309 research outputs found
Optimal Quantum Cloning Machines
We present Quantum Cloning Machines (QCM) that transform N identical qubits
into identical copies and we prove that the fidelity (quality) of these
copies is optimal. The connection between cloning and measurement is discussed
in detail. When the number of clones M tends towards infinity, the fidelity of
each clone tends towards the optimal fidelity that can be obtained by a
measurement on the input qubits. More generally, the QCM are universal devices
to translate quantum information into classical information.Comment: 4 pages, Latex, 1 postscript figure, (very) minor modification
Collective versus local measurements on two parallel or antiparallel spins
We give a complete analysis of covariant measurements on two spins. We
consider the cases of two parallel and two antiparallel spins, and we consider
both collective measurements on the two spins, and measurements which require
only Local Quantum Operations and Classical Communication (LOCC). In all cases
we obtain the optimal measurements for arbitrary fidelities. In particular we
show that if the aim is determine as well as possible the direction in which
the spins are pointing, it is best to carry out measurements on antiparallel
spins (as already shown by Gisin and Popescu), second best to carry out
measurements on parallel spins and worst to be restricted to LOCC measurements.
If the the aim is to determine as well as possible a direction orthogonal to
that in which the spins are pointing, it is best to carry out measurements on
parallel spins, whereas measurements on antiparallel spins and LOCC
measurements are both less good but equivalent.Comment: 4 pages; minor revision
Black Hole Horizon Fluctuations
It is generally admitted that gravitational interactions become large at an
invariant distance of order from the black hole horizon. We show that due
to the ``atmosphere'' of high angular particles near the horizon strong
gravitational interactions already occur at an invariant distance of the order
of . The implications of these results for the origin of black
hole radiation, the meaning of black hole entropy and the information puzzle
are discussed.Comment: Latex, 22 pages (minor corrections and precisions added
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
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
Compression of quantum measurement operations
We generalize recent work of Massar and Popescu dealing with the amount of
classical data that is produced by a quantum measurement on a quantum state
ensemble. In the previous work it was shown how spurious randomness generally
contained in the outcomes can be eliminated without decreasing the amount of
knowledge, to achieve an amount of data equal to the von Neumann entropy of the
ensemble. Here we extend this result by giving a more refined description of
what constitute equivalent measurements (that is measurements which provide the
same knowledge about the quantum state) and also by considering incomplete
measurements. In particular we show that one can always associate to a POVM
with elements a_j, an equivalent POVM acting on many independent copies of the
system which produces an amount of data asymptotically equal to the entropy
defect of an ensemble canonically associated to the ensemble average state and
the initial measurement (a_j). In the case where the measurement is not
maximally refined this amount of data is strictly less than the von Neumann
entropy, as obtained in the previous work. We also show that this is the best
achievable, i.e. it is impossible to devise a measurement equivalent to the
initial measurement (a_j) that produces less data. We discuss the
interpretation of these results. In particular we show how they can be used to
provide a precise and model independent measure of the amount of knowledge that
is obtained about a quantum state by a quantum measurement. We also discuss in
detail the relation between our results and Holevo's bound, at the same time
providing a new proof of this fundamental inequality.Comment: RevTeX, 13 page
Quantum Computing on Lattices using Global Two-Qubit Gate
We study the computation power of lattices composed of two dimensional
systems (qubits) on which translationally invariant global two-qubit gates can
be performed. We show that if a specific set of 6 global two qubit gates can be
performed, and if the initial state of the lattice can be suitably chosen, then
a quantum computer can be efficiently simulatedComment: 9 page
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
Non locality, closing the detection loophole and communication complexity
It is shown that the detection loophole which arises when trying to rule out
local realistic theories as alternatives for quantum mechanics can be closed if
the detection efficiency is larger than
where is the dimension of the entangled system. Furthermore it is argued
that this exponential decrease of the detector efficiency required to close the
detection loophole is almost optimal. This argument is based on a close
connection that exists between closing the detection loophole and the amount of
classical communication required to simulate quantum correlation when the
detectors are perfect.Comment: 4 pages Latex, minor typos correcte
Violation of local realism vs detection efficiency
We put bounds on the minimum detection efficiency necessary to violate local
realism in Bell experiments. These bounds depends of simple parameters like the
number of measurement settings or the dimensionality of the entangled quantum
state. We derive them by constructing explicit local-hidden variable models
which reproduce the quantum correlations for sufficiently small detectors
efficiency.Comment: 6 pages, revtex. Modifications in the discussion for many parties in
section 3, small erros and typos corrected, conclusions unchange
- …