349 research outputs found
A Graphic Representation of States for Quantum Copying Machines
The aim of this paper is to introduce a new graphic representation of quantum
states by means of a specific application: the analysis of two models of
quantum copying machines. The graphic representation by diagrams of states
offers a clear and detailed visualization of quantum information's flow during
the unitary evolution of not too complex systems. The diagrams of states are
exponentially more complex in respect to the standard representation and this
clearly illustrates the discrepancy of computational power between quantum and
classical systems. After a brief introductive exposure of the general theory,
we present a constructive procedure to illustrate the new representation by
means of concrete examples. Elementary diagrams of states for single-qubit and
two-qubit systems and a simple scheme to represent entangled states are
presented. Quantum copying machines as imperfect cloners of quantum states are
introduced and the quantum copying machines of Griffiths and Niu and of Buzek
and Hillery are analyzed, determining quantum circuits of easier
interpretation. The method has indeed shown itself to be extremely successful
for the representation of the involved quantum operations and it has allowed to
point out the characteristic aspects of the quantum computations examined.Comment: 30 pages, 22 figure
A bird's eye view of quantum computers
Quantum computers are discussed in the general framework of computation, the
laws of physics and the foundations of quantum mechanics.Comment: 6 pages, 1 figur
Computing the distance between quantum channels: Usefulness of the Fano representation
The diamond norm measures the distance between two quantum channels. From an
operational vewpoint, this norm measures how well we can distinguish between
two channels by applying them to input states of arbitrarily large dimensions.
In this paper, we show that the diamond norm can be conveniently and in a
physically transparent way computed by means of a Monte-Carlo algorithm based
on the Fano representation of quantum states and quantum operations. The
effectiveness of this algorithm is illustrated for several single-qubit quantum
channels.Comment: 8 pages, 7 figure
Non-perturbative interpretation of the Bloch vector's path beyond rotating wave approximation
The Bloch vector's path of a two-level system exposed to a monochromatic
field exhibits, in the regime of strong coupling, complex corkscrew
trajectories. By considering the infinitesimal evolution of the two-level
system when the field is treated as a classical object, we show that the Bloch
vector's rotation speed oscillates between zero and twice the rotation speed
predicted by the rotating wave approximation. Cusps appear when the rotation
speed vanishes. We prove analytically that in correspondence to cusps the
curvature of the Bloch vector's path diverges. On the other hand, numerical
data show that the curvature is very large even for a quantum field in the deep
quantum regime with mean number of photons . We finally
compute numerically the typical error size in a quantum gate when the terms
beyond rotating wave approximation are neglected.Comment: 9 pages, 8 figure
Exotic States in the Dynamical Casimir Effect
We consider the interaction of a qubit with a single mode of the quantized
electromagnetic field and show that, in the ultrastrong coupling regime and
when the qubit-field interaction is switched on abruptly, the dynamical Casimir
effect leads to the generation of a variety of exotic states of the field,
which cannot be simply described as squeezed states. Such effect also appears
when initially both the qubit and the field are in their ground state. The
non-classicality of the obtained exotic states is characterized by means of a
parameter based on the volume of the negative part of the Wigner function. A
transition to non-classical states is observed by changing either the
interaction strength or the interaction time. The observed phenomena appear as
a general feature of nonadiabatic quantum gates, so that the dynamical Casimir
effect can be the origin of a fundamental upper limit to the maximum speed of
quantum computation and communication protocols.Comment: 5 pages, 4 figure
Landau-Zener quantum tunneling in disordered nanomagnets
We study Landau-Zener macroscopic quantum transitions in ferromagnetic metal
nanoparticles containing on the order of 100 atoms. The model that we consider
is described by an effective giant-spin Hamiltonian, with a coupling to a
random transverse magnetic field mimicking the effect of quasiparticle
excitations and structural disorder on the gap structure of the spin collective
modes. We find different types of time evolutions depending on the interplay
between the disorder in the transverse field and the initial conditions of the
system. In the absence of disorder, if the system starts from a low-energy
state, there is one main coherent quantum tunneling event where the
initial-state amplitude is completely depleted in favor of a few discrete
states, with nearby spin quantum numbers; when starting from the highest
excited state, we observe complete inversion of the magnetization through a
peculiar ``backward cascade evolution''. In the random case, the
disorder-averaged transition probability for a low-energy initial state becomes
a smooth distribution, which is nevertheless still sharply peaked around one of
the transitions present in the disorder-free case. On the other hand, the
coherent backward cascade phenomenon turns into a damped cascade with
frustrated magnetic inversion.Comment: 21 pages, 7 figures, to be published in Phys.Rev.
Dynamical Casimir Effect in Quantum Information Processing
We demonstrate, in the regime of ultrastrong matter-field coupling, the
strong connection between the dynamical Casimir effect (DCE) and the
performance of quantum information protocols. Our results are illustrated by
means of a realistic quantum communication channel and show that the DCE is a
fundamental limit for quantum computation and communication and that novel
schemes are required to implement ultrafast and reliable quantum gates.
Strategies to partially counteract the DCE are also discussed.Comment: 7 pages, 5 figure
Gaussian wave packets in phase space: The Fermi g_F function
Any pure quantum state can be equivalently represented by means of its wave
function psi(q) or of the Fermi function g_F(q,p), with q and p coordinates and
conjugate momenta of the system under investigation.We show that a Gaussian
wave packet can be conveniently visualized in phase space by means of the curve
g_F(q,p)=0. The evolution in time of the g_F=0 curve is then computed for a
Gaussian packet evolving freely or under a constant or a harmonic force. As a
result, the spreading or shrinking of the packet is easily interpreted in phase
space. Finally, we discuss a gedanken prism microscope experiment for measuring
the position-momentum correlation. This gedanken experiment, together with the
well-known Heisenberg microscope and von Neumann velocimeter, is sufficient to
fully determine the state of a Gaussian packet.Comment: 7 pages, 4 figures, remarks adde
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