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Register a new userEntanglement robustness in trace decreasing quantum dynamics caused by depolarization and polarization dependent losses
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Authors
Sergey N. Filippov
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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 though 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.
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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.
We propose a protocol using a tunable Xmon qubit chain to construct generalized Su-Schrieffer-Heeger (SSH) models that support various topological phases. We study the time evolution of a single-excitation quantum state in a SSH-type qubit chain and find that such dynamics is linked to topological winding number. We also investigate the adiabatic transfer of a single-excitation quantum state in a generalized SSH-type qubit chain and show that this process can be connected with topological Chern number and be used to generate a novel entanglement-dependent topological pumping. All results have been demonstrated to be robust against qubit coupling imperfections and can be observed in a short Xmon qubit chain. Our study provides a simple method to directly measure topological invariants rooted in momentum space using quantum dynamics in real space.
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 get a higher quantum communication rate by doubling the code length. The obtained results give a deeper understanding of useful multiletter codes and may serve as a benchmark for quantum capacity estimations and future approaches toward an optimal strategy to transfer quantum information.
The purity, Tr(rho^2), measures how pure or mixed a quantum state rho is. It is well known that quantum dynamical semigroups that preserve the identity operator (which we refer to as unital) are strictly purity-decreasing transformations. Here we provide an almost complete characterization of the class of strictly purity-decreasing quantum dynamical semigroups. We show that in the case of finite-dimensional Hilbert spaces a dynamical semigroup is strictly purity-decreasing if and only if it is unital, while in the infinite dimensional case, unitality is only sufficient.
Losses in quantum communication lines severely affect the rates of reliable information transmission and are usually considered to be state-independent. However, the loss probability does depend on the system state in general, with the polarization dependent losses being a prominent example. Here we analyze biased trace decreasing quantum operations that assign different loss probabilities to states and introduce the concept of a generalized erasure channel. We find lower and upper bounds for the classical and quantum capacities of the generalized erasure channel as well as characterize its degradability and antidegradability. We reveal superadditivity of coherent information in the case of the polarization dependent losses, with the difference between the two-letter quantum capacity and the single-letter quantum capacity exceeding $7.197 cdot 10^{-3}$ bit per qubit sent, the greatest value among qubit-input channels reported so far.
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