Topic
Coherent information
About: Coherent information is a research topic. Over the lifetime, 1225 publications have been published within this topic receiving 46672 citations.
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TL;DR: The results demonstrate that Quantum Darwinism is robust with respect to nonideal initial states of the environment: the environment almost always acquires redundant information about the system but its rate of acquisition can be reduced.
Abstract: Quantum Darwinism provides an information-theoretic framework for the emergence of the objective, classical world from the quantum substrate. The key to this emergence is the proliferation of redundant information throughout the environment where observers can then intercept it. We study this process for a purely decohering interaction when the environment, $\mathcal{E}$, is in a nonideal (e.g., mixed) initial state. In the case of good decoherence, that is, after the pointer states have been unambiguously selected, the mutual information between the system, $\mathcal{S}$, and an environment fragment, $\mathcal{F}$, is given solely by $\mathcal{F}$'s entropy increase. This demonstrates that the environment's capacity for recording the state of $\mathcal{S}$ is directly related to its ability to increase its entropy. Environments that remain nearly invariant under the interaction with $\mathcal{S}$, either because they have a large initial entropy or a misaligned initial state, therefore have a diminished ability to acquire information. To elucidate the concept of good decoherence, we show that, when decoherence is not complete, the deviation of the mutual information from $\mathcal{F}$'s entropy change is quantified by the quantum discord, i.e., the excess mutual information between $\mathcal{S}$ and $\mathcal{F}$ is information regarding the initial coherence between pointer states of $\mathcal{S}$. In addition to illustrating these results with a single-qubit system interacting with a multiqubit environment, we find scaling relations for the redundancy of information acquired by the environment that display a universal behavior independent of the initial state of $\mathcal{S}$. Our results demonstrate that Quantum Darwinism is robust with respect to nonideal initial states of the environment: the environment almost always acquires redundant information about the system but its rate of acquisition can be reduced.
77 citations
TL;DR: A brief history of this interaction between information theory and entropy, together with a more detailed look at three areas of connection, namely, recurrence theory, blowing-up bounds, and direct sample-path methods.
Abstract: Information theorists frequently use the ergodic theorem; likewise entropy concepts are often used in information theory. Recently, the two subjects have become partially intertwined as deeper results from each discipline find use in the other. A brief history of this interaction is presented in this paper, together with a more detailed look at three areas of connection, namely, recurrence theory, blowing-up bounds, and direct sample-path methods.
77 citations
TL;DR: In this paper, the channel capacity of an entangled photonic state in high-dimensional position and momentum bases is characterized and a correspondingly highdimensional separability bound is provided for the channel performance.
Abstract: High-dimensional Hilbert spaces used for quantum communication channels offer the possibility of large data transmission capabilities. We propose a method of characterizing the channel capacity of an entangled photonic state in high-dimensional position and momentum bases. We use this method to measure the channel capacity of a parametric down-conversion state by measuring in up to 576 dimensions per detector. We achieve a channel capacity over 7 bits/photon in either the position or momentum basis. Furthermore, we provide a correspondingly high-dimensional separability bound that suggests that the channel performance cannot be replicated classically.
76 citations
TL;DR: Using strong subadditivity of entropy, it is proved that the Holevo quantity is not larger than an exchange entropy, which implies an upper bound for coherent information.
Abstract: The mutual information between the sender of a classical message encoded in quantum carriers and a receiver is fundamentally limited by the Holevo quantity. Using strong subadditivity of entropy, we prove that the Holevo quantity is not larger than an exchange entropy. This implies an upper bound for coherent information. Moreover, restricting our attention to classical information, we bound the transmission distance between probability distributions by their entropic distance, which is a concave function of their Hellinger distance.
75 citations
TL;DR: In this article, the authors consider quantum channels with two senders and one receiver and give multi-letter characterizations of two different two-dimensional capacity regions, the first region is comprised of the rates at which it is possible for one sender to send classical information, while the other sends quantum information.
Abstract: We consider quantum channels with two senders and one receiver. For an arbitrary such channel, we give multi-letter characterizations of two different two-dimensional capacity regions. The first region is comprised of the rates at which it is possible for one sender to send classical information, while the other sends quantum information. The second region consists of the rates at which each sender can send quantum information. For each region, we give an example of a channel for which the corresponding region has a single-letter description. One of our examples relies on a new result proved here, perhaps of independent interest, stating that the coherent information over any degradable channel is concave in the input density operator. We conclude with connections to other work and a discussion on generalizations where each user simultaneously sends classical and quantum information.
75 citations