Papers by Sergey Filippov
Entropy
Entanglement distribution task encounters a problem of how the initial entangled state should be ... more Entanglement distribution task encounters a problem of how the initial entangled state should be prepared in order to remain entangled the longest possible time when subjected to local noises. In the realm of continuous-variable states and local Gaussian channels it is tempting to assume that the optimal initial state with the most robust entanglement is Gaussian too; however, this is not the case. Here we prove that specific non-Gaussian two-mode states remain entangled under the effect of deterministic local attenuation or amplification (Gaussian channels with the attenuation factor/power gain κi and the noise parameter μi for modes i=1,2) whenever κ1μ22+κ2μ12<14(κ1+κ2)(1+κ1κ2), which is a strictly larger area of parameters as compared to where Gaussian entanglement is able to tolerate noise. These results shift the “Gaussian world” paradigm in quantum information science (within which solutions to optimization problems involving Gaussian channels are supposed to be attained at...
Physical Review A
Quantum collision models are receiving increasing attention as they describe many nontrivial phen... more Quantum collision models are receiving increasing attention as they describe many nontrivial phenomena in dynamics of open quantum systems. In a general scenario of both fundamental and practical interest, a quantum system repeatedly interacts with individual particles or modes forming a correlated and structured reservoir; however, classical and quantum environment correlations greatly complicate the calculation and interpretation of the system dynamics. Here we propose an exact solution to this problem based on the tensor network formalism. We find a natural Markovian embedding for the system dynamics, where the role of an auxiliary system is played by virtual indices of the network. The constructed embedding is amenable to analytical treatment for a number of timely problems like the system interaction with two-photon wavepackets, structured photonic states, and one-dimensional spin chains. We also derive a time-convolution master equation and relate its memory kernel with the environment correlation function, thus revealing a clear physical picture of memory effects in the dynamics. The results advance tensor-network methods in the fields of quantum optics and quantum transport.
Quantum collision models are receiving increasing attention as they describe many nontrivial phen... more Quantum collision models are receiving increasing attention as they describe many nontrivial phenomena in dynamics of open quantum systems. In a general scenario of both fundamental and practical interest, a quantum system repeatedly interacts with individual particles or modes forming a correlated and structured reservoir; however, classical and quantum environment correlations greatly complicate the calculation and interpretation of the system dynamics. Here we propose an exact solution to this problem based on the tensor network formalism. We find a natural Markovian embedding for the system dynamics, where the role of an auxiliary system is played by virtual indices of the network. The constructed embedding is amenable to analytical treatment for a number of timely problems like the system interaction with two-photon wavepackets, structured photonic states, and one-dimensional spin chains. We also derive a time-convolution master equation and relate its memory kernel with the environment correlation function, thus revealing a clear physical picture of memory effects in the dynamics. The results advance tensor-network methods in the fields of quantum optics and quantum transport.
Entanglement distribution task encounters a problem of how the initial entangled state should be ... more Entanglement distribution task encounters a problem of how the initial entangled state should be prepared in order to remain entangled the longest possible time when subjected to local noises. In the realm of continuousvariable states and local Gaussian channels it is tempting to assume that the optimal initial state with the most robust entanglement is Gaussian too; however, this is not the case. Here we prove that specific non-Gaussian two-mode states remain entangled under the effect of deterministic local attenuation or amplification (Gaussian channels with the attenuation factor/power gain κi and the noise parameter µi for modes i = 1, 2) whenever κ1µ 2 2 + κ2µ 2 1 < 1 4 (κ1 + κ2)(1 + κ1κ2), which is a strictly larger area of parameters as compared to where Gaussian entanglement is able to tolerate noise. These results shift the "Gaussian world" paradigm in quantum information science (within which solutions to optimization problems involving Gaussian channels are supposed to be attained at Gaussian states).
Quantum processing units boost entanglement at the level of hardware and enable physical simulati... more Quantum processing units boost entanglement at the level of hardware and enable physical simulations of highly correlated electron states in molecules and intermolecular chemical bonds. The variational quantum eigensolver provides a hardware-efficient toolbox for ground state simulation; however, with limitations in precision. Even in the absence of noise, the algorithm may result into a biased energy estimation, particularly with some shallower ansatz types. Noise additionally degrades entanglement and hinders the ground state energy estimation (especially if the noise is not fully characterized). Here we develop a method to exploit the quantum-classical interface provided by informationally complete measurements to use classical software on top of the hardware entanglement booster for ansatz-and noise-related error reduction. We use the tensor network representation of a quantum channel that drives the noisy state toward the ground one. The tensor network is a completely positive map by construction, but we elaborate on making the trace preservation condition local so as to activate the sweeping variational optimization. This method brings into reach energies below the noiseless ansatz by creating additional correlations among the qubits and denoising them. Analyzing the example of the stretched water molecule with a tangible entanglement, we argue that a hybrid strategy of using the quantum hardware together with the classical software outperforms a purely classical strategy provided the classical parts have the same bond dimension. As a byproduct we discuss the expressivity of matrix product channels and address the overfitting problem emerging in postprocessing actual measurement data. The proposed optimization algorithm extends the variety of noise mitigation methods and facilitates the more accurate study of the energy landscape for deformed molecules. The algorithm can be applied as the final postprocessing step in the quantum hardware simulation of protein-ligand complexes in the context of drug design.
