91 research outputs found
The phase of scalar field wormholes at one loop in the path integral formulation for Euclidean quantum gravity
We here calculate the one-loop approximation to the Euclidean Quantum Gravity
coupled to a scalar field around the classical Carlini and Miji\'c wormhole
solutions. The main result is that the Euclidean partition functional
in the ``little wormhole'' limit is real. Extension of the CM solutions with
the inclusion of a bare cosmological constant to the case of a sphere can
lead to the elimination of the destabilizing effects of the scalar modes of
gravity against those of the matter. In particular, in the asymptotic region of
a large 4-sphere, we recover the Coleman's peak at the effective cosmological constant
, with no phase ambiguities in .Comment: 11 page
On the time optimal thermalization of single mode Gaussian states
We consider the problem of time optimal control of a continuous bosonic
quantum system subject to the action of a Markovian dissipation. In particular,
we consider the case of a one mode Gaussian quantum system prepared in an
arbitrary initial state and which relaxes to the steady state due to the action
of the dissipative channel. We assume that the unitary part of the dynamics is
represented by Gaussian operations which preserve the Gaussian nature of the
quantum state, i.e. arbitrary phase rotations, bounded squeezing and unlimited
displacements. In the ideal ansatz of unconstrained quantum control (i.e. when
the unitary phase rotations, squeezing and displacement of the mode can be
performed instantaneously), we study how control can be optimized for speeding
up the relaxation towards the fixed point of the dynamics and we analytically
derive the optimal relaxation time. Our model has potential and interesting
applications to the control of modes of electromagnetic radiation and of
trapped levitated nanospheres.Comment: 10 pages, 1 figur
Optimal thermodynamic control in open quantum systems
We apply advanced methods of control theory to open quantum systems and we
determine finite-time processes which are optimal with respect to thermodynamic
performances. General properties and necessary conditions characterizing
optimal drivings are derived, obtaining bang-bang type solutions corresponding
to control strategies switching between adiabatic and isothermal
transformations. A direct application of these results is the maximization of
the work produced by a generic quantum heat engine, where we show that the
maximum power is directly linked to a particular conserved quantity naturally
emerging from the control problem. Finally we apply our general approach to the
specific case of a two level system, which can be put in contact with two
different baths at fixed temperatures, identifying the processes which minimize
heat dissipation. Moreover, we explicitly solve the optimization problem for a
cyclic two-level heat engine driven beyond the linear-response regime,
determining the corresponding optimal cycle, the maximum power, and the
efficiency at maximum power.Comment: 11 pages, 5 figures; corrected typos, added references, all results
unchange
Variational approach to the optimal control of coherently driven, open quantum system dynamics
Quantum coherence inherently affects the dynamics and the performances of a
quantum machine. Coherent control can, at least in principle, enhance the work
extraction and boost the velocity of evolution in an open quantum system. Using
advanced tools from the calculus of variations and reformulating the control
problem in the instantaneous Hamiltonian eigenframe, we develop a general
technique for minimizing a wide class of cost functionals when the external
control has access to full rotations of the system Hamiltonian. The method is
then applied both to time and heat loss minimization problems and explicitly
solved in the case of a two level system in contact with either bosonic or
fermionic thermal environments.Comment: 13 pages, 2 figures, added references, corrected typo
Time-optimal Unitary Operations in Ising Chains II: Unequal Couplings and Fixed Fidelity
We analytically determine the minimal time and the optimal control laws
required for the realization, up to an assigned fidelity and with a fixed
energy available, of entangling quantum gates () between
indirectly coupled qubits of a trilinear Ising chain. The control is coherent
and open loop, and it is represented by a local and continuous magnetic field
acting on the intermediate qubit. The time cost of this local quantum operation
is not restricted to be zero. When the matching with the target gate is perfect
(fidelity equal to one) we provide exact solutions for the case of equal Ising
coupling. For the more general case when some error is tolerated (fidelity
smaller than one) we give perturbative solutions for unequal couplings.
Comparison with previous numerical solutions for the minimal time to generate
the same gates with the same Ising Hamiltonian but with instantaneous local
controls shows that the latter are not time-optimal.Comment: 11 pages, no figure
Time-Optimal Transfer of Coherence
We provide exact analytical solutions for the problem of time-optimal
transfer of coherence from one spin polarization to a three-fold coherence in a
trilinear Ising chain with a fixed energy available and subject to local
controls with a non negligible time cost. The time of transfer is optimal and
consistent with a previous numerical result obtained assuming instantaneous
local controls.Comment: Published version (with typos in eqs. (25)-(27) corrected
Brachistochrone of Entanglement for Spin Chains
We analytically investigate the role of entanglement in time-optimal state
evolution as an appli- cation of the quantum brachistochrone, a general method
for obtaining the optimal time-dependent Hamiltonian for reaching a target
quantum state. As a model, we treat two qubits indirectly cou- pled through an
intermediate qubit that is directly controllable, which represents a typical
situation in quantum information processing. We find the time-optimal unitary
evolution law and quantify residual entanglement by the two-tangle between the
indirectly coupled qubits, for all possible sets of initial pure quantum states
of a tripartite system. The integrals of the motion of the brachistochrone are
determined by fixing the minimal time at which the residual entanglement is
maximized. Entan- glement plays a role for W and GHZ initial quantum states,
and for the bi-separable initial state in which the indirectly coupled qubits
have a nonzero value of the 2-tangle.Comment: 9 pages, 4 figure
Speeding up and slowing down the relaxation of a qubit by optimal control
We consider a two-level quantum system prepared in an arbitrary initial state
and relaxing to a steady state due to the action of a Markovian dissipative
channel. We study how optimal control can be used for speeding up or slowing
down the relaxation towards the fixed point of the dynamics. We analytically
derive the optimal relaxation times for different quantum channels in the ideal
ansatz of unconstrained quantum control (a magnetic field of infinite
strength). We also analyze the situation in which the control Hamiltonian is
bounded by a finite threshold. As byproducts of our analysis we find that: (i)
if the qubit is initially in a thermal state hotter than the environmental
bath, quantum control cannot speed up its natural cooling rate; (ii) if the
qubit is initially in a thermal state colder than the bath, it can reach the
fixed point of the dynamics in finite time if a strong control field is
applied; (iii) in the presence of unconstrained quantum control it is possible
to keep the evolved state indefinitely and arbitrarily close to special initial
states which are far away from the fixed points of the dynamics.Comment: 11 pages, 6 figure
Stabilizing the gravitational action and Coleman's solution to the cosmological constant problem
We use the 5-th time action formalism introduced by Halpern and Greensite to
stabilize the unbounded Euclidean 4-D gravity in two simple minisuperspace
models. In particular, we show that, at the semiclassical level (), we still have as a leading saddle point the solution and
the Coleman peak at zero cosmological constant, for a fixed De Witt
supermetric. At the quantum (one-loop) level the scalar gravitational modes
give a positive semi-definite Hessian contribution to the 5-D partition
function, thus removing the Polchinski phase ambiguity.Comment: 7 page
Time Optimal Unitary Operations
Extending our previous work on time optimal quantum state evolution, we
formulate a variational principle for the time optimal unitary operation, which
has direct relevance to quantum computation. We demonstrate our method with
three examples, i.e. the swap of qubits, the quantum Fourier transform and the
entangler gate, by choosing a two-qubit anisotropic Heisenberg model.Comment: 4 pages, 1 figure. References adde
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