics and optoelectronics changed our society.
On the other hand, when the intensity of few-photon signals is
reduced, we unavoidably enter the realm of quantum physics.
Quantum communication, namely the art of transferring quantum
states from one place to another, has arrived at a crucial stage
of developing a commercial and technological impact on our
society. This is witnessed by the first quantum cryptosystems
available on the market. At the same time, quantum communication
is a fascinating field: it combines concepts and techniques from
basic quantum physics and information science to optical
engineering.
Quantum communication channels use quantum systems to transfer
classical or quantum information. In the first case, classical
bits are encoded by means of quantum states. In the latter, one
may want to distribute entanglement between two or more
communicating parties or to transfer an unknown quantum state
between different units of a quantum computer. The fundamental
quantities characterizing a quantum channel are the classical
and the quantum channel capacities, that are defined as the
maximum number of bits/qubits that can be reliably transmitted
per channel use .
Quantum channels are the natural theoretical framework to
investigate both quantum communication and computation in a
noisy environment. In the first case, information is transmitted
in space, in the latter in time. In both cases, noise can have
relevant low frequency components, which traduce themselves in
memory effects. That is, consecutive uses of a channel can be
correlated. Memory effects may be important, for instance, in
quantum communication protocols realized by means of photons
travelling across fibers with birefringence fluctuating with
characteristic time scales longer than the separation between
successive light pulses. Moreover, solid state implementations
of quantum hardware show a characteristic low-frequency noise.
Dephasing channel with memory
In spite of their physical relevance, quantum channels
with memory are very hard to analyze and their classical and
quantum capacities rarely known. Indeed, due to the peculiar
features of quantum entanglement, one has to solve a sequence of
optimization problems of increasing size (Hilbert space
dimension) as the number of channel uses grows, and then take
the limit of infinite number of uses. We have
computed [1] the quantum capacity of a Markov chain dephasing
channel with memory and shown that it is greater than in the
memoryless case. Furthermore, based on theoretical arguments and
numerical simulations, we have conjectured that memory-induced
quantum capacity enhancement takes place also when the dephasing
environment is modelled by a bosonic bath. We plan to further
explore the connection between quantum channels with memory and
the statistical mechanics of interacting many-body systems. This
may open fruitful new possibilities for the study of information
transmission across quantum channels with memory.
Quantum capacity of a Markov
chain dephasing channel (in the asymptotic limit when number n of channel uses tends to
infinite)
Enhancement of transmission rates in quantum
memory channels with damping
We have considered the
transfer of quantum information down a single-mode quantum
transmission line. Such quantum channel is modeled as a damped harmonic
oscillator, the interaction between the information carriers -a
train of n qubits- and the oscillator being of the
Jaynes-Cummings kind [2,3]. The oscillator acts as a local environment,
coupled to a memoryless reservoir damping both its phases and
populations, which mimics any cooling process resetting the
oscillator to its ground state. Memory effects appear if the
state of the oscillator is not reset after each channel use. The
model is visualized by a qubit-micromaser system, the qubit
train being a stream of two-level Rydberg atoms injected at low
rate into the cavity; it also describes the dynamics of a
quantum memory, which may be implemented by coupling n
superconducting qubits to a microstrip cavity, in a circuit-QED
architecture.
We have shown [2] that the quantum information transmission
worsens with increasing transmission frequency due to the
increase of memory effects. However, the decrease is found to be
only moderate, so that the quantum transmission rate increases
with increasing transmission frequency. Therefore, operating the
memory channel at high transmission frequency, thus accepting
prima facie deleterious memory effects, will be more beneficial
than using low frequency. These results are relevant also for
the secure transmission of classical information, that is, for
cryptographic purposes.
Finally, we have analytically computed the single-shot classical
capacity and the quantum capacity for a fully correlated (i.e.,
with full memory) channel with damping [4], and also
investigated the performance of a partially correlated amplitude
dampig channel [5].
Enhancement of transmission
rate when increasing the memory factor
References
[1] A. D'Arrigo, G. Benenti and
G. Falci, Quantum capacity of
dephasing channels with memory, New J. Phys. 9, 310 (2007).
[2] G. Benenti, A. D'Arrigo and
G. Falci, Enhancement of
transmission rates in quantum memory channels with damping,
Phys. Rev. Lett. 103,
020502 (2009).
[3] A. D'Arrigo, G. Benenti and
G. Falci, Transmission of
classical and quantum information through a quantum memory
channel with damping, Eur. Phys. J. D66, 147 (2012).
[4] A. D'Arrigo, G. Benenti, G. Falci and C. Macchiavello, Classical and quantum capacities
of a fully correlated amplitude damping channel, Phys.
Rev. A 88, 042337
(2013).
[5] A. D'Arrigo, G. Benenti, G. Falci and C.
Macchiavello,
Information transmission over an amplitude damping channel
with an
arbitrary degree of memory,
Phys. Rev. A 92, 062342 (2015).