41,825 research outputs found
Investigating decoherence in a simple system
The results of some simple calculations designed to study quantum decoherence are presented. The physics of quantum decoherence are briefly reviewed, and a very simple 'toy' model is analyzed. Exact solutions are found using numerical techniques. The type of incoherence exhibited by the model can be changed by varying a coupling strength. The author explains why the conventional approach to studying decoherence by checking the diagonality of the density matrix is not always adequate. Two other approaches, the decoherence functional and the Schmidt paths approach, are applied to the toy model and contrasted to each other. Possible problems with each are discussed
Analysis of the Security of BB84 by Model Checking
Quantum Cryptography or Quantum key distribution (QKD) is a technique that
allows the secure distribution of a bit string, used as key in cryptographic
protocols. When it was noted that quantum computers could break public key
cryptosystems based on number theory extensive studies have been undertaken on
QKD. Based on quantum mechanics, QKD offers unconditionally secure
communication. Now, the progress of research in this field allows the
anticipation of QKD to be available outside of laboratories within the next few
years. Efforts are made to improve the performance and reliability of the
implemented technologies. But several challenges remain despite this big
progress. The task of how to test the apparatuses of QKD For example did not
yet receive enough attention. These devises become complex and demand a big
verification effort. In this paper we are interested in an approach based on
the technique of probabilistic model checking for studying quantum information.
Precisely, we use the PRISM tool to analyze the security of BB84 protocol and
we are focused on the specific security property of eavesdropping detection. We
show that this property is affected by the parameters of quantum channel and
the power of eavesdropper.Comment: 12 Pages, IJNS
Quantum speedup for active learning agents
Can quantum mechanics help us in building intelligent robots and agents? One
of the defining characteristics of intelligent behavior is the capacity to
learn from experience. However, a major bottleneck for agents to learn in any
real-life situation is the size and complexity of the corresponding task
environment. Owing to, e.g., a large space of possible strategies, learning is
typically slow. Even for a moderate task environment, it may simply take too
long to rationally respond to a given situation. If the environment is
impatient, allowing only a certain time for a response, an agent may then be
unable to cope with the situation and to learn at all. Here we show that
quantum physics can help and provide a significant speed-up for active learning
as a genuine problem of artificial intelligence. We introduce a large class of
quantum learning agents for which we show a quadratic boost in their active
learning efficiency over their classical analogues. This result will be
particularly relevant for applications involving complex task environments.Comment: Minor updates, 14 pages, 3 figure
Kak's three-stage protocol of secure quantum communication revisited: Hitherto unknown strengths and weaknesses of the protocol
Kak's three-stage protocol for quantum key distribution is revisited with
special focus on its hitherto unknown strengths and weaknesses. It is shown
that this protocol can be used for secure direct quantum communication.
Further, the implementability of this protocol in the realistic situation is
analyzed by considering various Markovian noise models. It is found that the
Kak's protocol and its variants in their original form can be implemented only
in a restricted class of noisy channels, where the protocols can be transformed
to corresponding protocols based on logical qubits in decoherence free
subspace. Specifically, it is observed that Kak's protocol can be implemented
in the presence of collective rotation and collective dephasing noise, but
cannot be implemented in its original form in the presence of other types of
noise, like amplitude damping and phase damping noise. Further, the performance
of the protocol in the noisy environment is quantified by computing average
fidelity under various noise models, and subsequently a set of preferred states
for secure communication in noisy environment have also been identified.Comment: Kak's protocol is not suitable for quantum cryptography in presence
of nois
Rogue Quantum Harmonic Oscillations
We show the existence and investigate the dynamics and statistics of rogue
oscillations (standing waves) generated in the frame of the nonlinear quantum
harmonic oscillator (NQHO). With this motivation, in this paper, we develop a
split-step Fourier scheme for the computational analysis of NQHO. We show that
modulation instability excites the generation of rogue oscillations in the
frame of the NQHO. We also discuss the effects of various parameters such as
the strength of trapping well potential, nonlinearity, dissipation, fundamental
wave number and perturbation amplitude on rogue oscillation formation
probabilities
Exponential Quantum Speed-ups are Generic
A central problem in quantum computation is to understand which quantum
circuits are useful for exponential speed-ups over classical computation. We
address this question in the setting of query complexity and show that for
almost any sufficiently long quantum circuit one can construct a black-box
problem which is solved by the circuit with a constant number of quantum
queries, but which requires exponentially many classical queries, even if the
classical machine has the ability to postselect.
We prove the result in two steps. In the first, we show that almost any
element of an approximate unitary 3-design is useful to solve a certain
black-box problem efficiently. The problem is based on a recent oracle
construction of Aaronson and gives an exponential separation between quantum
and classical bounded-error with postselection query complexities.
In the second step, which may be of independent interest, we prove that
linear-sized random quantum circuits give an approximate unitary 3-design. The
key ingredient in the proof is a technique from quantum many-body theory to
lower bound the spectral gap of local quantum Hamiltonians.Comment: 24 pages. v2 minor correction
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