We show that the amount of coherent quantum information that can be reliably transmitted down a dephasing channel with memory is maximized by separable input states. In particular, we model the channel as a Markov chain or a multimode environment of oscillators. While in the first model the maximization is achieved for the maximally mixed input state, in the latter it is convenient to exploit the presence of a decoherence-protected subspace generated by memory effects. We explicitly compute the quantum channel capacity for the first model while numerical simulations suggest a lower bound for the latter. In both cases memory effects enhance the coherent information. We present results valid for arbitrary size of the input.
We study a dephasing channel with memory, modelled by a multimode environment of oscillators. Focusing on the case of two channel uses, we show that memory effects can enhance the amount of coherent quantum information transmitted down the channel. We also show the Kraus representation for two channel uses. Finally, we propose a coding-decoding scheme that takes advantage of memory to improve the fidelity of transmission.
We study the quantum capacity of continuous variable dephasing channel, which is a notable example of non-Gaussian quantum channel. We prove that a single letter formula applies. We then consider input energy restriction and show that by increasing it, the capacity saturates to a finite value. The optimal input state is found to be diagonal in the Fock basis and with a distribution that is a discrete version of a Gaussian. Relations between its mean/variance and dephasing rate/input energy are put forward. We also show that quantum capacity decays exponentially for large values of dephasing ra…
Bosonic qubits encoded in continuous-variable systems provide a promising alternative to two-level qubits for quantum computation and communication. So far, photon loss has been the dominant source of errors in bosonic qubits, but the significant reduction of photon loss in recent bosonic qubit experiments suggests that dephasing errors should also be considered. However, a detailed understanding of the combined photon loss and dephasing channel is lacking. Here, we show that, unlike its constituent parts, the combined loss-dephasing channel is non-degradable, pointing towards a richer structu…
In this paper, using the notion of nonlinear coherent states, we define a deformed bosonic dephasing channel modelling the impact of a Kerr medium on a quantum state, as it occurs, for instance, in quantum communication based on optical fibers. We show that, in certain regimes, the Kerr nonlinearity is able to compensate the dephasing. In addition, our studies reveal that the quantum capacity of the deformed bosonic dephasing channel can be greater than that of the undeformed, standard bosonic dephasing channel for certain nonlinearity parameters.
We study a dephasing channel with memory, modelled by a Markov chain. We show that even weak memory effects have a detrimental impact on the performance of quantum error correcting schemes designed for uncorrelated errors. We also discuss an alternative scheme that takes advantage of memory effects to protect quantum information.
We study a dephasing channel with memory, described by a Hamiltonian model in which the system-environment interaction is described by a stochastic process. We propose a useful way to describe the channel uses correlations. Moreover, we give a general expression for the coherences decay factors as a function of the number of channel uses and of the stochastic process power spectrum. We also study the impact of memory on the three qubit code, showing that correlations among channel uses affect very little the code performance.
The developing of (non-Markovian) memory effects strongly depends on the underlying system-environment dynamics. Here we study this problem in multipartite arrangements where all subsystems are coupled to each other by non-diagonal Markovian (Lindblad) dephasing mechanisms. Taking as system and environment arbitrary sets of complementary subsystems it is shown that both operational and non-operational approaches to quantum non-Markovianity can be characterized in an exact analytical way. Similarly to previous studies about dissipative-entanglement-generation in this kind of dynamics [Seif, Wan…
Motion-induced dephasing is a dominant decoherence mechanism for atom-gas quantum memories. In this paper, we develop a new coherent manipulation technique which enables arbitrary engineering of the spin-wave momentum with neglectable noise. By zeroing the spin-wave momentum, motion-induced dephasing can be frozen completely. We experimentally demonstrate this scheme with laser-cooled atoms in a DLCZ configuration. By applying the freezing pulses, memory lifetime gets extended significantly to the limit of atom cloud expansion and does not depend on the detection angle anymore. The observed hi…
No advantage from classical assistance for energy-constrained bosonic dephasing channels
Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo（量子计算研究所与物理和天文学系，滑铁卢大学）；Institute for Quantum Computing and Department of Applied Mathematics, University of Waterloo（量子计算研究所与应用数学系，滑铁卢大学）
Capacity-Achieving Entanglement Purification Protocol for Pauli Dephasing Channel
