22 research outputs found
When quantum tomography goes wrong: drift of quantum sources and other errors
The principle behind quantum tomography is that a large set of observations—many samples from a 'quorum' of distinct observables—can all be explained satisfactorily as measurements on a single underlying quantum state or process. Unfortunately, this principle may not hold. When it fails, any standard tomographic estimate should be viewed skeptically. Here we propose a simple way to test for this kind of failure using the Akaike information criterion. We point out that the application of this criterion in a quantum context, while still powerful, is not as straightforward as it is in classical physics. This is especially the case when future observables differ from those constituting the quorum
Entanglement verification with finite data
Suppose an experimentalist wishes to verify that his apparatus produces
entangled quantum states. A finite amount of data cannot conclusively
demonstrate entanglement, so drawing conclusions from real-world data requires
statistical reasoning. We propose a reliable method to quantify the weight of
evidence for (or against) entanglement, based on a likelihood ratio test. Our
method is universal in that it can be applied to any sort of measurements. We
demonstrate the method by applying it to two simulated experiments on two
qubits. The first measures a single entanglement witness, while the second
performs a tomographically complete measurement.Comment: 4 pages, 3 pretty picture
Quantum Darwinism in quantum Brownian motion: the vacuum as a witness
We study quantum Darwinism -- the redundant recording of information about a
decohering system by its environment -- in zero-temperature quantum Brownian
motion. An initially nonlocal quantum state leaves a record whose redundancy
increases rapidly with its spatial extent. Significant delocalization (e.g., a
Schroedinger's Cat state) causes high redundancy: many observers can measure
the system's position without perturbing it. This explains the objective (i.e.
classical) existence of einselected, decoherence-resistant pointer states of
macroscopic objects.Comment: 5 page
Optimal, reliable estimation of quantum states
Accurately inferring the state of a quantum device from the results of
measurements is a crucial task in building quantum information processing
hardware. The predominant state estimation procedure, maximum likelihood
estimation (MLE), generally reports an estimate with zero eigenvalues. These
cannot be justified. Furthermore, the MLE estimate is incompatible with error
bars, so conclusions drawn from it are suspect. I propose an alternative
procedure, Bayesian mean estimation (BME). BME never yields zero eigenvalues,
its eigenvalues provide a bound on their own uncertainties, and it is the most
accurate procedure possible. I show how to implement BME numerically, and how
to obtain natural error bars that are compatible with the estimate. Finally, I
briefly discuss the differences between Bayesian and frequentist estimation
techniques.Comment: RevTeX; 14 pages, 2 embedded figures. Comments enthusiastically
welcomed
The structure of preserved information in quantum processes
We introduce a general operational characterization of information-preserving
structures (IPS) -- encompassing noiseless subsystems, decoherence-free
subspaces, pointer bases, and error-correcting codes -- by demonstrating that
they are isometric to fixed points of unital quantum processes. Using this, we
show that every IPS is a matrix algebra. We further establish a structure
theorem for the fixed states and observables of an arbitrary process, which
unifies the Schrodinger and Heisenberg pictures, places restrictions on
physically allowed kinds of information, and provides an efficient algorithm
for finding all noiseless and unitarily noiseless subsystems of the process
Exponential speed-up with a single bit of quantum information: Testing the quantum butterfly effect
We present an efficient quantum algorithm to measure the average fidelity
decay of a quantum map under perturbation using a single bit of quantum
information. Our algorithm scales only as the complexity of the map under
investigation, so for those maps admitting an efficient gate decomposition, it
provides an exponential speed up over known classical procedures. Fidelity
decay is important in the study of complex dynamical systems, where it is
conjectured to be a signature of quantum chaos. Our result also illustrates the
role of chaos in the process of decoherence.Comment: 4 pages, 2 eps figure
Two-Qubit Gate Set Tomography with Fewer Circuits
Gate set tomography (GST) is a self-consistent and highly accurate method for
the tomographic reconstruction of a quantum information processor's quantum
logic operations, including gates, state preparations, and measurements.
However, GST's experimental cost grows exponentially with qubit number. For
characterizing even just two qubits, a standard GST experiment may have tens of
thousands of circuits, making it prohibitively expensive for platforms. We show
that, because GST experiments are massively overcomplete, many circuits can be
discarded. This dramatically reduces GST's experimental cost while still
maintaining GST's Heisenberg-like scaling in accuracy. We show how to exploit
the structure of GST circuits to determine which ones are superfluous. We
confirm the efficacy of the resulting experiment designs both through numerical
simulations and via the Fisher information for said designs. We also explore
the impact of these techniques on the prospects of three-qubit GST.Comment: 46 pages, 13 figures. V2: Minor edits to acknowledgment