24 research outputs found
Optimal Quantum Clocks
A quantum clock must satisfy two basic constraints. The first is a bound on
the time resolution of the clock given by the difference between its maximum
and minimum energy eigenvalues. The second follows from Holevo's bound on how
much classical information can be encoded in a quantum system. We show that
asymptotically, as the dimension of the Hilbert space of the clock tends to
infinity, both constraints can be satisfied simultaneously. The experimental
realization of such an optimal quantum clock using trapped ions is discussed.Comment: 4 pages, revtex, 1 figure, revision contains some new result
Quantum disentanglers
It is not possible to disentangle a qubit in an unknown state from a
set of (N-1) ancilla qubits prepared in a specific reference state . That
is, it is not possible to {\em perfectly} perform the transformation
. The question is then how well we can do? We consider a number of
different methods of extracting an unknown state from an entangled state formed
from that qubit and a set of ancilla qubits in an known state. Measuring the
whole system is, as expected, the least effective method. We present various
quantum ``devices'' which disentangle the unknown qubit from the set of ancilla
qubits. In particular, we present the optimal universal disentangler which
disentangles the unknown qubit with the fidelity which does not depend on the
state of the qubit, and a probabilistic disentangler which performs the perfect
disentangling transformation, but with a probability less than one.Comment: 8 pages, 1 eps figur
Universal Algorithm for Optimal Estimation of Quantum States from Finite Ensembles
We present a universal algorithm for the optimal quantum state estimation of
an arbitrary finite dimensional system. The algorithm specifies a physically
realizable positive operator valued measurement (POVM) on a finite number of
identically prepared systems. We illustrate the general formalism by applying
it to different scenarios of the state estimation of N independent and
identically prepared two-level systems (qubits).Comment: 4 pages, RevTeX, minor modifications to the tex
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, 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
Nonlinear Qubit Transformations
We generalise our previous results of universal linear manipulations [Phys.
Rev. A63, 032304 (2001)] to investigate three types of nonlinear qubit
transformations using measurement and quantum based schemes. Firstly, nonlinear
rotations are studied. We rotate different parts of a Bloch sphere in opposite
directions about the z-axis. The second transformation is a map which sends a
qubit to its orthogonal state (which we define as ORTHOG). We consider the case
when the ORTHOG is applied to only a partial area of a Bloch sphere. We also
study nonlinear general transformation, i.e. (theta,phi)->(theta-alpha,phi),
again, applied only to part of the Bloch sphere. In order to achieve these
three operations, we consider different measurement preparations and derive the
optimal average (instead of universal) quantum unitary transformations. We also
introduce a simple method for a qubit measurement and its application to other
cases.Comment: minor corrections. To appear in PR
Phase-covariant quantum cloning of qudits
We study the phase-covariant quantum cloning machine for qudits, i.e. the
input states in d-level quantum system have complex coefficients with arbitrary
phase but constant module. A cloning unitary transformation is proposed. After
optimizing the fidelity between input state and single qudit reduced density
opertor of output state, we obtain the optimal fidelity for 1 to 2
phase-covariant quantum cloning of qudits and the corresponding cloning
transformation.Comment: Revtex, 6 page
Quantum Bayes rule
We state a quantum version of Bayes's rule for statistical inference and give
a simple general derivation within the framework of generalized measurements.
The rule can be applied to measurements on N copies of a system if the initial
state of the N copies is exchangeable. As an illustration, we apply the rule to
N qubits. Finally, we show that quantum state estimates derived via the
principle of maximum entropy are fundamentally different from those obtained
via the quantum Bayes rule.Comment: REVTEX, 9 page
Quantum asymmetric cryptography with symmetric keys
Based on quantum encryption, we present a new idea for quantum public-key
cryptography (QPKC) and construct a whole theoretical framework of a QPKC
system. We show that the quantum-mechanical nature renders it feasible and
reasonable to use symmetric keys in such a scheme, which is quite different
from that in conventional public-key cryptography. The security of our scheme
is analyzed and some features are discussed. Furthermore, the state-estimation
attack to a prior QPKC scheme is demonstrated.Comment: 8 pages, 1 figure, Revtex
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