Entropy
Quantum collision models have proved to be useful for a clear and concise description of many phy... more Quantum collision models have proved to be useful for a clear and concise description of many physical phenomena in the field of open quantum systems: thermalization, decoherence, homogenization, nonequilibrium steady state, entanglement generation, simulation of many-body dynamics, and quantum thermometry. A challenge in the standard collision model, where the system and many ancillas are all initially uncorrelated, is how to describe quantum correlations among ancillas induced by successive system-ancilla interactions. Another challenge is how to deal with initially correlated ancillas. Here we develop a tensor network formalism to address both challenges. We show that the induced correlations in the standard collision model are well captured by a matrix product state (a matrix product density operator) if the colliding particles are in pure (mixed) states. In the case of the initially correlated ancillas, we construct a general tensor diagram for the system dynamics and derive a ...
Quanta, 2021
Trace decreasing dynamical maps are as physical as trace preserving ones; however, they are much ... more Trace decreasing dynamical maps are as physical as trace preserving ones; however, they are much less studied. Here we overview how the quantum Sinkhorn theorem can be successfully applied to find a two-qubit entangled state which has the strongest robustness against local noises and losses of quantum information carriers. We solve a practically relevant problem of finding an optimal initial encoding to distribute entangled polarized qubits through communication lines with polarization dependent losses and extra depolarizing noise. The longest entanglement lifetime is shown to be attainable with a state that is not maximally entangled.Quanta 2021; 10: 15–21.
The are several non-equivalent notions of Markovian quantum evolution. In this paper we show that... more The are several non-equivalent notions of Markovian quantum evolution. In this paper we show that the one based on the so-called CP-divisibility of the corresponding dynamical map enjoys the following stability property: the dynamical map Λ_t is CP-divisible iff the second tensor power Λ_t⊗Λ_t is CP-divisible as well. Moreover, the P-divisibility of the map Λ_t⊗Λ_t is equivalent to the CP-divisibility of the map Λ_t. Interestingly, the latter property is no longer true if we replace the P-divisibility of Λ_t⊗Λ_t by simple positivity and the CP-divisibility of Λ_t by complete positivity. That is, unlike when Λ_t has a time-independent generator, positivity of Λ_t⊗Λ_t does not imply complete positivity of Λ_t.
A quantum system interacting with a diluted gas experiences the irreversible dynamics. The corres... more A quantum system interacting with a diluted gas experiences the irreversible dynamics. The corresponding master equation can be derived within two different approaches: the fully quantum description in the low-density limit and the semiclassical collision model, where the motion of gas particles is classical whereas their internal degrees of freedom are quantum. The two approaches have been extensively studied in the literature but their predictions have not been compared. This is mainly due to a fact that the low-density limit is extensively studied for mathematical physics analysis, whereas the collision models have been essentially developed for quantum information tasks as a tractable description of the open quantum dynamics. Here we develop and for the first time compare both approaches for a spin system interacting with a gas of spin particles. Using some approximations, we explicitly find the corresponding master equations including the Lamb shifts and the dissipators. The lo...
Lobachevskii Journal of Mathematics, 2020
State of a d-dimensional quantum system can only be inferred by performing an informationally com... more State of a d-dimensional quantum system can only be inferred by performing an informationally complete measurement with m d 2 outcomes. However, an experimentally accessible measurement can be informationally incomplete. Here we show that a single informationally incomplete measuring apparatus is still able to provide all the information about the quantum system if applied several times in a row. We derive a necessary and sufficient condition for such a measuring apparatus and give illustrative examples for qubits, qutrits, general d-level systems, and composite systems of n qubits, where such a measuring apparatus exists. We show that projective measurements and L¨uders measurements with 2 outcomes are useless in the considered scenario.
Trace decreasing quantum operations naturally emerge in experiments involving postselection. Howe... more Trace decreasing quantum operations naturally emerge in experiments involving postselection. However, the experiments usually focus on dynamics of the conditional output states as if the dynamics were trace preserving. Here we show that this approach leads to incorrect conclusions about the dynamics divisibility, namely, one can observe an increase in the trace distance or the system-ancilla entanglement although the trace decreasing dynamics is completely positive divisible. We propose solutions to that problem and introduce proper indicators of the information backflow and the indivisibility. We also review a recently introduced concept of the generalized erasure dynamics that includes more experimental data in the dynamics description. The ideas are illustrated by explicit physical examples of polarization dependent losses.