The Australian National University（澳大利亚国立大学）；University of Queensland（昆士兰大学）；Commonwealth Scientific and Industrial Research Organisation（联邦科学与工业研究组织）；Agency for Science, Technology and Research (A*STAR)（科学技术研究局）
We theoretically study the dynamical dephasing of a quantum two level system interacting with an environment exhibiting non-Markovian random telegraph fluctuations. The time evolution of the conditional probability of the environmental noise is governed by a generalized master equation depending on the environmental memory effect. The expression of the dephasing factor is derived exactly which is closely associated with the memory kernel in the generalized master equation for the conditional probability of the environmental noise. In terms of three important types memory kernels, we discuss th…
We consider a class of multi-qubit dephasing models that combine classical noise sources and linear coupling to a bosonic environment, and are controlled by arbitrary sequences of dynamical decoupling pulses. Building on a general transfer filter-function framework for open-loop control, we provide an exact representation of the controlled dynamics for arbitrary stationary non-Gaussian classical and quantum noise statistics, with analytical expressions emerging when all dephasing sources are Gaussian. This exact characterization is used to establish two main results. First, we construct multi-…
We study the performance of two measures of non-Markovianity in detecting memory effects in two-qubit dephasing channels. By combining independent Markovian and non-Markovian noise on the qubits, our results show that the trace distance measure is able to detect the memory effects when at least one of the local channels displays non-Markovianity. A measure based on channel capacity, in turn, becomes non-zero when the global two-qubit dynamics shows memory effects. We apply these schemes to a well-known superdense coding protocol and demonstrate an optimal noise configuration to maximize the in…
We probe dephasing mechanisms within a quantum network node consisting of a single nitrogen-vacancy centre electron spin that is hyperfine coupled to surrounding $^{13} \text{C}$ nuclear-spin quantum memories. Previous studies have analysed memory dephasing caused by the stochastic electron-spin reset process, which is a component of optical internode entangling protocols. Here, we find, by using dynamical decoupling techniques and exploiting phase matching conditions in the electron-nuclear dynamics, that control infidelities and quasi-static noise are the major contributors to memory dephasi…
Memory effects can be studied through a conditional past-future correlation, which measures departure with respect to a conditional past-future independence valid in a memoryless Markovian regime. In a quantum regime this property leads to an operational definition of quantum non-Markovianity based on three consecutive system measurement processes and postselection [Budini, Phys. Rev. Lett. 121, 240401 (2018)]. Here, we study the conditional past-future correlation for a qubit system coupled to different dephasing environments. Exact solutions are obtained for a quantum spin bath as well as fo…
We investigate the dynamics of quantum and classical correlations in a system of two qubits under local colored-noise dephasing channels. The time evolution of a single qubit interacting with its own environment is described by a memory kernel non-Markovian master equation. The memory effects of the non-Markovian reservoirs introduce new features in the dynamics of quantum and classical correlations compared to the white noise Markovian case. Depending on the geometry of the initial state, the system can exhibit frozen discord and multiple sudden transitions between classical and quantum decoh…
We characterise a class of environmental noises that decrease coherent properties of quantum channels by introducing and analysing the properties of dephasing superchannels. These are defined as superchannels that affect only non-classical properties of a quantum channel $\mathcal{E}$, i.e., they leave invariant the transition probabilities induced by $\mathcal{E}$ in the distinguished basis. We prove that such superchannels $Ξ_C$ form a particular subclass of Schur-product supermaps that act on the Jamiolkowski state $J(\mathcal{E})$ of a channel $\mathcal{E}$ via a Schur product, $J'=J\circ …
We study discrete quantum dynamics where single evolution step consists of unitary system transformation followed by decoherence via coupling to an environment. Often non-Markovian memory effects are attributed to structured environments whereas here we take a more general approach within discrete setting. In addition of controlling the structure of the environment, we are interested in how local unitaries on the open system allow the appearance and control of memory effects. Our first simple qubit model, where local unitary is followed by dephasing, illustrates how memory effects arise despit…
We demonstrate active control of inhomogeneous dephasing and rephasing for single collective atomic spin excitations (spin-waves) created by spontaneous Raman scattering in a quantum memory based on cold $^{87}$Rb atoms. The control is provided by a reversible external magnetic field gradient inducing an inhomogeneous broadening of the atomic hyperfine levels. We demonstrate experimentally that active rephasing preserves the single photon nature of the retrieved photons. Finally, we show that the control of the inhomogeneous dephasing enables the creation of time-separated spin-waves in a sing…
