857 research outputs found
Quantum parallelism of the controlled-NOT operation: an experimental criterion for the evaluation of device performance
It is shown that a quantum controlled-NOT gate simultaneously performs the
logical functions of three distinct conditional local operations. Each of these
local operations can be verified by measuring a corresponding truth table of
four local inputs and four local outputs. The quantum parallelism of the gate
can then be observed directly in a set of three simple experimental tests, each
of which has a clear intuitive interpretation in terms of classical logical
operations. Specifically, quantum parallelism is achieved if the average
fidelity of the three classical operations exceeds 2/3. It is thus possible to
evaluate the essential quantum parallelism of an experimental controlled-NOT
gate by testing only three characteristic classical operations performed by the
gate.Comment: 6 pages, no figures, added references and discussio
Distance measures to compare real and ideal quantum processes
With growing success in experimental implementations it is critical to
identify a "gold standard" for quantum information processing, a single measure
of distance that can be used to compare and contrast different experiments. We
enumerate a set of criteria such a distance measure must satisfy to be both
experimentally and theoretically meaningful. We then assess a wide range of
possible measures against these criteria, before making a recommendation as to
the best measures to use in characterizing quantum information processing.Comment: 15 pages; this version in line with published versio
Approximate quantum error correction can lead to better codes
We present relaxed criteria for quantum error correction which are useful
when the specific dominant noise process is known. These criteria have no
classical analogue. As an example, we provide a four-bit code which corrects
for a single amplitude damping error. This code violates the usual Hamming
bound calculated for a Pauli description of the error process, and does not fit
into the GF(4) classification.Comment: 7 pages, 2 figures, submitted to Phys. Rev.
Direct Characterization of Quantum Dynamics: General Theory
The characterization of the dynamics of quantum systems is a task of both
fundamental and practical importance. A general class of methods which have
been developed in quantum information theory to accomplish this task is known
as quantum process tomography (QPT). In an earlier paper [M. Mohseni and D. A.
Lidar, Phys. Rev. Lett. 97, 170501 (2006)] we presented a new algorithm for
Direct Characterization of Quantum Dynamics (DCQD) of two-level quantum
systems. Here we provide a generalization by developing a theory for direct and
complete characterization of the dynamics of arbitrary quantum systems. In
contrast to other QPT schemes, DCQD relies on quantum error-detection
techniques and does not require any quantum state tomography. We demonstrate
that for the full characterization of the dynamics of n d-level quantum systems
(with d a power of a prime), the minimal number of required experimental
configurations is reduced quadratically from d^{4n} in separable QPT schemes to
d^{2n} in DCQD.Comment: 17 pages, 6 figures, minor modifications are mad
Unambiguous discrimination among quantum operations
We address the problem of unambiguous discrimination among a given set of
quantum operations. The necessary and sufficient condition for them to be
unambiguously distinguishable is derived in the cases of single use and
multiple uses respectively. For the latter case we explicitly construct the
input states and corresponding measurements that accomplish the task. It is
found that the introduction of entanglement can improve the discrimination.Comment: 5 pages, no figur
Quantum gate characterization in an extended Hilbert space
We describe an approach for characterizing the process of quantum gates using
quantum process tomography, by first modeling them in an extended Hilbert
space, which includes non-qubit degrees of freedom. To prevent unphysical
processes from being predicted, present quantum process tomography procedures
incorporate mathematical constraints, which make no assumptions as to the
actual physical nature of the system being described. By contrast, the
procedure presented here ensures physicality by placing physical constraints on
the nature of quantum processes. This allows quantum process tomography to be
performed using a smaller experimental data set, and produces parameters with a
direct physical interpretation. The approach is demonstrated by example of
mode-matching in an all-optical controlled-NOT gate. The techniques described
are non-specific and could be applied to other optical circuits or quantum
computing architectures.Comment: 4 pages, 2 figures, REVTeX (published version
Quantum process reconstruction based on mutually unbiased basis
We study a quantum process reconstruction based on the use of mutually
unbiased projectors (MUB-projectors) as input states for a D-dimensional
quantum system, with D being a power of a prime number. This approach connects
the results of quantum-state tomography using mutually unbiased bases (MUB)
with the coefficients of a quantum process, expanded in terms of
MUB-projectors. We also study the performance of the reconstruction scheme
against random errors when measuring probabilities at the MUB-projectors.Comment: 6 pages, 1 figur
Memory for Light as a Quantum Process
We report complete characterization of an optical memory based on
electromagnetically induced transparency. We recover the superoperator
associated with the memory, under two different working conditions, by means of
a quantum process tomography technique that involves storage of coherent states
and their characterization upon retrieval. In this way, we can predict the
quantum state retrieved from the memory for any input, for example, the
squeezed vacuum or the Fock state. We employ the acquired superoperator to
verify the nonclassicality benchmark for the storage of a Gaussian distributed
set of coherent states
A simple representation of quantum process tomography
We show that the Fano representation leads to a particularly simple and
appealing form of the quantum process tomography matrix , in that
the matrix is real, the number of matrix elements is exactly equal
to the number of free parameters required for the complete characterization of
a quantum operation, and these matrix elements are directly related to
evolution of the expectation values of the system's polarization measurements.
These facts are illustrated in the examples of one- and two-qubit quantum noise
channels.Comment: 5 page
Framework for classifying logical operators in stabilizer codes
Entanglement, as studied in quantum information science, and non-local
quantum correlations, as studied in condensed matter physics, are fundamentally
akin to each other. However, their relationship is often hard to quantify due
to the lack of a general approach to study both on the same footing. In
particular, while entanglement and non-local correlations are properties of
states, both arise from symmetries of global operators that commute with the
system Hamiltonian. Here, we introduce a framework for completely classifying
the local and non-local properties of all such global operators, given the
Hamiltonian and a bi-partitioning of the system. This framework is limited to
descriptions based on stabilizer quantum codes, but may be generalized. We
illustrate the use of this framework to study entanglement and non-local
correlations by analyzing global symmetries in topological order, distribution
of entanglement and entanglement entropy.Comment: 20 pages, 9 figure
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