158 research outputs found
Capacities of Quantum Amplifier Channels
Quantum amplifier channels are at the core of several physical processes. Not
only do they model the optical process of spontaneous parametric
down-conversion, but the transformation corresponding to an amplifier channel
also describes the physics of the dynamical Casimir effect in superconducting
circuits, the Unruh effect, and Hawking radiation. Here we study the
communication capabilities of quantum amplifier channels. Invoking a recently
established minimum output-entropy theorem for single-mode phase-insensitive
Gaussian channels, we determine capacities of quantum-limited amplifier
channels in three different scenarios. First, we establish the capacities of
quantum-limited amplifier channels for one of the most general communication
tasks, characterized by the trade-off between classical communication, quantum
communication, and entanglement generation or consumption. Second, we establish
capacities of quantum-limited amplifier channels for the trade-off between
public classical communication, private classical communication, and secret key
generation. Third, we determine the capacity region for a broadcast channel
induced by the quantum-limited amplifier channel, and we also show that a fully
quantum strategy outperforms those achieved by classical coherent detection
strategies. In all three scenarios, we find that the capacities significantly
outperform communication rates achieved with a naive time-sharing strategy.Comment: 16 pages, 2 figures, accepted for publication in Physical Review
Energy-Constrained Quantum Communication and Digital Dynamical Decoupling
This is a two-part thesis glued together by an everlasting theme in Quantum Information Science \-- to save the quantum state, or the information stored in it, from unavoidably environment-induced noise. The first part of this thesis studies the ultimate rate of reliably transmitting information, stored in quantum systems, through a noisy evolution. Specifically, we consider communication over optical links, upon which future inter-city quantum communication networks will be built. We show how to treat the infinite-dimensional bosonic system rigorously and establish the theory of energy-constrained private and quantum communication over quantum channels. Our result represents important progress in the field of energy-constrained quantum communication theory. As an example of communication over optical channels, we solve the triple trade-off capacity and broadcast capacity of quantum-limited amplifier channels. Our result not only includes two single-letter capacities, which are rare in quantum communication theory, but it is also the only known application of a recently proved minimum output-entropy conjecture. The second part of my thesis includes two of my works on dynamical decoupling (DD). DD is an open-loop technique to keep a qubit alive during decoherence, which is important for the actual implementation of quantum memory or a quantum computer. Instead of treating quantum evolution as a completely positive trace preserving map like in communication theory, we consider time-dependent evolution of a specific quantum system in quantum control theory. With more than decade of development of the theory of DD, people started to focus on pulse sequences with low sequencing complexity (called digital pulse sequences), which are required for large-scale implementation of quantum computation devices. We propose two unifying frameworks to systematically generate these engineering-friendly pulse sequences. Surprisingly, we prove that these two frameworks are actually two sides of the same coin, and thus our work greatly deepens our understanding of the underlying structure and the decoupling performance of digital pulse sequences
Applications of position-based coding to classical communication over quantum channels
Recently, a coding technique called position-based coding has been used to
establish achievability statements for various kinds of classical communication
protocols that use quantum channels. In the present paper, we apply this
technique in the entanglement-assisted setting in order to establish lower
bounds for error exponents, lower bounds on the second-order coding rate, and
one-shot lower bounds. We also demonstrate that position-based coding can be a
powerful tool for analyzing other communication settings. In particular, we
reduce the quantum simultaneous decoding conjecture for entanglement-assisted
or unassisted communication over a quantum multiple access channel to open
questions in multiple quantum hypothesis testing. We then determine achievable
rate regions for entanglement-assisted or unassisted classical communication
over a quantum multiple-access channel, when using a particular quantum
simultaneous decoder. The achievable rate regions given in this latter case are
generally suboptimal, involving differences of Renyi-2 entropies and
conditional quantum entropies.Comment: v4: 44 pages, v4 includes a simpler proof for an upper bound on
one-shot entanglement-assisted capacity, also found recently and
