arXiv subjects

Sergey N. Filippov

Publications and source records attributed to Sergey N. Filippov.

32 records · Page 2Linked to original sources

arXiv2019

Time deformations of master equations

Convolutionless and convolution master equations are the two mostly used physical descriptions of open quantum systems dynamics. We subject these equations to time deformations: local dilations and contractions of time scale. We prove that the convolutionless equation remains legitimate under any time deformation (results in a completely positive dynamical map) if and only if the original dynamics is completely positive divisible. Similarly, for a specific class of convolution master equations we show that uniform time dilations preserve positivity of the deformed map if the original map is positive divisible. These results allow witnessing different types of non-Markovian behavior: the absence of complete positivity for a deformed convolutionless master equation clearly indicates that the original dynamics is at least weakly non-Markovian; the absence of positivity for a class of time-dilated convolution master equations is a witness of essentially non-Markovian original dynamics.

quant-ph↗

arXiv2018

Simulability of observables in general probabilistic theories

The existence of incompatibility is one of the most fundamental features of quantum theory, and can be found at the core of many of the theory's distinguishing features, such as Bell inequality violations and the no-broadcasting theorem. A scheme for obtaining new observables from existing ones via classical operations, the so-called simulation of observables, has led to an extension of the notion of compatibility for measurements. We consider the simulation of observables within the operational framework of general probabilistic theories and introduce the concept of simulation irreducibility. While a simulation irreducible observable can only be simulated by itself, we show that any observable can be simulated by simulation irreducible observables, which in the quantum case correspond to extreme rank-1 positive-operator-valued measures. We also consider cases where the set of simulators is restricted in one of two ways: in terms of either the number of simulating observables or their number of outcomes. The former is seen to be closely connected to compatibility and $k$-compatibility, whereas the latter leads to a partial characterization for dichotomic observables. In addition to the quantum case, we further demonstrate these concepts in state spaces described by regular polygons.

quant-ph↗

arXiv2018

Ultimate entanglement robustness of two-qubit states against general local noises

We study the problem of optimal preparation of a bipartite entangled state, which remains entangled the longest time under action of local qubit noises. We show that for unital noises such a state is always maximally entangled, whereas for nonunital noises, it is not. We develop a decomposition technique relating nonunital and unital qubit channels, based on which we find the explicit form of the ultimately robust state for general local noises. We illustrate our findings by amplitude damping processes at finite temperature, for which the ultimately robust state remains entangled up to two times longer than conventional maximally entangled states.

quant-ph↗

arXiv2018

Quantum dynamics intervened by repeated nonselective measurements

We derive the theory of open quantum system dynamics intervened by a series of nonselective measurements. We analyze the cases of time independent and time dependent Hamiltonian dynamics in between the measurements and find the approximate master equation in the stroboscopic limit. We also consider a situation, in which the measurement basis changes in time, and illustrate it by nonselective measurements in the basis of diabatic states of the Landau-Zener model.

quant-ph↗

arXiv2017

Absolutely separating quantum maps and channels

Absolutely separable states $\varrho$ remain separable under arbitrary unitary transformations $U \varrho U^†$. By example of a three qubit system we show that in multipartite scenario neither full separability implies bipartite absolute separability nor the reverse statement holds. The main goal of the paper is to analyze quantum maps resulting in absolutely separable output states. Such absolutely separating maps affect the states in a way, when no Hamiltonian dynamics can make them entangled afterwards. We study general properties of absolutely separating maps and channels with respect to bipartitions and multipartitions and show that absolutely separating maps are not necessarily entanglement breaking. We examine stability of absolutely separating maps under tensor product and show that $Φ^{\otimes N}$ is absolutely separating for any $N$ if and only if $Φ$ is the tracing map. Particular results are obtained for families of local unital multiqubit channels, global generalized Pauli channels, and combination of identity, transposition, and tracing maps acting on states of arbitrary dimension. We also study the interplay between local and global noise components in absolutely separating bipartite depolarizing maps and discuss the input states with high resistance to absolute separability.

