Related Experiment Video
Updated: May 22, 2026
09:23
Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans
Published on: August 16, 2017
Majorization theory approach to the Gaussian channel minimum entropy conjecture.
Raúl García-Patrón1, Carlos Navarrete-Benlloch, Seth Lloyd
1Research Laboratory of Electronics, MIT, Cambridge, Massachusetts 02139, USA.
Physical Review Letters
|May 1, 2012
Summary
Researchers proved a conjecture on the classical capacity of optical communication channels. This finding confirms that random coding of coherent states achieves maximum channel capacity, a significant advancement in quantum information theory.
Area of Science:
- Quantum Information Theory
- Quantum Communication
- Optical Channels
Background:
- The classical capacity of Gaussian bosonic channels remains an open problem in quantum information theory.
- A key conjecture suggests capacity is achieved via random coding of coherent states with isotropic Gaussian distributions.
Purpose of the Study:
- To confirm the conjecture regarding the classical capacity of Gaussian bosonic channels.
- To establish a link between quantum entanglement, majorization theory, and channel capacity.
Main Methods:
- Proving the Gaussian minimum entropy conjecture for a quantum-limited amplifier.
- Utilizing connections between quantum entanglement and majorization theory.
Main Results:
- Demonstrated that proving the Gaussian minimum entropy conjecture is sufficient to confirm the capacity conjecture.
- Developed a strong argument supporting the capacity conjecture through entanglement and majorization theory.
Conclusions:
- The study provides a pathway to confirm the conjectured classical capacity of Gaussian bosonic channels.
- The findings highlight the role of quantum entanglement and majorization in understanding quantum communication limits.
Related Concept Videos
01:14Central Limit Theorem
The central limit theorem, abbreviated as clt, is one of the most powerful and useful ideas in all of statistics. The central limit theorem for sample means says that if you repeatedly draw samples of a given size and calculate their means, and create a histogram of those means, then the resulting histogram will tend to have an approximate normal bell shape. In other words, as sample sizes increase, the distribution of means follows the normal distribution more closely.
The sample size, n, that...
The sample size, n, that...
00:59Propagation of Uncertainty from Random Error
An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
01:10Entropy Change in Reversible Processes
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
01:20The Maximum Power Transfer Theorem
Consider a linear AC Thevenin equivalent circuit connected to a load impedance.
The load connected draws the current, and the circuit delivers the power to the load. The alternating current flowing through the load is determined using the rectangular form of voltages, currents, network impedance, and load impedance. The average power delivered to the load is obtained from the product of the square of current and load resistance.
The load connected draws the current, and the circuit delivers the power to the load. The alternating current flowing through the load is determined using the rectangular form of voltages, currents, network impedance, and load impedance. The average power delivered to the load is obtained from the product of the square of current and load resistance.
01:10Propagation of Uncertainty from Systematic Error
The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...
01:26Entropy and the Second Law of Thermodynamics
Consider an isolated system in which a hot object is placed in contact with a cold one. This is an irreversible process that eventually leads both objects to reach the same equilibrium temperature. It is crucial to note that the constituents of any substance exhibit increased disorder at higher temperatures. As a cold substance absorbs heat, its constituents become more disordered. The energy transfer from a hotter object to a cooler one increases the system's disorder or randomness. This...