1,560 research outputs found
Optimal Asymmetric Quantum Cloning
While the no-cloning theorem, which forbids the perfect copying of quantum
states, is well-known as one of the defining features of quantum mechanics, the
question of how well the theory allows a state to be cloned is yet to be
completely solved. In this paper, rigorous solutions to the problem of M to N
asymmetric cloning of qudits are obtained in a number of interesting cases. The
central result is the solution to the 1 to N universal asymmetric qudit cloning
problem for which the exact trade-off in the fidelities of the clones for every
N and d is derived. Analogous results are proven for qubits when M=N-1. We also
consider state-dependent 1 to N qubit cloning, providing a general
parametrization in terms of a Heisenberg star Hamiltonian. In all instances, we
determine the feasibility of implementing the cloning economically, i.e.,
without an ancilla, and determine the dimension of the ancilla when an economic
implementation is not possible.Comment: 12 page
Compatibility of quantum measurements and inclusion constants for the matrix jewel
In this work, we establish the connection between the study of free
spectrahedra and the compatibility of quantum measurements with an arbitrary
number of outcomes. This generalizes previous results by the authors for
measurements with two outcomes. Free spectrahedra arise from matricial
relaxations of linear matrix inequalities. A particular free spectrahedron
which we define in this work is the matrix jewel. We find that the
compatibility of arbitrary measurements corresponds to the inclusion of the
matrix jewel into a free spectrahedron defined by the effect operators of the
measurements under study. We subsequently use this connection to bound the set
of (asymmetric) inclusion constants for the matrix jewel using results from
quantum information theory and symmetrization. The latter translate to new
lower bounds on the compatibility of quantum measurements. Among the techniques
we employ are approximate quantum cloning and mutually unbiased bases.Comment: v5: section 3.3 has been expanded significantly to incorporate the
generalization of the Cartesian product and the direct sum to matrix convex
sets. Many other minor modifications. Closed to the published versio
Sequential Quantum Cloning
Not all unitary operations upon a set of qubits can be implemented by
sequential interactions between each qubit and an ancillary system. We analyze
the specific case of sequential quantum cloning 1->M and prove that the minimal
dimension D of the ancilla grows linearly with the number of clones M. In
particular, we obtain D = 2M for symmetric universal quantum cloning and D =
M+1 for symmetric phase-covariant cloning. Furthermore, we provide a recipe for
the required ancilla-qubit interactions in each step of the sequential
procedure for both cases.Comment: 4 pages, no figures. New version with changes. Accepted in Physical
Review Letter
Equi-entangled bases in arbitrary dimensions
For the space of two identical systems of arbitrary dimensions, we introduce
a continuous family of bases with the following properties: i) the bases are
orthonormal, ii) in each basis, all the states have the same values of
entanglement, and iii) they continuously interpolate between the product basis
and the maximally entangled basis. The states thus constructed may find
applications in many areas related to quantum information science including
quantum cryptography, optimal Bell tests and investigation of enhancement of
channel capacity due to entanglement.Comment: 10 pages, 2 figures, 1 table, Accepted for publication in Phys. Rev.
Twisted Photons: New Quantum Perspectives in High Dimensions
Quantum information science and quantum information technology have seen a
virtual explosion world-wide. It is all based on the observation that
fundamental quantum phenomena on the individual particle or system-level lead
to completely novel ways of encoding, processing and transmitting information.
Quantum mechanics, a child of the first third of the 20th century, has found
numerous realizations and technical applications, much more than was thought at
the beginning. Decades later, it became possible to do experiments with
individual quantum particles and quantum systems. This was due to technological
progress, and for light in particular, the development of the laser. Hitherto,
nearly all experiments and also nearly all realizations in the fields have been
performed with qubits, which are two-level quantum systems. We suggest that
this limitation is again mainly a technological one, because it is very
difficult to create, manipulate and measure more complex quantum systems. Here,
we provide a specific overview of some recent developments with
higher-dimensional quantum systems. We mainly focus on Orbital Angular Momentum
(OAM) states of photons and possible applications in quantum information
protocols. Such states form discrete higher-dimensional quantum systems, also
called qudits. Specifically, we will first address the question what kind of
new fundamental properties exist and the quantum information applications which
are opened up by such novel systems. Then we give an overview of recent
developments in the field by discussing several notable experiments over the
past 2-3 years. Finally, we conclude with several important open questions
which will be interesting for investigations in the future.Comment: 15 pages, 7 figure
Quantum state decorrelation
We address the general problem of removing correlations from quantum states
while preserving local quantum information as much as possible. We provide a
complete solution in the case of two qubits, by evaluating the minimum amount
of noise that is necessary to decorrelate covariant sets of bipartite states.
We show that two harmonic oscillators in arbitrary Gaussian state can be
decorrelated by a Gaussian covariant map. Finally, for finite-dimensional
Hilbert spaces, we prove that states obtained from most cloning channels (e.g.,
universal and phase-covariant cloning) can be decorrelated only at the expense
of a complete erasure of information about the copied state. More generally, in
finite dimension, cloning without correlations is impossible for continuous
sets of states. On the contrary, for continuos variables cloning, a slight
modification of the customary set-up for cloning coherent states allows one to
obtain clones without correlations.Comment: 11 pages, 2 figures, RevTex
Quantum information with continuous variables
Quantum information is a rapidly advancing area of interdisciplinary
research. It may lead to real-world applications for communication and
computation unavailable without the exploitation of quantum properties such as
nonorthogonality or entanglement. We review the progress in quantum information
based on continuous quantum variables, with emphasis on quantum optical
implementations in terms of the quadrature amplitudes of the electromagnetic
field.Comment: accepted for publication in Reviews of Modern Physic
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