Quantum information distance based on classical descriptions

Jeffrey Bub

Abhay K. Ram, Efstratios Koukoutsis, Kyriakos Hizanidis +3 more

The presence of waves in laboratory and space plasma is due to collective processes which are inherently classical in nature. The linear propagation of electromagnetic waves follows from Maxwell equations in which the constitutive relations are obtained using either a kinetic or a fluid description of the plasma. Even though these descriptions require a large number of charged particles inside a Debye sphere, the interparticle distance is long compared to the de Broglie wavelength of any electron or ion in the plasma. As such, quantum effects are negligible and classical treatments have been successful in providing insight into plasma behavior in fusion, terrestrial, and space plasma. However, this does not preclude the exploitation of quantum computers for simulating classical plasma. It requires us to formulate appropriate theoretical models that appear to be “quantum-like” while maintaining the integrity of the classical description of electromagnetic wave propagation in plasma.

Richard Jozsa

Harold Ollivier, Jean–Pierre Tillich

We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances in classical communication. The particular example shown here uses the stabilizer formalism. We provide an explicit encoding circuit and its associated error estimation algorithm. The latter gives the most likely error over any memoryless quantum channel, with a complexity growing only linearly with the number of encoded qubits.

John Watrous

Bartosz Regula, Ludovico Lami, Mario Berta +1 more

The measures of distance frequently used in quantum information, such as trace distance or fidelity-based purified distance, are the smallest extensions of the corresponding distance measures in classical information theory. However, this way of extending classical distances is not unique, and a whole spectrum of other extensions can be defined. Here we study the question of how quantum information processing tasks are affected by a change of the error metrics to the maximal extensions of the classical distance measures, imposing more demanding error requirements on operational tasks. We find that the performance of some tasks, such as channel coding or quantum resource distillation, is not affected whatsoever by this change. However, for other tasks such as channel simulation and quantum resource dilution, we show that the rates are now given not by functions of the standard (Umegaki) quantum relative entropy, but ones based on the Belavkin-Staszewski relative entropy. Our results connect the Belavkin-Staszewski relative entropy with operational tasks and reveal that known reversibility results in quantum information, including the reverse Shannon theorem and the asymptotic reversibility of quantum resource transformations, no longer hold under maximal distance measures.