156 research outputs found
Another convex combination of product states for the separable Werner state
In this paper, we write down the separable Werner state in a two-qubit system
explicitly as a convex combination of product states, which is different from
the convex combination obtained by Wootters' method. The Werner state in a
two-qubit system has a single real parameter and varies from inseparable state
to separable state according to the value of its parameter. We derive a hidden
variable model that is induced by our decomposed form for the separable Werner
state. From our explicit form of the convex combination of product states, we
understand the following: The critical point of the parameter for separability
of the Werner state comes from positivity of local density operators of the
qubits.Comment: 7 pages, Latex2e; v2: 9 pages, title changed, an appendix and a
reference added, minor correction
The intercept/resend attack and the collective attack on the six-state protocol of the quantum key distribution
In this paper, we discuss security of the six-state quantum key distribution
protocol against intercept/resend attacks and collective attacks. For the
intercept/resend attacks, we evaluate a probability that the legitimate users,
Alice and Bob, do not notice interference caused by the eavesdropper Eve and a
probability that Eve obtains a secret bit sent by Alice. For the collective
attacks, we estimate not only the above two probabilities but also Eve's
Shannon information. In the assessment of the security against the collective
attacks, imposing looser constraints upon Eve's strategies than
Bechmann-Pasquinucci and Gisin, we reach substantially the same result as their
study. In other words, although we let Eve's strategies satisfy lower symmetry
than Bechmann-Pasquinucci and Gisin, both their work and ours attain the same
conclusion, i.e. the identical, unique, and optimum strategy. This implies that
we obtain Eve's best tactic by applying simpler conditions to it than
Bechmann-Pasquinucci and Gisin, so that this result is novel. Finally, we
consider a relation between the six-state protocol and the E91 scheme. We show
that the intercept/resend attacks can always be described by hidden variable
models. In contrast, we demonstrate that we cannot regard the collective
attacks as the hidden variable theories if the disturbance is smaller than
.Comment: 24 pages, 2 eps figures, latex2
The Leggett-Garg inequalities and the relative entropy of coherence in the Bixon-Jortner model
We investigate the Leggett-Garg inequalities and the relative entropy of
coherence in the Bixon-Jortner model. First, we analytically derive the general
solution of the Bixon-Jortner model by a technique of the Laplace transform. So
far, only a special solution has been known for this model. The model has a
single state coupled to equally spaced quasi-continuum states. These couplings
cause discontinuities in the time evolution of the occupation probability of
each state. Second, using the analytical solution, we show that the probability
distribution of the quasi-continuum states approaches the Lorentzian function
in a period of time between the initial time and the first discontinuity.
Third, we examine violation of the Leggett-Garg inequalities and temporal
variation of the relative entropy of coherence in the model. We prove that both
the inequalities and the relative entropy are invariant under transformations
of the energy-level detuning of the single state.Comment: 22 pages, 7 eps figures, latex2e; v2: Section 1 has been rewritten;
v3: minor corrections; v4: references added; v5: minor correction
Violations of the Leggett-Garg inequality for coherent and cat states
We show that in some cases the coherent state can have a larger violation of
the Leggett-Garg inequality (LGI) than the cat state by numerical calculations.
To achieve this result, we consider the LGI of the cavity mode weakly coupled
to a zero-temperature environment as a practical instance of the physical
system. We assume that the bosonic mode undergoes dissipation because of an
interaction with the environment but is not affected by dephasing. Solving the
master equation exactly, we derive an explicit form of the violation of the
inequality for both systems prepared initially in the coherent state
and the cat state . For the
evaluation of the inequality, we choose the displaced parity operators
characterized by a complex number . We look for the optimum parameter
that lets the upper bound of the inequality be maximum numerically.
Contrary to our expectations, the coherent state occasionally exhibits quantum
quality more strongly than the cat state for the upper bound of the violation
of the LGI in a specific range of three equally spaced measurement times
(spacing ). Moreover, as we let approach zero, the optimized
parameter diverges and the LGI reveals intense singularity.Comment: 29 pages, 14 eps figures, latex2e; v2: The title has been changed. We
have improved Sect. 8 and added many references; v3: Equation (57) has been
modifie
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