We introduce a figure of merit for a quantum memory which measures the preservation of entanglement between a qubit stored in and retrieved from the memory and an auxiliary qubit. We consider a general quantum memory system consisting of a medium of two level absorbers, with the qubit to be stored encoded in a single photon. We derive an analytic expression for our figure of merit taking into account Gaussian fluctuations in the Hamiltonian parameters, which for example model inhomogeneous broadening and storage time dephasing. Finally we specialize to the case of an atomic quantum memory wher…
We demonstrate experimentally the creation and measurement of an entangled state between a microscopic two level system and a macroscopic superconducting resonator where their indirect interaction is mediated by an artificial atom, a superconducting persistent current qubit (PCQB). We show that the microscopic two level system, formed by a defect in an oxide layer, exhibits an order of magnitude longer dephasing time than the PCQB, while the dephasing time of the entangled states between the microscopic two level system and macroscopic superconducting resonator is significantly longer than the…
In this article we treat the subject of chaotic environments with few degrees of freedom in quantum communication by investigating a conservative dynamical map as a model of a dephasing quantum channel. When the channel's dynamics is chaotic, we investigate the model's semi-classical limit and show that the entropy exchange grows at a constant rate which depends on a single parameter (the interaction strength), analogous to stochastic models of dephasing channels. We analyze memory effects in the channel and present strong physical arguments to support that the present model is forgetful in th…
We investigate the quantum temporal steering (TS), i.e., a temporal analogue of Einstein-Podolsky-Rosen steering, in a dephasing channel which is modeled by a central spin half surrounded by a spin-1/2 \textit{XY} chain where quantum phase transition happens. The TS parameter $S_{\text{TS}}$ and the TS weight $W_{\text{TS}}$ are employed to characterize the TS dynamics. We analytically obtain the dependence of $S_{\text{TS}}$ on the decoherence factor. The numerical results show an obvious suppression of $S_{\text{TS}}$ and $W_{\text{TS}}$ when the \textit{XY} chain approaches to the critical …
The classical product state capacity of a noisy quantum channel with memory is investigated. A forgetful noise-memory channel is constructed by Markov switching between two depolarizing channels which introduces non-Markovian noise correlations between successive channel uses. The computation of the capacity is reduced to an entropy computation for a function of a Markov process. A reformulation in terms of algebraic measures then enables its calculation. The effects of the hidden-Markovian memory on the capacity are explored. An increase in noise-correlations is found to increase the capacity…
Based on numerically-optimized real-device gates and parameters we study the performance of the phase-flip (repetition) code on a linear array of Gallium Arsenide (GaAs) quantum dots hosting singlet-triplet qubits. We first examine the expected performance of the code using simple error models of circuit-level and phenomenological noise, reporting, for example, a circuit-level depolarizing noise threshold of approximately 3%. We then perform density-matrix simulations using a maximum-likelihood and minimum-weight matching decoder to study the effect of real-device dephasing, read-out error, qu…
We study the classical capacity of a forgetful quantum memory channel that switches between two qubit depolarizing channels according to an ergodic Markov chain. The capacity of this quantum memory channel depends on the parameters of the two depolarizing channels and the memory of the ergodic Markov chain. When the number of input qubit's is two, we show that depending on channel parameters either the maximally entangled input states or product input states achieve the classical capacity. Our conjecture based on numerics is that as the number of input qubits are increased the classical capaci…
There exist memoryless zero-capacity quantum channels that when used jointly result in the channel with positive capacity. This phenomenon is called superactivation. Making use of Parrondo's paradox, we exhibit examples of superactivation-like effect for the capacity of classical communication channels as well as quantum and private capacity of quantum channels with memory. There are several ingredients necessary for superactivation of quantum capacity to occur in memoryless case. The first one is the requirement for the quantum channels which are amenable for superactivation to come from two …
We investigate the classical capacity of two quantum channels with memory: a periodic channel with depolarizing channel branches, and a convex combination of depolarizing channels. We prove that the capacity is additive in both cases. As a result, the channel capacity is achieved without the use of entangled input states. In the case of a convex combination of depolarizing channels the proof provided can be extended to other quantum channels whose classical capacity has been proved to be additive in the memoryless case.
