20,254 research outputs found
H-theorem in quantum physics
Remarkable progress of quantum information theory (QIT) allowed to formulate
mathematical theorems for conditions that data-transmitting or data-processing
occurs with a non-negative entropy gain. However, relation of these results
formulated in terms of entropy gain in quantum channels to temporal evolution
of real physical systems is not thoroughly understood. Here we build on the
mathematical formalism provided by QIT to formulate the quantum H-theorem in
terms of physical observables. We discuss the manifestation of the second law
of thermodynamics in quantum physics and uncover special situations where the
second law can be violated. We further demonstrate that the typical evolution
of energy-isolated quantum systems occurs with non-diminishing entropy.Comment: 8 pages, 4 figure
Quantum information can be negative
Given an unknown quantum state distributed over two systems, we determine how
much quantum communication is needed to transfer the full state to one system.
This communication measures the "partial information" one system needs
conditioned on it's prior information. It turns out to be given by an extremely
simple formula, the conditional entropy. In the classical case, partial
information must always be positive, but we find that in the quantum world this
physical quantity can be negative. If the partial information is positive, its
sender needs to communicate this number of quantum bits to the receiver; if it
is negative, the sender and receiver instead gain the corresponding potential
for future quantum communication. We introduce a primitive "quantum state
merging" which optimally transfers partial information. We show how it enables
a systematic understanding of quantum network theory, and discuss several
important applications including distributed compression, multiple access
channels and multipartite assisted entanglement distillation (localizable
entanglement). Negative channel capacities also receive a natural
interpretation
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
Entropy of a quantum channel
The von Neumann entropy of a quantum state is a central concept in physics
and information theory, having a number of compelling physical interpretations.
There is a certain perspective that the most fundamental notion in quantum
mechanics is that of a quantum channel, as quantum states, unitary evolutions,
measurements, and discarding of quantum systems can each be regarded as certain
kinds of quantum channels. Thus, an important goal is to define a consistent
and meaningful notion of the entropy of a quantum channel. Motivated by the
fact that the entropy of a state can be formulated as the difference of
the number of physical qubits and the "relative entropy distance" between
and the maximally mixed state, here we define the entropy of a channel
as the difference of the number of physical qubits of the channel
output with the "relative entropy distance" between and the
completely depolarizing channel. We prove that this definition satisfies all of
the axioms, recently put forward in [Gour, IEEE Trans. Inf. Theory 65, 5880
(2019)], required for a channel entropy function. The task of quantum channel
merging, in which the goal is for the receiver to merge his share of the
channel with the environment's share, gives a compelling operational
interpretation of the entropy of a channel. We define Renyi and min-entropies
of a channel and prove that they satisfy the axioms required for a channel
entropy function. Among other results, we also prove that a smoothed version of
the min-entropy of a channel satisfies the asymptotic equipartition property.Comment: v2: 29 pages, 1 figur
Approximate reversibility in the context of entropy gain, information gain, and complete positivity
There are several inequalities in physics which limit how well we can process
physical systems to achieve some intended goal, including the second law of
thermodynamics, entropy bounds in quantum information theory, and the
uncertainty principle of quantum mechanics. Recent results provide physically
meaningful enhancements of these limiting statements, determining how well one
can attempt to reverse an irreversible process. In this paper, we apply and
extend these results to give strong enhancements to several entropy
inequalities, having to do with entropy gain, information gain, entropic
disturbance, and complete positivity of open quantum systems dynamics. Our
first result is a remainder term for the entropy gain of a quantum channel.
This result implies that a small increase in entropy under the action of a
subunital channel is a witness to the fact that the channel's adjoint can be
used as a recovery map to undo the action of the original channel. Our second
result regards the information gain of a quantum measurement, both without and
with quantum side information. We find here that a small information gain
implies that it is possible to undo the action of the original measurement if
it is efficient. The result also has operational ramifications for the
information-theoretic tasks known as measurement compression without and with
quantum side information. Our third result shows that the loss of Holevo
information caused by the action of a noisy channel on an input ensemble of
quantum states is small if and only if the noise can be approximately corrected
on average. We finally establish that the reduced dynamics of a
system-environment interaction are approximately completely positive and
trace-preserving if and only if the data processing inequality holds
approximately.Comment: v3: 12 pages, accepted for publication in Physical Review
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