5,757 research outputs found

### Stability of a generalized particle method for a Poisson equation by discrete Sobolev norms

Numerical analysis is conducted for a generalized particle method for a
Poisson equation. Unique solvability is derived for the discretized Poisson
equation by introducing a connectivity condition for particle distributions.
Moreover, by introducing discrete Sobolev norms and a semi-regularity of a
family of discrete parameters, stability is obtained for the discretized
Poisson equation based on the norms.Comment: 7 pages, 1 figur

### Teleportation cost and hybrid compression of quantum signals

The amount of entanglement necessary to teleport quantum states drawn from
general ensemble $\{p_i,\rho_i\}$ is derived. The case of perfect transmission
of individual states and that of asymptotically faithful transmission are
discussed. Using the latter result, we also derive the optimum compression rate
when the ensemble is compressed into qubits and bits.Comment: 9 pages, 1 figur

### Negation of photon loss provided by negative weak value

We propose a usage of a weak value for a quantum processing between
preselection and postselection. While the weak value of a projector of 1
provides a process with certainty like the probability of 1, the weak value of
-1 negates the process completely. Their mutually opposite effect is approved
without a conventional `weak' condition. In addition the quantum process is not
limited to be unitary; in particular we consider a loss of photons and
experimentally demonstrate the negation of the photon loss by using the
negative weak value of -1 against the positive weak value of 1.Comment: 12 pages, 6 figures, close to published versio

### A strange weak value in spontaneous pair productions via a supercritical step potential

We consider a case where a weak value is introduced as a physical quantity
rather than an average of weak measurements. The case we treat is a time
evolution of a particle by 1+1 dimensional Dirac equation. Particularly in a
spontaneous pair production via a supercritical step potential, a quantitative
explanation can be given by a weak value for the group velocity of the
particle. We also show the condition for the pair production (supercriticality)
corresponds to the condition when the weak value takes a strange value
(superluminal velocity).Comment: 12 pages, 3 figures, close to published versio

### Maxwell boundary conditions imply non-Lindblad master equation

From the Hamiltonian connecting the inside and outside of an Fabry-Perot
cavity, which is derived from the Maxwell boundary conditions at a mirror of
the cavity, a master equation of a non-Lindblad form is derived when the cavity
embeds matters, although we can transform it to the Lindblad form by performing
the rotating-wave approximation to the connecting Hamiltonian. We calculate
absorption spectra by these Lindblad and non-Lindblad master equations and also
by the Maxwell boundary conditions in the framework of the classical
electrodynamics, which we consider the most reliable approach. We found that,
compared to the Lindblad master equation, the absorption spectra by the
non-Lindblad one agree better with those by the Maxwell boundary conditions.
Although the discrepancy is highlighted only in the ultra-strong light-matter
interaction regime with a relatively large broadening, the master equation of
the non-Lindblad form is preferable rather than of the Lindblad one for
pursuing the consistency with the classical electrodynamics.Comment: 22 pages, 9 figure

### What is Possible Without Disturbing Partially Known Quantum States?

Consider a situation in which a quantum system is secretly prepared in a
state chosen from the known set of states. We present a principle that gives a
definite distinction between the operations that preserve the states of the
system and those that disturb the states. The principle is derived by
alternately applying a fundamental property of classical signals and a
fundamental property of quantum ones. The principle can be cast into a simple
form by using a decomposition of the relevant Hilbert space, which is uniquely
determined by the set of possible states. The decomposition implies the
classification of the degrees of freedom of the system into three parts
depending on how they store the information on the initially chosen state: one
storing it classically, one storing it nonclassically, and the other one
storing no information. Then the principle states that the nonclassical part is
inaccessible and the classical part is read-only if we are to preserve the
state of the system. From this principle, many types of no-cloning,
no-broadcasting, and no-imprinting conditions can easily be derived in general
forms including mixed states. It also gives a unified view on how various
schemes of quantum cryptography work. The principle helps to derive optimum
amount of resources (bits, qubits, and ebits) required in data compression or
in quantum teleportation of mixed-state ensembles.Comment: 24 pages, no fogur

### A weak-value model for virtual particles supplying the electric current in graphene: the minimal conductivity and the Schwinger mechanism

We propose a model for the electric current in graphene in which electric
carriers are supplied by virtual particles allowed by the uncertainty
relations. The process to make a virtual particle real is described by a weak
value of a group velocity: the velocity is requisite for the electric field to
give the virtual particle the appropriate changes of both energy and momentum.
With the weak value, we approximately estimate the electric current,
considering the ballistic transport of the electric carriers. The current shows
the quasi-Ohimic with the minimal conductivity of the order of e^2/h per
channel. Crossing a certain ballistic time scale, it is brought to obey the
Schwinger mechanism.Comment: 15 pages, 3 figures, close to published versio

### When a negative weak value -1 plays the counterpart of a probability 1

When the weak value of a projector is 1, a quantum system behaves as in that
eigenstate with probability 1. By definition, however, the weak value may take
an anomalous value lying outside the range of probability like -1. From the
viewpoint of a physical effect, we show that such a negative weak value of -1
can be regarded as the counterpart of the ordinary value of 1. Using photons,
we experimentally verify it as the symmetrical shift in polarization depending
on the weak value given by pre-postselection of the path state. Unlike
observation of a weak value as an ensemble average via weak measurements, the
effect of a weak value is definitely confirmed in two photon interference: the
symmetrical shift corresponding to the weak value can be directly observed as
the rotation angle of a half wave plate.Comment: 10 pages, 5 figures, close to published versio

### A weak-value interpretation of the Schwinger mechanism of massless/massive pair productions

According to the Schwinger mechanism, a uniform electric field brings about
pair productions in vacuum; the relationship between the production rate and
the electric field is different, depending on the dimension of the system. In
this paper, we make an offer of another model for the pair productions, in
which weak values are incorporated: energy fluctuations trigger the pair
production, and a weak value appears as the velocity of a particle there.
Although our model is only available for the approximation of the pair
production rates, the weak value reveals a new aspect of the pair production.
Especially, within the first order, our estimation approximately agrees with
the exponential decreasing rate of the Landau-Zener tunneling through the mass
energy gap. In other words, such tunneling can be associated with energy
fluctuations via the weak value, when the tunneling gap can be regarded as so
small due to the high electric field.Comment: 15 pages, 2 figure

### Circuit configurations which can/cannot show super-radiant phase transitions

Several superconducting circuit configurations are examined on the existence
of super-radiant phase transitions (SRPTs) in thermal equilibrium. For some
configurations consisting of artificial atoms, whose circuit diagrams are
however not specified, and an LC resonator or a transmission line, we confirm
the absence of SRPTs in the thermal equilibrium following the similar analysis
as the no-go theorem for atomic systems. We also show some other configurations
where the absence of SRPTs cannot be confirmed.Comment: 12 pages, 6 figure

- …