In this paper we evaluate the entanglement assisted classical capacity of a class of quantum channels with long-term memory, which are convex combinations of memoryless channels. The memory of such channels can be considered to be given by a Markov chain which is aperiodic but not irreducible.
The quantum model of the brain proposed by Ricciardi and Umezawa is extended to dissipative dynamics in order to study the problem of memory capacity. It is shown that infinitely many vacua are accessible to memory printing in a way that in sequential information recording the storage of a new information does not destroy the previously stored ones, thus allowing a huge memory capacity. The mechanism of information printing is shown to induce breakdown of time-reversal symmetry. Thermal properties of the memory states as well as their relation with squeezed coherent states are finally discusse…
We study the capacity of a quantum channel where channel acts like controlled phase gate with the control being provided by a one-dimensional quantum spin chain environment. Due to the correlations in the spin chain, we get a quantum channel with memory. We derive formulas for the quantum capacity of this channel when the spin state is a matrix product state. Particularly, we derive exact formulas for the capacity of the quantum memory channel when the environment state is the ground state of the AKLT model and the Majumdar-Ghosh model. We find that the behavior of the capacity for the range o…
An expression is derived characterizing the set of admissible rate pairs for simultaneous transmission of classical and quantum information over a given quantum channel, generalizing both the classical and quantum capacities of the channel. Although our formula involves regularization, i.e. taking a limit over many copies of the channel, it reduces to a single-letter expression in the case of generalized dephasing channels. Analogous formulae are conjectured for the simultaneous public-private capacity of a quantum channel and for the simultaneously 1-way distillable common randomness and enta…
The maximal amount of information which is reliably transmitted over two uses of general Pauli channels with memory is proven to be achieved by maximally entangled states beyond some memory threshold. In particular, this proves a conjecture on the depolarizing channel by Macchiavello and Palma [Phys. Rev. A {\bf 65}, 050301(R) (2002)]. Below the memory threshold, for arbitrary Pauli channels, the two-use classical capacity is only achieved by a particular type of product states.
The classical capacity of phase-invariant Gaussian channels has been recently determined under the assumption that such channels are memoryless. In this work we generalize this result by deriving the classical capacity of a model of quantum memory channel, in which the output states depend on the previous input states. In particular we extend the analysis of [C. Lupo, et al., PRL and PRA (2010)] from quantum limited channels to thermal attenuators and thermal amplifiers. Our result applies in many situations in which the physical communication channel is affected by nonzero memory and by therm…
We calculate the quantum capacity of an amplitude-damping channel with time correlated Markov noise, for two channel uses. Our results show that memory of the channel increases it's ability to transmit quantum information significantly. We analyze and compare our findings with earlier numerical results on amplitude-damping channel with memory. An upper bound on the amount of quantum information transmitted over the channel in presence of memory, for an arbitrary number of channel uses is also presented.
Classical feedback is defined here as the knowledge by the transmitter of the quantum state of the qubit received by the receiver. Such classical feedback doubles capacities of certain memoryless quantum channels without preexisting entanglement between transmitter and receiver. The increase in capacity, which is absent on classical memoryless channels, occurs because we can transform an entangled qubit pair into any other entangled state by applying a unitary operator to only one of the qubits.
We prove that a general upper bound on the maximal mutual information of quantum channels is saturated in the case of Pauli channels with an arbitrary degree of memory. For a subset of such channels we explicitly identify the optimal signal states. We show analytically that for such a class of channels entangled states are indeed optimal above a given memory threshold. It is noteworthy that the resulting channel capacity is a non-differentiable function of the memory parameter.
