34 research outputs found
Approximate programmable quantum processors
A quantum processor is a programmable quantum circuit in which both the data
and the program, which specifies the operation that is carried out on the data,
are quantum states. We study the situation in which we want to use such a
processor to approximate a set of unitary operators to a specified level of
precision. We measure how well an operation is performed by the process
fidelity between the desired operation and the operation produced by the
processor. We show how to find the program for a given processor that produces
the best approximation of a particular unitary operation. We also place bounds
on the dimension of the program space that is necessary to approximate a set of
unitary operators to a specified level of precision.Comment: 8 page
Robustness of optimal probabilistic storage and retrieval of unitary channels to noise
We investigate robustness of probabilistic storage and retrieval device
optimized for phase gates to noise. We use noisy input composed of convex
combination of unitary channel with either depolarizing or dephasing channel.
We find out that the resistance to dephasing noise is higher than to
depolarization. Interestingly, for the depolarisation the retrieval reduces the
degree of noise. We also examine the possible realizations showing that their
performance is different when the noise is present.Comment: 8 pages, 7 figures, accepted in PR
Concurrence vs. purity: Influence of local channels on Bell states of two qubits
We analyze how a maximally entangled state of two-qubits (e.g., the singlet
) is affected by action of local channels described by completely
positive maps \cE . We analyze the concurrence and the purity of states
\varrho_\cE=\cE\otimes\cI[\psi_s].Using the concurrence-{\it vs}-purity phase
diagram we characterize local channels \cE by their action on the singlet
state . We specify a region of the concurrence-{\it vs.}-purity diagram
that is achievable from the singlet state via the action of unital channels. We
show that even most general (including non-unital) local channels acting just
on a single qubit of the original singlet state cannot generate the maximally
entangled mixed states (MEMS). We study in detail various time evolutions of
the original singlet state induced by local Markovian semigroups. We show that
the decoherence process is represented in the concurrence-{\it vs.}-purity
diagram by a line that forms the lower bound of the achievable region for
unital maps. On the other hand, the depolarization process is represented by a
line that forms the upper bound of the region of maps induced by unital maps.Comment: 9 pages, 6 figure
Probability-based comparison of quantum states
We address the following state comparison problem: is it possible to design
an experiment enabling us to unambiguously decide (based on the observed
outcome statistics) on the sameness or difference of two unknown state
preparations without revealing complete information about the states? We find
that the claim "the same" can never be concluded without any doubts unless the
information is complete. Moreover, we prove that a universal comparison (that
perfectly distinguishes all states) also requires complete information about
the states. Nevertheless, for some measurements, the probability distribution
of outcomes still allows one to make an unambiguous conclusion regarding the
difference between the states even in the case of incomplete information. We
analyze an efficiency of such a comparison of qudit states when it is based on
the SWAP-measurement. For qubit states, we consider in detail the performance
of special families of two-valued measurements enabling us to successfully
compare at most half of the pairs of states. Finally, we introduce almost
universal comparison measurements which can distinguish almost all
non-identical states (up to a set of measure zero). The explicit form of such
measurements with two and more outcomes is found in any dimension.Comment: 12 pages, 6 figures, 1 table, some results are extende
All (qubit) decoherences: Complete characterization and physical implementation
We investigate decoherence channels that are modelled as a sequence of
collisions of a quantum system (e.g., a qubit) with particles (e.g., qubits) of
the environment. We show that collisions induce decoherence when a bi-partite
interaction between the system qubit and an environment (reservoir) qubit is
described by the controlled-U unitary transformation (gate). We characterize
decoherence channels and in the case of a qubit we specify the most general
decoherence channel and derive a corresponding master equation. Finally, we
analyze entanglement that is generated during the process of decoherence
between the system and its environment.Comment: 10 pages, 3 figure
Divisibility of qubit channels and dynamical maps
The concept of divisibility of dynamical maps is used to introduce an analogous concept for quantum channels by analyzing the simulability of channels by means of dynamical maps. In particular, this is addressed for Lindblad divisible, completely positive divisible and positive divisible dynamical maps. The corresponding L-divisible, CP-divisible and P-divisible subsets of channels are characterized (exploiting the results by Wolf et al. [25]) and visualized for the case of qubit channels. We discuss the general inclusions among divisibility sets and show several equivalences for qubit channels. To this end we study the conditions of L-divisibility for finite dimensional channels, especially the cases with negative eigen-values, extending and completing the results of Ref. [26]. Furthermore we show that transitions between every two of the defined divisibility sets are allowed. We explore particular examples of dynamical maps to compare these concepts. Finally, we show that every divisible but not infinitesimal divisible qubit channel (in positive maps) is entanglement-breaking, and open the question if something similar occurs for higher dimensions
Entanglement, purity and energy: Two qubits vs Two modes
We study the relationship between the entanglement, mixedness and energy of
two-qubit and two-mode Gaussian quantum states. We parametrize the set of
allowed states of these two fundamentally different physical systems using
measures of entanglement, mixedness and energy that allow us to compare and
contrast the two systems using a phase diagram. This phase diagram enables one
to clearly identify not only the physically allowed states, but the set of
states connected under an arbitrary quantum operation. We pay particular
attention to the maximally entangled mixed states (MEMS) of each system.
Following this we investigate how efficiently one may transfer entanglement
from two-mode to two-qubit states.Comment: 13 figures. References and 1 figure adde