23 research outputs found
Minimal optimal generalized quantum measurements
Optimal and finite positive operator valued measurements on a finite number
of identically prepared systems have been presented recently. With physical
realization in mind we propose here optimal and minimal generalized quantum
measurements for two-level systems.
We explicitly construct them up to N=7 and verify that they are minimal up to
N=5. We finally propose an expression which gives the size of the minimal
optimal measurements for arbitrary .Comment: 9 pages, Late
Optimal generalized quantum measurements for arbitrary spin systems
Positive operator valued measurements on a finite number of N identically
prepared systems of arbitrary spin J are discussed. Pure states are
characterized in terms of Bloch-like vectors restricted by a SU(2 J+1)
covariant constraint. This representation allows for a simple description of
the equations to be fulfilled by optimal measurements. We explicitly find the
minimal POVM for the N=2 case, a rigorous bound for N=3 and set up the analysis
for arbitrary N.Comment: LateX, 12 page
Optimal minimal measurements of mixed states
The optimal and minimal measuring strategy is obtained for a two-state system
prepared in a mixed state with a probability given by any isotropic a priori
distribution. We explicitly construct the specific optimal and minimal
generalized measurements, which turn out to be independent of the a priori
probability distribution, obtaining the best guesses for the unknown state as
well as a closed expression for the maximal mean averaged fidelity. We do this
for up to three copies of the unknown state in a way which leads to the
generalization to any number of copies, which we then present and prove.Comment: 20 pages, no figure
Optimal estimation of two-qubit pure-state entanglement
We present optimal measuring strategies for the estimation of the
entanglement of unknown two-qubit pure states and of the degree of mixing of
unknown single-qubit mixed states, of which N identical copies are available.
The most general measuring strategies are considered in both situations, to
conclude in the first case that a local, although collective, measurement
suffices to estimate entanglement, a non-local property, optimally.Comment: REVTEX, 9 pages, 1 figur
Communication of Spin Directions with Product States and Finite Measurements
Total spin eigenstates can be used to intrinsically encode a direction, which
can later be decoded by means of a quantum measurement. We study the optimal
strategy that can be adopted if, as is likely in practical applications, only
product states of -spins are available. We obtain the asymptotic behaviour
of the average fidelity which provides a proof that the optimal states must be
entangled. We also give a prescription for constructing finite measurements for
general encoding eigenstates.Comment: 4 pages, minor changes, version to appear in PR
Universal Quantum Information Compression
Suppose that a quantum source is known to have von Neumann entropy less than
or equal to S but is otherwise completely unspecified. We describe a method of
universal quantum data compression which will faithfully compress the quantum
information of any such source to S qubits per signal (in the limit of large
block lengths).Comment: RevTex 4 page
Optimal strategies for sending information through a quantum channel
Quantum states can be used to encode the information contained in a
direction, i.e., in a unit vector. We present the best encoding procedure when
the quantum state is made up of spins (qubits). We find that the quality of
this optimal procedure, which we quantify in terms of the fidelity, depends
solely on the dimension of the encoding space. We also investigate the use of
spatial rotations on a quantum state, which provide a natural and less
demanding encoding. In this case we prove that the fidelity is directly related
to the largest zeros of the Legendre and Jacobi polynomials. We also discuss
our results in terms of the information gain.Comment: 4 pages, RevTex, final version to appear in Phys.Rev.Let
Fidelity trade-off for finite ensembles of identically prepared qubits
We calculate the trade-off between the quality of estimating the quantum
state of an ensemble of identically prepared qubits and the minimum level of
disturbance that has to be introduced by this procedure in quantum mechanics.
The trade-off is quantified using two mean fidelities: the operation fidelity
which characterizes the average resemblance of the final qubit state to the
initial one, and the estimation fidelity describing the quality of the obtained
estimate. We analyze properties of quantum operations saturating the
achievability bound for the operation fidelity versus the estimation fidelity,
which allows us to reduce substantially the complexity of the problem of
finding the trade-off curve. The reduced optimization problem has the form of
an eigenvalue problem for a set of tridiagonal matrices, and it can be easily
solved using standard numerical tools.Comment: 26 pages, REVTeX, 2 figures. Few minor corrections, accepted for
publication in Physical Review
Asymmetric universal entangling machine
We give a definition of asymmetric universal entangling machine which
entangles a system in an unknown state to a specially prepared ancilla. The
machine produces a fixed state-independent amount of entanglement in exchange
to a fixed degradation of the system state fidelity. We describe explicitly
such a machine for any quantum system having levels and prove its
optimality. We show that a -dimensional ancilla is sufficient for reaching
optimality. The introduced machine is a generalization to a number of widely
investigated universal quantum devices such as the symmetric and asymmetric
quantum cloners, the symmetric quantum entangler, the quantum information
distributor and the universal-NOT gate.Comment: 28 pages, 3 figure
Information, disturbance and Hamiltonian quantum feedback control
We consider separating the problem of designing Hamiltonian quantum feedback
control algorithms into a measurement (estimation) strategy and a feedback
(control) strategy, and consider optimizing desirable properties of each under
the minimal constraint that the available strength of both is limited. This
motivates concepts of information extraction and disturbance which are distinct
from those usually considered in quantum information theory. Using these
concepts we identify an information trade-off in quantum feedback control.Comment: 13 pages, multicol Revtex, 2 eps figure