arXiv subjects

E. Karpov

Publications and source records attributed to E. Karpov.

12 recordsLinked to original sources

arXiv2019

Optimal estimation of parameters encoded in coherent states quadratures

In the context of multiparameter quantum estimation theory, we investigate the construction of linear schemes in order to infer two classical parameters that are encoded in the quadratures of two quantum coherent states. The optimality of the scheme built on two phase-conjugate coherent states is proven with the saturation of the quantum Cramér--Rao bound under some global energy constraint. In a more general setting, we consider and analyze a variety of $n$-mode schemes that can be used to encode $n$ classical parameters into $n$ quantum coherent states and then estimate all parameters optimally and simultaneously.

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arXiv2013

Purity and Gaussianity bounded uncertainty relation

Bounded uncertainty relations provide the minimum value of the uncertainty assuming some additional information on the state. We derive analytically an uncertainty relation bounded by a pair of constraints, those of purity and Gaussianity. In a limiting case this uncertainty relation reproduces the purity-bounded derived by V I Man'ko and V V Dodonov and the Gaussianity-bounded one [Phys. Rev. A 86, 030102R (2012)].

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arXiv2012

A probabilistic phase-insensitive optical squeezer in peaceful coexistence with causality

A non trace-preserving map describing a probabilistic but heralded noiseless linear amplifier has recently been proposed and experimentally demonstrated. Here, we exhibit another remarkable feature of this peculiar transformation, namely its ability to serve as a universal single-mode squeezer regardless of the quadrature that is initially squeezed. Hence, it acts as an heralded phase-insensitive optical squeezer, conserving the signal-to-noise ratio just as a phase-sensitive optical amplifier but for all quadratures at the same time, which may offer new perspectives in quantum optical communications. Although this ability to squeeze all quadratures seemingly opens a way to instantaneous signaling by circumventing the quantum no-cloning theorem, we explain the subtle mechanism by which the probability for such a causality violation vanishes, even on an heralded basis.

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arXiv2009

Extending Hudson's theorem to mixed quantum states

According to Hudson's theorem, any pure quantum state with a positive Wigner function is necessarily a Gaussian state. Here, we make a step towards the extension of this theorem to mixed quantum states by finding upper and lower bounds on the degree of non-Gaussianity of states with positive Wigner functions. The bounds are expressed in the form of parametric functions relating the degree of non-Gaussianity of a state, its purity, and the purity of the Gaussian state characterized by the same covariance matrix. Although our bounds are not tight, they permit us to visualize the set of states with positive Wigner functions.

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arXiv2006

Entanglement may enhance the channel capacity in arbitrary dimensions

We consider explicitly two examples of d-dimensional quantum channels with correlated noise and show that, in agreement with previous results on Pauli qubit channels, there are situations where maximally entangled input states achieve higher values of the output mutual information than product states. We obtain a strong dependence of this effect on the nature of the noise correlations as well as on the parity of the space dimension, and conjecture that when entanglement gives an advantage in terms of mutual information, maximally entangled states achieve the channel capacity.

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arXiv2006

Entanglement enhanced classical capacity of quantum communication channels with correlated noise in arbitrary dimensions

We study the capacity of d-dimensional quantum channels with memory modeled by correlated noise. We show that, in agreement with previous results on Pauli qubit channels, there are situations where maximally entangled input states achieve higher values of mutual information than product states. Moreover, a strong dependence of this effect on the nature of the noise correlations as well as on the parity of the space dimension is found. We conjecture that when entanglement gives an advantage in terms of mutual information, maximally entangled states saturate the channel capacity.

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arXiv2005

An exactly solvable model of two three-dimensional harmonic oscillators interacting with the quantum electromagnetic field: the Casimir-Polder potential

We consider two three-dimensional isotropic harmonic oscillators interacting with the quantum electromagnetic field in the Coulomb gauge and within dipole approximation. Using a Bogoliubov-like transformation, we can obtain transformed operators such that the Hamiltonian of the system, when expressed in terms of these operators, assumes a diagonal form. We are also able to obtain an expression for the energy shift of the ground state, which is valid at all orders in the coupling constant. From this energy shift the nonperturbative Casimir-Polder potential energy between the two oscillators can be obtained. When approximated to the fourth order in the electric charge, the well-known expression of the Casimir-Polder potential in terms of the polarizabilities of the oscillators is recovered.

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arXiv2005

Cloning quantum entanglement in arbitrary dimensions

We have found a quantum cloning machine that optimally duplicates the entanglement of a pair of $d$-dimensional quantum systems. It maximizes the entanglement of formation contained in the two copies of any maximally-entangled input state, while preserving the separability of unentangled input states. Moreover, it cannot increase the entanglement of formation of all isotropic states. For large $d$, the entanglement of formation of each clone tends to one half the entanglement of the input state, which corresponds to a classical behavior. Finally, we investigate a local entanglement cloner, which yields entangled clones with one fourth the input entanglement in the large-$d$ limit.

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arXiv2004

Zeno era and non-decaying subspaces for multilevel Friedrichs model

We study the short-time and medium-time behavior of the survival probability of decaying states in the framework of the $N$-level Friedrichs model. The degenerated and nearly degenerated systems are discussed in detail. We show that in these systems decay can be considerably slowed down or even stopped by appropriate choice of initial conditions. We analyze the behaviour of the multilevel system within the so-called Zeno era. We examine and compare two different definitions of the Zeno time. We demonstrate that the Zeno era can be considerably enlarged by proper choice of the system parameters.

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arXiv2001

Oscillating decay of an unstable system

We study the short-time and medium-time behavior of the survival probability in the frame of the $N$-level Friedrichs model. The time evolution of an arbitrary unstable initial state is determined. We show that the survival probability may oscillate significantly during the so-called exponential era. This result explains qualitatively the experimental observations of the NaI decay.

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arXiv2001

Quantum Zeno and anti-Zeno effects in the Friedrichs model

We analyze the short-time behavior of the survival probability in the frame of the Friedrichs model for different formfactors. We have shown that this probability is not necessary analytic at the time origin. The time when the quantum Zeno effect could be observed is found to be much smaller than usually estimated. We have also studied the anti-Zeno era and have estimated its duration.

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arXiv2000

Causality, delocalization and positivity of energy

In a series of interesting papers G. C. Hegerfeldt has shown that quantum systems with positive energy initially localized in a finite region, immediately develop infinite tails. In our paper Hegerfeldt's theorem is analysed using quantum and classical wave packets. We show that Hegerfeldt's conclusion remains valid in classical physics. No violation of Einstein's causality is ever involved. Using only positive frequencies, complex wave packets are constructed which at $t = 0$ are real and finitely localized and which, furthemore, are superpositions of two nonlocal wave packets. The nonlocality is initially cancelled by destructive interference. However this cancellation becomes incomplete at arbitrary times immediately afterwards. In agreement with relativity the two nonlocal wave packets move with the velocity of light, in opposite directions.

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