Establishing the strong converse theorem for a communication channel confirms that the capacity of that channel, that is, the maximum achievable rate of reliable information communication, is the ultimate limit of communication over that channel. Indeed, the strong converse theorem for a channel states that coding at a rate above the capacity of the channel results in the convergence of the error to its maximum value 1 and that there is no trade-off between communication rate and decoding error. Here we prove that the strong converse theorem holds for the product-state capacity of quantum chan…
We experimentally demonstrate an angularly-multiplexed holographic memory capable of intrinsic generation, storage and retrieval of multiple photons, based on off-resonant Raman interaction in warm rubidium-87 vapors. The memory capacity of up to 60 independent atomic spin-wave modes is evidenced by analyzing angular distributions of coincidences between Stokes and time-delayed anti-Stokes light, observed down to the level of single spin-wave excitation during several-$μ$s memory lifetime. We also propose how to practically enhance rates of single and multiple photons generation by combining o…
The bosonic quantum channels have recently attracted a growing interest, motivated by the hope that they open a tractable approach to the generally hard problem of evaluating quantum channel capacities. These studies, however, have always been restricted to memoryless channels. Here, it is shown that the classical capacity of a bosonic Gaussian channel with memory can be significantly enhanced if entangled symbols are used instead of product symbols. For example, the capacity of a photonic channel with 70%-correlated thermal noise of one third the shot noise is enhanced by about 11% when using…
The information-carrying capacity of a memory is known to be a thermodynamic resource facilitating the conversion of heat to work. Szilard's engine explicates this connection through a toy example involving an energy-degenerate two-state memory. We devise a formalism to quantify the thermodynamic value of memory in general quantum systems with nontrivial energy landscapes. Calling this the thermal information capacity, we show that it converges to the non-equilibrium Helmholtz free energy in the thermodynamic limit. We compute the capacity exactly for a general two-state (qubit) memory away fr…
We analyze the ultimate quantum limit on the accessible information for an optical communication scheme when time bins carry coherent light pulses prepared in one of several orthogonal modes and the phase undergoes diffusion after each channel use. This scheme, an example of a quantum memory channel, can be viewed as noisy pulse position modulation (PPM) keying with phase fluctuations occurring between consecutive PPM symbols. We derive a general expression for the output states in the Fock basis and implement a numerical procedure to calculate the Holevo quantity. Using asymptotic properties …
We address the classical capacity of a quantum bosonic memory channel with additive noise, subject to an input energy constraint. The memory is modeled by correlated noise emerging from a Gauss-Markov process. Under reasonable assumptions, we show that the optimal modulation results from a "quantum water-filling" solution above a certain input energy threshold, similar to the optimal modulation for parallel classical Gaussian channels. We also derive analytically the optimal multimode input state above this threshold, which enables us to compute the capacity of this memory channel in the limit…
We study the bandwidth and multiplexing capacity of an erbium-doped optical memory for quantum storage purposes. We concentrate on the protocol ROSE (Revival of a Silenced Echo) because it has the largest potential multiplexing capacity. Our analysis is applicable to other protocols that involve strong optical excitation. We show that the memory performance is limited by instantaneous spectral diffusion and we describe how this effect can be minimised to achieve optimal performance.
We consider the fundamental protocol of dense coding of classical information assuming that noise affects both the forward and backward communication lines between Alice and Bob. Assuming that this noise is described by the same quantum channel, we define its dense coding capacity by optimizing over all adaptive strategies that Alice can implement, while Bob encodes the information by means of Pauli operators. Exploiting techniques of channel simulation and protocol stretching, we are able to establish the dense coding capacity of Pauli channels in arbitrary finite dimension, with simple formu…
Long-lived storage of arbitrary transverse multimodes is important for establishing a high-channel-capacity quantum network. Most of the pioneering works focused on atomic diffusion as the dominant impact on the retrieved pattern in an atom-based memory. In this work, we demonstrate that the unsynchronized Larmor precession of atoms in the inhomogeneous magnetic field dominates the distortion of the pattern stored in a cold-atom-based memory. We find that this distortion effect can be eliminated by applying a strong uniform polarization magnetic field. By preparing atoms in magnetically insens…
We introduce and demonstrate a scheme for eliminating the inhomogeneous dephasing of a collective quantum state. The scheme employs off-resonant fields that continuously dress the collective state with an auxiliary sensor state, which has an enhanced and opposite sensitivity to the same source of inhomogeneity. We derive the optimal conditions under which the dressed state is fully protected from dephasing, when using either one or two dressing fields. The latter provides better protection, circumvents qubit phase rotation, and suppresses the sensitivity to drive noise. We further derive expre…
A phase reference has been a standard requirement in continuous-variable quantum sensing and communication protocols. However, maintaining a phase reference is challenging due to environmental fluctuations, preventing quantum phenomena such as entanglement and coherence from being utilized in many scenarios. We show that quantum communication and entanglement-assisted communication without a phase reference are possible, when a short-time memory effect is present. The degradation in the communication rate of classical or quantum information transmission decreases inversely with the correlation…