Coherent information quantifies the achievable rate of the reliable quantum information transmiss... more Coherent information quantifies the achievable rate of the reliable quantum information transmission through a communication channel. Use of the correlated quantum states (multiletter codes) instead of the factorized ones (single-letter codes) may result in an increase in the achievable rate, a phenomenon known as the coherent-information superadditivity. However, even for simple physical models of channels it is rather difficult to detect the superadditivity and find the advantageous multiletter codes. Here we consider the case of polarization dependent losses and propose some physically motivated multiletter codes which outperform all single-letter ones in a wide range of the channel parameters. We show that in the asymptotic limit of the infinite code length the superadditivity phenomenon takes place whenever the communication channel is neither degradable nor antidegradable. Besides the superadditivity identification, we also provide a method how to modify the proposed codes and...
Foundations of Physics, 2020
The formalism of general probabilistic theories provides a universal paradigm that is suitable fo... more The formalism of general probabilistic theories provides a universal paradigm that is suitable for describing various physical systems including classical and quantum ones as particular cases. Contrary to the usual no-restriction hypothesis, the set of accessible meters within a given theory can be limited for different reasons, and this raises a question of what restrictions on meters are operationally relevant. We argue that all operational restrictions must be closed under simulation, where the simulation scheme involves mixing and classical post-processing of meters. We distinguish three classes of such operational restrictions: restrictions on meters originating from restrictions on effects; restrictions on meters that do not restrict the set of effects in any way; and all other restrictions. We fully characterize the first class of restrictions and discuss its connection to convex effect subalgebras. We show that the restrictions belonging to the second class can impose severe...
Lobachevskii Journal of Mathematics, 2020
Phase covariant qubit dynamics describes an evolution of a two-level system under simultaneous ac... more Phase covariant qubit dynamics describes an evolution of a two-level system under simultaneous action of pure dephasing, energy dissipation, and energy gain with time-dependent rates γz(t), γ−(t), and γ+(t), respectively. Non-negative rates correspond to completely positive divisible dynamics, which can still exhibit such peculiarities as non-monotonicity of populations for any initial state. We find a set of quantum channels attainable in the completely positive divisible phase covariant dynamics and show that this set coincides with the set of channels attainable in semigroup phase covariant dynamics. We also construct new examples of eternally indivisible dynamics with γz(t) < 0 for all t > 0 that is neither unital nor commutative. Using the quantum Sinkhorn theorem, we for the first time derive a restriction on the decoherence rates under which the dynamics is positive divisible, namely, γ±(t) ≥ 0, γ+(t)γ−(t) + 2γz(t) > 0. Finally, we consider phase covariant convolution master equations and find a class of admissible memory kernels that guarantee complete positivity of the dynamical map.
Journal of Russian Laser Research, 2020
We realize Landau-Streater (LS) and Werner-Holevo (WH) quantum channels for qutrits on the IBM qu... more We realize Landau-Streater (LS) and Werner-Holevo (WH) quantum channels for qutrits on the IBM quantum computers. These channels correspond to interaction between the qutrit and its environment that result in the globally unitarily covariant qutrit transformation violating multiplicativity of the maximal p-norm. Our realization of LS and WH channels is based on embedding qutrit states into states of two qubits and using single-qubit and two-qubit CNOT gates to implement the specific interaction. We employ the standard quantum gates hence the developed algorithm suits any quantum computer. We run our algorithm on a 5-qubit and a 20-qubit computer as well as on a simulator. We quantify the quality of the implemented channels comparing their action on different input states with theoretical predictions. The overall efficiency is quantified by fidelity between the theoretical and experimental Choi states implemented on the 20-qubit computer.
Physical Review A, 2019
Pumping a nonlinear crystal by an intense radiation results in the optical parametric generation ... more Pumping a nonlinear crystal by an intense radiation results in the optical parametric generation of photons in two modes (the signal and the idler). The quantized electromagnetic field in these modes is described by a continuous-variable quantum state, which is entangled if the pump is a coherent state produced by a laser. The signal and the idler modes remain populated by photons even if the pump becomes incoherent (dephased by a medium, superposed with a thermal state, or produced by an alternative source such as the superluminescent diode). However, the incoherent pump does effect the entanglement and purity of the signal and the idler modes, which is of vital importance for the quantum information applications and the interferometry. Here we develop an approach to infer the signal-idler entanglement and purity for a general quantum incoherent pump with the given Glauber-Sudarshan function. We show that the signal-idler entanglement is extremely sensitive to the phase distribution of the pump and illustrate our findings by physically relevant examples of the incoherent pump: the noisy coherent state, slightly dephased and phase-averaged coherent states, thermal state, and states modulated by the Kerr medium. The effect of incoherent pump on the combined quadratures is discussed as well.
Physical Review A, 2018
Convolutionless and convolution master equations are the two mostly used physical descriptions of... more 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.
International Journal of Quantum Information, 2017
We derive the theory of open quantum system dynamics intervened by a series of nonselective measu... more 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 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.
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Papers by Sergey Filippov