306 research outputs found
Probabilistic quantum multimeters
We propose quantum devices that can realize probabilistically different
projective measurements on a qubit. The desired measurement basis is selected
by the quantum state of a program register. First we analyze the
phase-covariant multimeters for a large class of program states, then the
universal multimeters for a special choice of program. In both cases we start
with deterministic but erroneous devices and then proceed to devices that never
make a mistake but from time to time they give an inconclusive result. These
multimeters are optimized (for a given type of a program) with respect to the
minimum probability of inconclusive result. This concept is further generalized
to the multimeters that minimize the error rate for a given probability of an
inconclusive result (or vice versa). Finally, we propose a generalization for
qudits.Comment: 12 pages, 3 figure
CP^n, or, entanglement illustrated
We show that many topological and geometrical properties of complex
projective space can be understood just by looking at a suitably constructed
picture. The idea is to view CP^n as a set of flat tori parametrized by the
positive octant of a round sphere. We pay particular attention to submanifolds
of constant entanglement in CP^3 and give a few new results concerning them.Comment: 28 pages, 9 figure
Experimental Demonstration of Optimal Unambiguous State Discrimination
We present the first full demonstration of unambiguous state discrimination
between non-orthogonal quantum states. Using a novel free space interferometer
we have realised the optimum quantum measurement scheme for two non-orthogonal
states of light, known as the Ivanovic-Dieks-Peres (IDP) measurement. We have
for the first time gained access to all three possible outcomes of this
measurement. All aspects of this generalised measurement scheme, including its
superiority over a standard von Neumann measurement, have been demonstrated
within 1.5% of the IDP predictions
Distinguishing two-qubit states using local measurements and restricted classical communication
The problem of unambiguous state discrimination consists of determining which
of a set of known quantum states a particular system is in. One is allowed to
fail, but not to make a mistake. The optimal procedure is the one with the
lowest failure probability. This procedure has been extended to bipartite
states where the two parties, Alice and Bob, are allowed to manipulate their
particles locally and communicate classically in order to determine which of
two possible two-particle states they have been given. The failure probability
of this local procedure has been shown to be the same as if the particles were
together in the same location. Here we examine the effect of restricting the
classical communication between the parties, either allowing none or
eliminating the possibility that one party's measurement depends on the result
of the other party's. These issues are studied for two-qubit states, and
optimal procedures are found. In some cases the restrictions cause increases in
the failure probability, but in other cases they do not. Applications of these
procedures, in particular to secret sharing, are discussed.Comment: 18 pages, two figure
Strategies and Networks for State-Dependent Quantum Cloning
State-dependent cloning machines that have so far been considered either
deterministically copy a set of states approximately, or probablistically copy
them exactly. In considering the case of two equiprobable pure states, we
derive the maximum global fidelity of approximate clones given initial
exact copies, where . We also consider strategies which interpolate
between approximate and exact cloning. A tight inequality is obtained which
expresses a trade-off between the global fidelity and success probability. This
inequality is found to tend, in the limit as , to a known
inequality which expresses the trade-off between error and inconclusive result
probabilities for state-discrimination measurements. Quantum-computational
networks are also constructed for the kinds of cloning machine we describe. For
this purpose, we introduce two gates: the distinguishability transfer and state
separation gates. Their key properties are describedComment: 12 pages, 6 eps figures, submitted to Phys. Rev.
Nonlocality without inequalities has not been proved for maximally entangled states
Two approaches to extend Hardy's proof of nonlocality without inequalities to
maximally entangled states of bipartite two-level systems are shown to fail. On
one hand, it is shown that Wu and co-workers' proof [Phys. Rev. A 53, R1927
(1996)] uses an effective state which is not maximally entangled. On the other
hand, it is demonstrated that Hardy's proof cannot be generalized by the
replacement of one of the four von Neumann measurements involved in the
original proof by a generalized measurement to unambiguously discriminate
between non-orthogonal states.Comment: 7 pages, 2 figures. To appear in Phys. Rev.
Maximal Entanglement, Collective Coordinates and Tracking the King
Maximal entangled states (MES) provide a basis to two d-dimensional particles
Hilbert space, d=prime . The MES forming this basis are product states
in the collective, center of mass and relative, coordinates. These states are
associated (underpinned) with lines of finite geometry whose constituent points
are associated with product states carrying Mutual Unbiased Bases (MUB) labels.
This representation is shown to be convenient for the study of the Mean King
Problem and a variant thereof, termed Tracking the King which proves to be a
novel quantum communication channel. The main topics, notions used are reviewed
in an attempt to have the paper self contained.Comment: 8. arXiv admin note: substantial text overlap with arXiv:1206.3884,
arXiv:1206.035
An expectation value expansion of Hermitian operators in a discrete Hilbert space
We discuss a real-valued expansion of any Hermitian operator defined in a
Hilbert space of finite dimension N, where N is a prime number, or an integer
power of a prime. The expansion has a direct interpretation in terms of the
operator expectation values for a set of complementary bases. The expansion can
be said to be the complement of the discrete Wigner function.
We expect the expansion to be of use in quantum information applications
since qubits typically are represented by a discrete, and finite-dimensional
physical system of dimension N=2^p, where p is the number of qubits involved.
As a particular example we use the expansion to prove that an intermediate
measurement basis (a Breidbart basis) cannot be found if the Hilbert space
dimension is 3 or 4.Comment: A mild update. In particular, I. D. Ivanovic's earlier derivation of
the expansion is properly acknowledged. 16 pages, one PS figure, 1 table,
written in RevTe
- …