29 research outputs found
Decoherence and Measurement in Open Quantum Systems
We review results of a recently developed model of a microscopic quantum
system interacting with the macroscopic world components which are modeled by
collections of bosonic modes. The interaction is via a general operator
of the system, coupled to the creation and annihilation operators of
the environment modes. We assume that in the process of a nearly instantaneous
quantum measurement, the function of the environment involves two distinct
parts: the pointer and the bath. Interaction of the system with the bath leads
to decoherence such that the system and the pointer both evolve into a
statistical mixture state described by the density matrix such that the system
is in one of the eigenstates of with the correct quantum mechanical
probability, whereas the expectation values of pointer operators retain
amplified information on that eigenstate. We argue that this process represents
the initial step of a quantum measurement. Calculation of the elements of the
reduced density matrix of the system and pointer is carried out exactly, and
time dependence of decoherence is identified. We discuss general implications
of our model of energy-conserving coupling to a heat bath for processes of
adiabatic quantum decoherence. We also evaluate changes in the expectation
values of certain pointer operators and suggest that these can be interpreted
as macroscopic indicators of the measurement outcome.Comment: 12 pages in LaTeX, requires the spie.sty style fil
A Hamiltonian for quantum copying
We derive an explicit Hamiltonian for copying the basis up and down states of
a quantum two-state system - a qubit - onto n "copy" qubits initially all
prepared in the down state. In terms of spin components, for spin-1/2 particle
spin states, the resulting Hamiltonian involves n- and (n+1)-spin interactions.
The case n=1 also corresponds to a quantum-computing controlled-NOT gate.Comment: 16 pages in plain Te
Design of gates for quantum computation: the NOT gate
We offer an alternative to the conventional network formulation of quantum
computing. We advance the analog approach to quantum logic gate/circuit
construction. As an illustration, we consider the spatially extended NOT gate
as the first step in the development of this approach. We derive an explicit
form of the interaction Hamiltonian corresponding to this gate and analyze its
properties. We also discuss general extensions to the case of certain
time-dependent interactions which may be useful for practical realization of
quantum logic gates.Comment: 9 pages in LaTe
Semiconductor quantum computer design with 100 nm separation of nuclear-spin qubits
We combine elements of the 1998 quantum computing proposals by Privman,
Vagner and Kventsel, and by Kane, with the new idea of nuclear-spin qubit
interactions mediated indirectly via the bound outer electrons of impurity
atoms whose nuclear spins 1/2 are the qubits. These electrons, in turn,
interact via the two-dimensional electron gas in the quantum Hall effect
regime. The resulting quantum computing scheme retains all the gate-control and
measurement aspects of the proposal by Kane, but allows qubit spacing at
distances of order 100 nm, attainable with the present-day
semiconductor-heterostructure device technologies.Comment: 3 pages in PD
Extended Quantum XOR Gate in Terms of Two-Spin Interactions
Considerations of feasibility of quantum computing lead to the study of
multispin quantum gates in which the input and output two-state systems (spins)
are not identical. We provide a general discussion of this approach and then
propose an explicit two-spin interaction Hamiltonian which accomplishes the
quantum XOR gate function for a system of three spins: two input and one
output.Comment: 15 pages in plain TeX with 1 Postscript figur
Measurement of a Quantum System Coupled to Independent Heat-Bath and Pointer Modes
We present an exact derivation of a process in which a microscopic measured
system interacts with heat-bath and pointer modes of a measuring device, via a
coupling involving a general Hermitian operator of the system. In the
limit of strong interaction with these modes, over a small time interval, we
derive the exact effective many-body density matrix of the measured system plus
pointer. We then discuss the interpretation of the dynamics considered as the
first stage in the process of quantum measurement, eventually involving the
wave-function collapse due to interactions with "the rest of the universe." We
establish that the effective density matrix represents the required framework
for the measured system and the pointer part of the measuring device to evolve
into a statistical mixture described by direct-product states such that the
system is in each eigenstate of with the correct quantum-mechanical
probability, whereas the expectation values of pointer-space operators retain
amplified information of the system's eigenstate.Comment: 19 pages in plain Te
Relaxation of Shallow Donor Electron Spin due to Interaction with Nuclear Spin Bath
We study the low-temperature dynamics of a shallow donor, e.g., P,
impurity electron spin in silicon, interacting with the bath of nuclear spins
of the Si isotope. For small applied magnetic fields, the electron spin
relaxation is controlled by the steady state distribution of the nuclear spins.
We calculate the relaxation times and as functions of the external
magnetic field, and conclude that nuclear spins play an important role in the
donor electron spin decoherence in Si:P at low magnetic fields.Comment: 12 pages in PD