quant-ph↗

arXiv2017

Positive tensor products of qubit maps and n-tensor-stable positive qubit maps

We analyze positivity of a tensor product of two linear qubit maps, $Φ_1 \otimes Φ_2$. Positivity of maps $Φ_1$ and $Φ_2$ is a necessary but not a sufficient condition for positivity of $Φ_1 \otimes Φ_2$. We find a non-trivial sufficient condition for positivity of the tensor product map beyond the cases when both $Φ_1$ and $Φ_2$ are completely positive or completely co-positive. We find necessary and (separately) sufficient conditions for $n$-tensor-stable positive qubit maps, i.e. such qubit maps $Φ$ that $Φ^{\otimes n}$ is positive. Particular cases of 2- and 3-tensor-stable positive qubit maps are fully characterized, and the decomposability of 2-tensor-stable positive qubit maps is discussed. The case of non-unital maps is reduced to the case of appropriate unital maps. Finally, $n$-tensor-stable positive maps are used in characterization of multipartite entanglement, namely, in the entanglement depth detection.

quant-ph↗

arXiv2016

Spectral properties of reduced fermionic density operators and parity superselection rule

We consider pure fermionic states with a varying number of quasiparticles and analyze two types of reduced density operators: one is obtained via tracing out modes, the other is obtained via tracing out particles. We demonstrate that spectra of mode-reduced states are not identical in general and fully characterize pure states with equispectral mode-reduced states. Such states are related via local unitary operations with states satisfying the parity superselection rule. Thus, valid purifications for fermionic density operators are found. To get particle-reduced operators for a general system, we introduce the operation $Φ(\varrho) = \sum_i a_i \varrho a_i^†$. We conjecture that spectra of $Φ^p(\varrho)$ and conventional $p$-particle reduced density matrix $\varrho_p$ coincide. Nontrivial generalized Pauli constraints are derived for states satisfying the parity superselection rule.

quant-ph↗

arXiv2014

PPT-inducing, distillation-prohibiting, and entanglement-binding quantum channels

Entanglement degradation in open quantum systems is reviewed in the Choi-Jamiołkowski representation of linear maps. In addition to physical processes of entanglement dissociation and entanglement annihilation, we consider quantum dynamics transforming arbitrary input states into those that remain positive under partial transpose (PPT-inducing channels). Such evolutions form a convex subset of distillation-prohibiting channels. A relation between the above channels and entanglement-binding ones is clarified. An example of the distillation-prohibiting map $Φ\otimesΦ$ is given, where $Φ$ is not entanglement binding.

quant-ph↗

arXiv2014

Entanglement sensitivity to signal attenuation and amplification

We analyze general laws of continuous-variable entanglement dynamics during the deterministic attenuation and amplification of the physical signal carrying the entanglement. These processes are inevitably accompanied by noises, so we find fundamental limitations on noise intensities that destroy entanglement of gaussian and non-gaussian input states. The phase-insensitive amplification $Φ_1 \otimes Φ_2 \otimes \ldots Φ_N$ with the power gain $κ_i \ge 2$ ($\approx 3$ dB, $i=1,\ldots,N$) is shown to destroy entanglement of any $N$-mode gaussian state even in the case of quantum limited performance. In contrast, we demonstrate non-gaussian states with the energy of a few photons such that their entanglement survives within a wide range of noises beyond quantum limited performance for any degree of attenuation or gain. We detect entanglement preservation properties of the channel $Φ_1 \otimes Φ_2$, where each mode is deterministically attenuated or amplified. Gaussian states of high energy are shown to be robust to very asymmetric attenuations, whereas non-gaussian states are at an advantage in the case of symmetric attenuation and general amplification. If $Φ_1 = Φ_2$, the total noise should not exceed $\frac{1}{2} \sqrt{κ^2+1}$ to guarantee entanglement preservation.

