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Register a new userInformation cloning of harmonic oscillator coherent states and its fidelity
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We show that in the case of unknown {em harmonic oscillator coherent states} it is possible to achieve what we call {it perfect information cloning}. By this we mean that it is still possible to make arbitrary number of copies of a state which has {it exactly} the same information content as the original unknown coherent state. By making use of this {it perfect information cloning} it would be possible to estimate the original state through measurements and make arbitrary number of copies of the estimator. We define the notion of a {em Measurement Fidelity}. We show that this information cloning gives rise, in the case of $1to N$, to a {em distribution} of {em measurement fidelities} whose average value is ${1over 2}$ irrespective of the number of copies originally made. Generalisations of this to the $Mto MN$ case as well as the measurement fidelities for Gaussian cloners are also given.
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We have withdrawn this paper due to a fatal flaw in eqn(38).
We present a new scheme for controlling the quantum state of a harmonic oscillator by coupling it to an anharmonic multilevel system (MLS) with first to second excited state transition frequency on-resonance with the oscillator. In this scheme that we call ef-resonant, the spurious oscillator Kerr non-linearity inherited from the MLS is very small, while its Fock states can still be selectively addressed via an MLS transition at a frequency that depends on the number of photons. We implement this concept in a circuit-QED setup with a microwave 3D cavity (the oscillator, with frequency 6.4 GHz and quality factor QO=2E-6) embedding a frequency tunable transmon qubit (the MLS). We characterize the system spectroscopically and demonstrate selective addressing of Fock states and a Kerr non-linearity below 350 Hz. At times much longer than the transmon coherence times, a non-linear cavity response with driving power is also observed and explained.
The notions of qubits and coherent states correspond to different physical systems and are described by specific formalisms. Qubits are associated with a two-dimensional Hilbert space and can be illustrated on the Bloch sphere. In contrast, the underlying Hilbert space of coherent states is infinite-dimensional and the states are typically represented in phase space. For the particular case of binary coherent state alphabets these otherwise distinct formalisms can equally be applied. We capitalize this formal connection to analyse the properties of optimally cloned binary coherent states. Several practical and near-optimal cloning schemes are discussed and the associated fidelities are compared to the performance of the optimal cloner.
We consider the optimal cloning of quantum coherent states with single-clone and joint fidelity as figures of merit. Both optimal fidelities are attained for phase space translation covariant cloners. Remarkably, the joint fidelity is maximized by a Gaussian cloner, whereas the single-clone fidelity can be enhanced by non-Gaussian operations: a symmetric non-Gaussian 1-to-2 cloner can achieve a single-clone fidelity of approximately 0.6826, perceivably higher than the optimal fidelity of 2/3 in a Gaussian setting. This optimal cloner can be realized by means of an optical parametric amplifier supplemented with a particular source of non-Gaussian bimodal states. Finally, we show that the single-clone fidelity of the optimal 1-to-infinity cloner, corresponding to a measure-and-prepare scheme, cannot exceed 1/2. This value is achieved by a Gaussian scheme and cannot be surpassed even with supplemental bound entangled states.
We propose a scheme to enhance the fidelity of symmetric quantum cloning machine using a weak measurement. By adjusting the intensity of weak measurement parameter $p$, we obtain the copies with different optimal fidelity. Choosing proper value of $p$, we can obtain the perfect copies for initial qubits. In this paper, we focus on $1-2$ quantum cloning for two nonorthogonal states. Sets containing more than two linear independent states are also discussed briefly. Due to weak measurements being probabilistic, we obtain high fidelity at risk of probability. If the weak measurement successes, we do the following operations to obtain copies with high fidelity, otherwise, the cloning process fails and we need do nothing. From this perspective, the scheme we propose is economical for saving quantum resource and time, which may be very useful in quantum information processing.
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