126 research outputs found
Quantum data gathering
Measurement of a quantum system – the process by which an observer gathers information about it – provides a link between the quantum and classical worlds. The nature of this process is the central issue for attempts to reconcile quantum and classical descriptions of physical processes. Here, we show that the conventional paradigm of quantum measurement is directly responsible for a well-known disparity between the resources required to extract information from quantum and classical systems. We introduce a simple form of quantum data gathering, “coherent measurement”, that eliminates this disparity and restores a pleasing symmetry between classical and quantum statistical inference. To illustrate the power of quantum data gathering, we demonstrate that coherent measurements are optimal and strictly more powerful than conventional one-at-a-time measurements for the task of discriminating quantum states, including certain entangled many-body states (e.g., matrix product states)
Climbing Mount Scalable: Physical-Resource Requirements for a Scalable Quantum Computer
The primary resource for quantum computation is Hilbert-space dimension.
Whereas Hilbert space itself is an abstract construction, the number of
dimensions available to a system is a physical quantity that requires physical
resources. Avoiding a demand for an exponential amount of these resources
places a fundamental constraint on the systems that are suitable for scalable
quantum computation. To be scalable, the effective number of degrees of freedom
in the computer must grow nearly linearly with the number of qubits in an
equivalent qubit-based quantum computer.Comment: LATEX, 24 pages, 1 color .eps figure. This new version has been
accepted for publication in Foundations of Physic
Physical-resource demands for scalable quantum computation
The primary resource for quantum computation is Hilbert-space dimension.
Whereas Hilbert space itself is an abstract construction, the number of
dimensions available to a system is a physical quantity that requires physical
resources. Avoiding a demand for an exponential amount of these resources
places a fundamental constraint on the systems that are suitable for scalable
quantum computation. To be scalable, the number of degrees of freedom in the
computer must grow nearly linearly with the number of qubits in an equivalent
qubit-based quantum computer.Comment: This paper will be published in the proceedings of the SPIE
Conference on Fluctuations and Noise in Photonics and Quantum Optics, Santa
Fe, New Mexico, June 1--4, 200
On the Optimal Choice of Spin-Squeezed States for Detecting and Characterizing a Quantum Process
Quantum metrology uses quantum states with no classical counterpart to
measure a physical quantity with extraordinary sensitivity or precision. Most
metrology schemes measure a single parameter of a dynamical process by probing
it with a specially designed quantum state. The success of such a scheme
usually relies on the process belonging to a particular one-parameter family.
If this assumption is violated, or if the goal is to measure more than one
parameter, a different quantum state may perform better. In the most extreme
case, we know nothing about the process and wish to learn everything. This
requires quantum process tomography, which demands an informationally-complete
set of probe states. It is very convenient if this set is group-covariant --
i.e., each element is generated by applying an element of the quantum system's
natural symmetry group to a single fixed fiducial state. In this paper, we
consider metrology with 2-photon ("biphoton") states, and report experimental
studies of different states' sensitivity to small, unknown collective SU(2)
rotations ("SU(2) jitter"). Maximally entangled N00N states are the most
sensitive detectors of such a rotation, yet they are also among the worst at
fully characterizing an a-priori unknown process. We identify (and confirm
experimentally) the best SU(2)-covariant set for process tomography; these
states are all less entangled than the N00N state, and are characterized by the
fact that they form a 2-design.Comment: 10 pages, 5 figure
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
Adaptive quantum state tomography improves accuracy quadratically
We introduce a simple protocol for adaptive quantum state tomography, which
reduces the worst-case infidelity between the estimate and the true state from
to . It uses a single adaptation step and just one
extra measurement setting. In a linear optical qubit experiment, we demonstrate
a full order of magnitude reduction in infidelity (from to ) for
a modest number of samples ().Comment: 8 pages, 7 figure
Effect of nonnegativity on estimation errors in one-qubit state tomography with finite data
We analyze the behavior of estimation errors evaluated by two loss functions,
the Hilbert-Schmidt distance and infidelity, in one-qubit state tomography with
finite data. We show numerically that there can be a large gap between the
estimation errors and those predicted by an asymptotic analysis. The origin of
this discrepancy is the existence of the boundary in the state space imposed by
the requirement that density matrices be nonnegative (positive semidefinite).
We derive an explicit form of a function reproducing the behavior of the
estimation errors with high accuracy by introducing two approximations: a
Gaussian approximation of the multinomial distributions of outcomes, and
linearizing the boundary. This function gives us an intuition for the behavior
of the expected losses for finite data sets. We show that this function can be
used to determine the amount of data necessary for the estimation to be treated
reliably with the asymptotic theory. We give an explicit expression for this
amount, which exhibits strong sensitivity to the true quantum state as well as
the choice of measurement.Comment: 9 pages, 4 figures, One figure (FIG. 1) is added to the previous
version, and some typos are correcte
Spectral thresholding quantum tomography for low rank states
The estimation of high dimensional quantum states is an important statistical problem arising in current quantum technology applications. A key example is the tomography of multiple ions states, employed in the validation of state preparation in ion trap experiments (Häffner et al 2005 Nature 438 643). Since full tomography becomes unfeasible even for a small number of ions, there is a need to investigate lower dimensional statistical models which capture prior information about the state, and to devise estimation methods tailored to such models. In this paper we propose several new methods aimed at the efficient estimation of low rank states and analyse their performance for multiple ions tomography. All methods consist in first computing the least squares estimator, followed by its truncation to an appropriately chosen smaller rank. The latter is done by setting eigenvalues below a certain 'noise level' to zero, while keeping the rest unchanged, or normalizing them appropriately. We show that (up to logarithmic factors in the space dimension) the mean square error of the resulting estimators scales as where r is the rank, is the dimension of the Hilbert space, and N is the number of quantum samples. Furthermore we establish a lower bound for the asymptotic minimax risk which shows that the above scaling is optimal. The performance of the estimators is analysed in an extensive simulations study, with emphasis on the dependence on the state rank, and the number of measurement repetitions. We find that all estimators perform significantly better than the least squares, with the 'physical estimator' (which is a bona fide density matrix) slightly outperforming the other estimators
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
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