920 research outputs found
Implementation of quantum maps by programmable quantum processors
A quantum processor is a device with a data register and a program register.
The input to the program register determines the operation, which is a
completely positive linear map, that will be performed on the state in the data
register. We develop a mathematical description for these devices, and apply it
to several different examples of processors. The problem of finding a processor
that will be able to implement a given set of mappings is also examined, and it
is shown that while it is possible to design a finite processor to realize the
phase-damping channel, it is not possible to do so for the amplitude-damping
channel.Comment: 10 revtex pages, no figure
Representation of entanglement by negative quasi-probabilities
Any bipartite quantum state has quasi-probability representations in terms of
separable states. For entangled states these quasi-probabilities necessarily
exhibit negativities. Based on the general structure of composite quantum
states, one may reconstruct such quasi-propabilities from experimental data.
Because of ambiguity, the quasi-probabilities obtained by the bare
reconstruction are insufficient to identify entanglement. An optimization
procedure is introduced to derive quasi-probabilities with a minimal amount of
negativity. Negativities of optimized quasi-probabilities unambiguously prove
entanglement, their positivity proves separability.Comment: 9 pages, 2 figures; An optimization procedure for the
quasi-probabilities has been adde
Quantum walks with random phase shifts
We investigate quantum walks in multiple dimensions with different quantum
coins. We augment the model by assuming that at each step the amplitudes of the
coin state are multiplied by random phases. This model enables us to study in
detail the role of decoherence in quantum walks and to investigate the
quantum-to-classical transition. We also provide classical analogues of the
quantum random walks studied. Interestingly enough, it turns out that the
classical counterparts of some quantum random walks are classical random walks
with a memory and biased coin. In addition random phase shifts "simplify" the
dynamics (the cross interference terms of different paths vanish on average)
and enable us to give a compact formula for the dispersion of such walks.Comment: to appear in Phys. Rev. A (10 pages, 5 figures
Quantum copying: A network
We present a network consisting of quantum gates which produces two imperfect
copies of an arbitrary qubit. The quality of the copies does not depend on the
input qubit. We also show that for a restricted class of inputs it is possible
to use a very similar network to produce three copies instead of two. For
qubits in this class, the copy quality is again independent of the input and is
the same as the quality of the copies produced by the two-copy network.Comment: 10 pages LaTeX, with 1 figure, submitted to the Physical Review
Optimal unambiguous filtering of a quantum state: An instance in mixed state discrimination
Deterministic discrimination of nonorthogonal states is forbidden by quantum
measurement theory. However, if we do not want to succeed all the time, i.e.
allow for inconclusive outcomes to occur, then unambiguous discrimination
becomes possible with a certain probability of success. A variant of the
problem is set discrimination: the states are grouped in sets and we want to
determine to which particular set a given pure input state belongs. We consider
here the simplest case, termed quantum state filtering, when the given
non-orthogonal states, , are divided into
two sets and the first set consists of one state only while the second consists
of all of the remaining states. We present the derivation of the optimal
measurement strategy, in terms of a generalized measurement (POVM), to
distinguish from the set and the
corresponding optimal success and failure probabilities. The results, but not
the complete derivation, were presented previously [\prl {\bf 90}, 257901
(2003)] as the emphasis there was on appplication of the results to novel
probabilistic quantum algorithms. We also show that the problem is equivalent
to the discrimination of a pure state and an arbitrary mixed state.Comment: 8 page
Searching via walking: How to find a marked subgraph of a graph using quantum walks
We show how a quantum walk can be used to find a marked edge or a marked
complete subgraph of a complete graph. We employ a version of a quantum walk,
the scattering walk, which lends itself to experimental implementation. The
edges are marked by adding elements to them that impart a specific phase shift
to the particle as it enters or leaves the edge. If the complete graph has N
vertices and the subgraph has K vertices, the particle becomes localized on the
subgraph in O(N/K) steps. This leads to a quantum search that is quadratically
faster than a corresponding classical search. We show how to implement the
quantum walk using a quantum circuit and a quantum oracle, which allows us to
specify the resource needed for a quantitative comparison of the efficiency of
classical and quantum searches -- the number of oracle calls.Comment: 4 pages, 2 figure
Verifying continuous-variable entanglement in finite spaces
Starting from arbitrary Hilbert spaces, we reduce the problem to verify
entanglement of any bipartite quantum state to finite dimensional subspaces.
Hence, entanglement is a finite dimensional property. A generalization for
multipartite quantum states is also given.Comment: 4 page
Quantum searches on highly symmetric graphs
We study scattering quantum walks on highly symmetric graphs and use the
walks to solve search problems on these graphs. The particle making the walk
resides on the edges of the graph, and at each time step scatters at the
vertices. All of the vertices have the same scattering properties except for a
subset of special vertices. The object of the search is to find a special
vertex. A quantum circuit implementation of these walks is presented in which
the set of special vertices is specified by a quantum oracle. We consider the
complete graph, a complete bipartite graph, and an -partite graph. In all
cases, the dimension of the Hilbert space in which the time evolution of the
walk takes place is small (between three and six), so the walks can be
completely analyzed analytically. Such dimensional reduction is due to the fact
that these graphs have large automorphism groups. We find the usual quadratic
quantum speedups in all cases considered.Comment: 11 pages, 6 figures; major revision
Decoherence in a double-slit quantum eraser
We study and experimentally implement a double-slit quantum eraser in the
presence of a controlled decoherence mechanism. A two-photon state, produced in
a spontaneous parametric down conversion process, is prepared in a maximally
entangled polarization state. A birefringent double-slit is illuminated by one
of the down-converted photons, and it acts as a single-photon two-qubits
controlled not gate that couples the polarization with the transversal momentum
of these photons. The other photon, that acts as a which-path marker, is sent
through a Mach-Zehnder-like interferometer. When the interferometer is
partially unbalanced, it behaves as a controlled source of decoherence for
polarization states of down-converted photons. We show the transition from
wave-like to particle-like behavior of the signal photons crossing the
double-slit as a function of the decoherence parameter, which depends on the
length path difference at the interferometer.Comment: Accepted in Physical Review
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
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