independently in arXiv:1804.0964
Regimes of classical simulability for noisy Gaussian boson sampling
As a promising candidate for exhibiting quantum computational supremacy,
Gaussian Boson Sampling (GBS) is designed to exploit the ease of experimental
preparation of Gaussian states. However, sufficiently large and inevitable
experimental noise might render GBS classically simulable. In this work, we
formalize this intuition by establishing a sufficient condition for approximate
polynomial-time classical simulation of noisy GBS --- in the form of an
inequality between the input squeezing parameter, the overall transmission rate
and the quality of photon detectors. Our result serves as a non-classicality
test that must be passed by any quantum computationalsupremacy demonstration
based on GBS. We show that, for most linear-optical architectures, where photon
loss increases exponentially with the circuit depth, noisy GBS loses its
quantum advantage in the asymptotic limit. Our results thus delineate
intermediate-sized regimes where GBS devices might considerably outperform
classical computers for modest noise levels. Finally, we find that increasing
the amount of input squeezing is helpful to evade our classical simulation
algorithm, which suggests a potential route to mitigate photon loss.Comment: 13 pages, 4 figures, final version accepted for publication in
Physical Review Letter
Energy-constrained private and quantum capacities of quantum channels
This paper establishes a general theory of energy-constrained quantum and private capacities of quantum channels. We begin by defining various energy-constrained communication tasks, including quantum communication with a uniform energy constraint, entanglement transmission with an average energy constraint, private communication with a uniform energy constraint, and secret key transmission with an average energy constraint. We develop several code conversions, which allow us to conclude non-trivial relations between the capacities corresponding to the above tasks. We then show how the regularized, energy-constrained coherent information is equal to the capacity for the first two tasks and is an achievable rate for the latter two tasks, whenever the energy observable satisfies the Gibbs condition of having a well-defined thermal state for all temperatures and the channel satisfies a finite output-entropy condition. For degradable channels satisfying these conditions, we find that the single-letter energy-constrained coherent information is equal to all of the capacities. We finally apply our results to degradable quantum Gaussian channels and recover several results already established in the literature (in some cases, we prove new results in this domain). Contrary to what may appear from some statements made in the literature recently, proofs of these results do not require the solution of any kind of minimum output entropy conjecture or entropy photon-number inequality
Entanglement-assisted private communication over quantum broadcast channels
We consider entanglement-assisted (EA) private communication over a quantum
broadcast channel, in which there is a single sender and multiple receivers. We
divide the receivers into two sets: the decoding set and the malicious set. The
decoding set and the malicious set can either be disjoint or can have a finite
intersection. For simplicity, we say that a single party Bob has access to the
decoding set and another party Eve has access to the malicious set, and both
Eve and Bob have access to the pre-shared entanglement with Alice. The goal of
the task is for Alice to communicate classical information reliably to Bob and
securely against Eve, and Bob can take advantage of pre-shared entanglement
with Alice. In this framework, we establish a lower bound on the one-shot EA
private capacity. When there exists a quantum channel mapping the state of the
decoding set to the state of the malicious set, such a broadcast channel is
said to be degraded. We establish an upper bound on the one-shot EA private
capacity in terms of smoothed min- and max-entropies for such channels. In the
limit of a large number of independent channel uses, we prove that the EA
private capacity of a degraded quantum broadcast channel is given by a
single-letter formula. Finally, we consider two specific examples of degraded
broadcast channels and find their capacities. In the first example, we consider
the scenario in which one part of Bob's laboratory is compromised by Eve. We
show that the capacity for this protocol is given by the conditional quantum
mutual information of a quantum broadcast channel, and so we thus provide an
operational interpretation to the dynamic counterpart of the conditional
quantum mutual information. In the second example, Eve and Bob have access to
mutually exclusive sets of outputs of a broadcast channel.Comment: v2: 23 pages, 2 figures, accepted for publication in the special
issue "Shannon's Information Theory 70 years on: applications in classical
and quantum physics" for Journal of Physics
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