Coherent information

About: Coherent information is a research topic. Over the lifetime, 1225 publications have been published within this topic receiving 46672 citations.

Entropic singularities give rise to quantum transmission.

Abstract: When can noiseless quantum information be sent across noisy quantum devices? And at what maximum rate? These questions lie at the heart of quantum technology, but remain unanswered because of non-additivity— a fundamental synergy which allows quantum devices (aka quantum channels) to send more information than expected. Previously, non-additivity was known to occur in very noisy channels with coherent information much smaller than that of a perfect channel; but, our work shows non-additivity in a simple low-noise channel. Our results extend even further. We prove a general theorem concerning positivity of a channel’s coherent information. A corollary of this theorem gives a simple dimensional test for a channel’s capacity. Applying this corollary solves an open problem by characterizing all qubit channels whose complement has non-zero capacity. Another application shows a wide class of zero quantum capacity qubit channels can assist an incomplete erasure channel in sending quantum information. These results arise from introducing and linking logarithmic singularities in the von-Neumann entropy with quantum transmission: changes in entropy caused by this singularity are a mechanism responsible for both positivity and non-additivity of the coherent information. Analysis of such singularities may be useful in other physics problems. Non-additivity of the quantum channel coherent information is known to occur in some very noisy channels, but its fundamental origin is unclear. Here, the author explains its link with log singularity of quantum entropy, and shows that it can also come up for low-noise channels.

Quantum information isomorphism: Beyond the dilemma of the Scylla of ontology and the Charybdis of instrumentalism

Abstract: In order to deal most effectively with the unanalyzable quantum whole, the Copenhagen interpretation takes as a "frame of reference" the preparation parameters and outcomes of measurements. It represents a passive, Ptolemaic-like instrumentalism directly related to "what we see in the sky," i.e., to the "surface" of reality. However, the notion of quantum information leads to an active, Copernican-like realism which involves an (intrinsic) ordering principle and the view that the quantum whole is analyzable. It is then possible to consider subsystems as localized in space, controlled individually, and communicated. This makes it natural to treat quantum information (quantum states) not merely as knowledge. Moreover, it involves complementarity between local and nonlocal information. To avoid the dilemma between the Scylla of ontology and the Charybdis of instrumentalism, we propose the concept of quantum information isomorphism, according to which the quantum description of nature is isomorphic to nature itself. By definition it is not just one-to-one mapping, but it preserves the full structure of nature. In particular, it allows the treatment of the wave function of isomorphic images of quantum systems in the laboratory, implying that quantum information is indeed carried by these quantum systems.

Coherent Classical Communication

Abstract: We introduce the concept of coherent classical communication and use it to relate other resources in quantum information theory. Using coherent classical communication, we are able to generalize super-dense coding to prepare arbitrary quantum states instead of only classical messages. We also derive single-letter formulae for the classical and quantum capacities of a bipartite unitary gate assisted by an arbitrary fixed amount of entanglement per use.

Leaking information to gain entanglement.

Abstract: Entanglement lies at the root of quantum theory. It is a remarkable resource that is generally believed to diminish when entangled systems interact with their environment. On the contrary, we find that engaging a system with its environment increases its ability to retain entanglement. The maximum rate of retaining entanglement is given by the quantum channel capacity. We counter-intuitively boost the quantum capacity of a channel by leaking almost all quantum information to the channel's environment. This boost exploits two-letter level non-additivity in the channel's coherent information. The resulting non-additivity has a far larger magnitude and a qualitatively wider extent than previously known. Our findings have a surprising implication for quantum key distribution: maximum rates for key distribution can be boosted by allowing leakage of information to the eavesdropping environment.

Decoherence, Quantum Zeno Effect, and the Efficacy of Mental Effort

Abstract: Recent theoretical and experimental papers support the prevailing opinion that large warm systems will rapidly lose quantum coherence, and that classical properties will emerge. This rapid loss of coherence would naturally be expected to block any critical role for quantum theory in explaining the interaction between our conscious experiences and the physical activities of our brains. However, there is a quantum theory of mind in which the efficacy of mental effort is not affected by decoherence effects. In this theory the effects of mental action on brain activity is achieved by a Quantum Zeno Effect that is not weakened by decoherence. The theory is based on a relativistic version of von Neumann's quantum theory. It encompasses all the predictions of Copenhagen quantum theory, which include all the validated predictions of classical physical theory. In addition, it forges two-way dynamical links between the physical and experiential aspects of nature. The theory has significant explanatory power.