8 research outputs found
A unification of the coding theory and OAQEC perspective on hybrid codes
It has been shown that there is an advantage in transmitting both quantum and
classical information simultaneously over a quantum channel, compared to
independent transmissions. The characterization and construction of such codes,
which we refer to as hybrid codes, has been done from a coding theory and an
operator algebra quantum error correction (OAQEC) perspective. In this work we
unify these two perspectives, and show that the coding theory formulation is a
specific case of the OAQEC perspective. We also generalize the quantum hamming
bound to the hybrid case. To date no such hybrid codes have been physically
implemented. In this work we develop a hybrid code and provide the encoding and
decoding circuit.Comment: 5 pages, 2 figure
Violation of an augmented set of Leggett-Garg inequalities and the implementation of a continuous in time velocity measurement
Macroscopic realism (MR) is the view that a system may possess definite properties at any time independent of past or future measurements, and may be tested experimentally using the Leggett-Garg inequalities (LGIs). In this work we advance the study of LGIs in two ways using experiments carried out on a nuclear magnetic resonance spectrometer. Firstly, we addresses the fact that the LGIs are only necessary conditions for MR but not sufficient ones. We implement a recently-proposed test of necessary and sufficient conditions for MR which consists of a combination of the original four three-time LGIs augmented with a set of twelve two-time LGIs. We explore different regimes in which the two- and three-time LGIs may each be satisfied or violated. Secondly, we implement a recent proposal for a measurement protocol which determines the temporal correlation functions in an approximately non-invasive manner. It employs a measurement of the velocity of a dichotomic variable Q, continuous in time, from which a possible sign change of Q may be determined in a single measurement of an ancilla coupled to the velocity. This protocol involves a significantly different set of assumptions to the traditional ideal negative measurement protocol and a comparison with the latter is carried out
Critical phase and spin sharpening in SU(2)-symmetric monitored quantum circuits
Monitored quantum circuits exhibit entanglement transitions at certain
measurement rates. Such a transition separates phases characterized by how much
information an observer can learn from the measurement outcomes. We study
SU(2)-symmetric monitored quantum circuits, using exact numerics and a mapping
onto an effective statistical-mechanics model. Due to the symmetry's
non-Abelian nature, measuring qubit pairs allows for nontrivial entanglement
scaling even in the measurement-only limit. We find a transition between a
volume-law entangled phase and a critical phase whose diffusive purification
dynamics emerge from the non-Abelian symmetry. Additionally, we numerically
identify a "spin-sharpening transition." On one side is a phase in which the
measurements can efficiently identify the system's total spin quantum number;
on the other side is a phase in which measurements cannot.Comment: 8.5 pages (6 figures) + appendices (11.5 pages
Noncommuting conserved charges in quantum thermodynamics and beyond
Thermodynamic systems typically conserve quantities ("charges") such as
energy and particle number. The charges are often assumed implicitly to commute
with each other. Yet quantum phenomena such as uncertainty relations rely on
observables' failure to commute. How do noncommuting charges affect
thermodynamic phenomena? This question, upon arising at the intersection of
quantum information theory and thermodynamics, spread recently across many-body
physics. Charges' noncommutation has been found to invalidate derivations of
the thermal state's form, decrease entropy production, conflict with the
eigenstate thermalization hypothesis, and more. This Perspective surveys key
results in, opportunities for, and work adjacent to the quantum thermodynamics
of noncommuting charges. Open problems include a conceptual puzzle: Evidence
suggests that noncommuting charges may hinder thermalization in some ways while
enhancing thermalization in others.Comment: 9.5 pages (3 figures) + appendices (10 pages
How to build Hamiltonians that transport noncommuting charges in quantum thermodynamics
Abstract Noncommuting conserved quantities have recently launched a subfield of quantum thermodynamics. In conventional thermodynamics, a system of interest and an environment exchange quantities—energy, particles, electric charge, etc.—that are globally conserved and are represented by Hermitian operators. These operators were implicitly assumed to commute with each other, until a few years ago. Freeing the operators to fail to commute has enabled many theoretical discoveries—about reference frames, entropy production, resource-theory models, etc. Little work has bridged these results from abstract theory to experimental reality. This paper provides a methodology for building this bridge systematically: we present a prescription for constructing Hamiltonians that conserve noncommuting quantities globally while transporting the quantities locally. The Hamiltonians can couple arbitrarily many subsystems together and can be integrable or nonintegrable. Our Hamiltonians may be realized physically with superconducting qudits, with ultracold atoms, and with trapped ions