quant-ph↗

arXiv2013

Dissociation and annihilation of multipartite entanglement structure in dissipative quantum dynamics

We study the dynamics of the entanglement structure of a multipartite system experiencing a dissipative evolution. We characterize the processes leading to a particular form of output system entanglement and provide a recipe for their identification via concatenations of particular linear maps with entanglement-breaking operations. We illustrate the applicability of our approach by considering local and global depolarizing noises acting on general multiqubit states. A difference in the typical entanglement behavior of systems subjected to these noises is observed: the originally genuine entanglement dissociates by splitting off particles one by one in the case of local noise, whereas intermediate stages of entanglement clustering are present in the case of global noise. We also analyze the definitive phase of evolution when the annihilation of the entanglement compound finally takes place.

quant-ph↗

arXiv2012

Probability-based comparison of quantum states

We address the following state comparison problem: is it possible to design an experiment enabling us to unambiguously decide (based on the observed outcome statistics) on the sameness or difference of two unknown state preparations without revealing complete information about the states? We find that the claim "the same" can never be concluded without any doubts unless the information is complete. Moreover, we prove that a universal comparison (that perfectly distinguishes all states) also requires complete information about the states. Nevertheless, for some measurements, the probability distribution of outcomes still allows one to make an unambiguous conclusion regarding the difference between the states even in the case of incomplete information. We analyze an efficiency of such a comparison of qudit states when it is based on the SWAP-measurement. For qubit states, we consider in detail the performance of special families of two-valued measurements enabling us to successfully compare at most half of the pairs of states. Finally, we introduce almost universal comparison measurements which can distinguish almost all non-identical states (up to a set of measure zero). The explicit form of such measurements with two and more outcomes is found in any dimension.

quant-ph↗

arXiv2012

Simulation of indivisible qubit channels in collision models

A sequence of controlled collisions between a quantum system and its environment (composed of a set of quantum objects) naturally simulates (with arbitrary precision) any Markovian quantum dynamics of the system under consideration. In this paper we propose and study the problem of simulation of an {\it arbitrary} quantum channel via collision models. We show that a correlated environment is capable to simulate {\it non-Markovian} evolutions leading to any indivisible qubit channel. In particular, we derive the corresponding master equation generating a continuous time non-Markovian dynamics implementing the universal NOT gate being an example of the most non-Markovian quantum channels.

quant-ph↗

arXiv2011

Local two-qubit entanglement-annihilating channels

We address the problem of the robustness of entanglement of bipartite systems (qubits) interacting with dynamically independent environments. In particular, we focus on characterization of so-called local entanglement-annihilating two-qubit channels, which set the maximum permissible noise level allowing to perform entanglement-enabled experiments. The differences, but also subtle relations between entanglement-breaking and local entanglement-annihilating channels are emphasized. A detailed characterization of latter ones is provided for a variety of channels including depolarizing, unital, (generalized) amplitude-damping, and extremal channels. We consider also the convexity structure of local entanglement-annihilating qubit channels and introduce a concept of entanglement-annihilation duality.

quant-ph↗

arXiv2011

Measuring microwave quantum states: tomogram and moments

Two measurable characteristics of microwave one-mode photon states are discussed: a rotated quadrature distribution (tomogram) and normally/antinormally ordered moments of photon creation and annihilation operators. Extraction of these characteristics from amplified microwave signal is presented. Relations between the tomogram and the moments are found and can be used as a cross check of experiments. Formalism of the ordered moments is developed. The state purity and generalized uncertainty relations are considered in terms of moments. Unitary and non-unitary time evolution of moments is obtained in the form of linear differential equations in contrast to partial differential equations for quasidistributions. Time evolution is specified for the cases of a harmonic oscillator and a damped harmonic oscillator, which describe noiseless and decoherence processes, respectively.

quant-ph↗