Quantum Capacity Research Articles

End-to-end capacities of imperfect-repeater quantum networks

The optimal performance of a communication network is limited not only by the quality of point-to-point channels, but by the efficacy of its constituent technologies. Understanding the limits of quantum networks requires an understanding of both the ultimate capacities of quantum channels and the efficiency of imperfect quantum repeaters. In this work, using a recently developed node-splitting technique which introduces internal losses and noise into repeater devices, we present achievable end-to-end rates for noisy-repeater quantum networks. These are obtained by extending the coherent and reverse coherent information (single channel capacity lower bounds) into end-to-end capacity lower bounds, both in the context of single-path and multi-path routing. These achievable rates are completely general, and apply to networks composed of arbitrary channels arranged in general topologies. Through this general formalism, we show how tight upper-bounds can also be derived by supplementing appropriate single-edge capacity bounds. As a result, we develop tools which provide tight performance bounds for quantum networks constituent of channels whose capacities are not exactly known, and reveal critical network properties which are necessary for high-rate quantum communications. This permits the investigation of pertinent classes of quantum networks with realistic technologies; qubit amplitude damping networks and bosonic thermal-loss networks.

Effect of vacancy modification on the quantum capacitance of silicene- based electrode in efficient supercapacitors

In this study, we tried to evaluate the application of defected silicene as an electrode in supercapacitors using density functional theory calculations. Researchers have focused on single and double-vacancy silicene. In this work, we investigated six types of vacancies, namely the structures of mono vacancy (MV), double vacancy (DV), triple vacancy (TV), quadruple vacancy (QV), five vacancy (FV) and six vacancy (SV). The density of state, the integrated quantum capacitance, and stored charge plots for the pristine and the vacancy-modified defected silicene structures were investigated. Our results showed that using the vacancy-modified defected structures in the voltage range of -0.50 to 0.50 V provides more quantum capacities than using the pristine silicene. The vacancies MV, TV, QV, FV, and SV can be used as negative and positive electrodes, and they are p-type semiconductors. According to our calculations, the charge stored in at the vacancy-modified defected structures is higher than the charge stored in the pristine silicene at 0 to 0.5 V. The values of the charge stored in all of the vacancy-modified defected structures are similar to those in the pristine silicene. According to our results, the defected silicene is considered as a promising material in high-efficiency supercapacitors.

Multipartite entanglement to boost superadditivity of coherent information in quantum communication lines with polarization-dependent losses

Coherent information quantifies the achievable rate of the reliable quantum information transmission through a communication channel. Use of the correlated quantum states instead of the factorized ones may result in an increase in the coherent information, a phenomenon known as superadditivity. However, even for simple physical models of channels it is rather difficult to detect the superadditivity and find the advantageous multipartite states. Here we consider the case of polarization dependent losses and propose some physically motivated multipartite entangled states which outperform all factorized states in a wide range of the channel parameters. We show that in the asymptotic limit of the infinite number of channel uses the superadditivity phenomenon takes place whenever the channel is neither degradable nor antidegradable. Besides the superadditivity identification, we also provide a method how to modify the proposed states and get a higher quantum communication rate by doubling the number of channel uses. The obtained results give a deeper understanding of coherent information in the multishot scenario and may serve as a benchmark for quantum capacity estimations and future approaches toward an optimal strategy to transfer quantum information.

Creating and destroying coherence with quantum channels

The emerging quantum technologies rely on our ability to establish and control quantum systems in nonclassical states, exhibiting entanglement and quantum coherence. It is thus crucial to understand how entanglement and coherence can be created in the most efficient way. In this work we study optimal ways to create a large amount of quantum coherence via quantum channels. For this, we compare different scenarios, where the channel is acting on an incoherent state, on states which have coherence, and also on subsystems of multipartite quantum states. We show that correlations in multipartite systems do not enhance the ability of a quantum channel to create coherence. We also study the ability of quantum channels to destroy coherence, proving that a channel can destroy more coherence when acting on a subsystem of a bipartite state. Crucially, we also show that the destroyed coherence on multipartite system can exceed the upper bound of those on the single system when the total state is entangled. Our results significantly simplify the evaluation of coherence generating capacity of quantum channels, which we also discuss.

Quantum coherence of thermal biphoton orbital angular momentum state and its distribution in non-Kolmogorov atmospheric turbulence.

Quantum coherence has been considered as a resource for quantum information process in recent years. Sharing the quantum resource distantly is a precondition for quantum communication. In this paper, we explore the quantum coherence properties of the prepared state starting from initially incoherent thermal light source. It is shown that the quantum coherence is directly proportional to the dimension of Hilbert space and therefore employ the orbital angular momentum (OAM) to encode resources. The distribution of biphoton thermal OAM state via the one-sided noisy channel (non-Kolmogorov turbulent atmosphere) is then investigated. It is found that the prepared OAM state can have large amount of quantum coherence, which is maximized when the thermal source is completely incoherent. The turbulence effects on quantum coherence are studied and compared to those on the fidelity and quantum channel capacity. Contrasting to the monotonic decay, the dynamics of coherence displays a peak during the propagation and the mechanism behind is presented. Finally, the dynamics of quantum thermal state can be more robust than that of Bell-like pure state since more interference can be induced. We believe our results is of importance to OAM quantum communication using quantum coherence as a resource.

Quantum Capacity and Vacuum Compressibility of Spacetime: Thermal Fields

An important yet perplexing result from work in the 1990s and 2000s is the near-unity value of the ratio of fluctuations in the vacuum energy density of quantum fields to the mean in a collection of generic spacetimes. This was carried out by way of calculating the noise kernels which are the correlators of the stress-energy tensor of quantum fields. In this paper, we revisit this issue via a quantum thermodynamics approach, by calculating two quintessential thermodynamic quantities: the heat capacity and the quantum compressibility of some model geometries filled with a quantum field at high and low temperatures. This is because heat capacity at constant volume gives a measure of the fluctuations of the energy density to the mean. When this ratio approaches or exceeds unity, the validity of the canonical distribution is called into question. Likewise, a system’s compressibility at constant pressure is a criterion for the validity of grand canonical ensemble. We derive the free energy density and, from it, obtain the expressions for these two thermodynamic quantities for thermal and quantum fields in 2d Casimir space, 2d Einstein cylinder and 4d (S1×S3 ) Einstein universe. To examine the dependence on the dimensionality of space, for completeness, we have also derived these thermodynamic quantities for the Einstein universes with even-spatial dimensions: S1×S2 and S1×S4. With this array of spacetimes we can investigate the thermodynamic stability of quantum matter fields in them and make some qualitative observations on the compatibility condition for the co-existence between quantum fields and spacetimes, a fundamental issue in the quantum and gravitation conundrum.

Control power of high-dimensional controlled dense coding

We quantitatively analyze and evaluate the control power in a high-dimensional noisy quantum channel for transmitting classical information. We calculate the control power of the controlled dense coding scheme in a four-dimensional extended Greenberger-Horne-Zeilinger (GHZ) class state channel. Different from controlled teleportation, there is no tradeoff between the control power and the classical capacity of the optimal four-dimensional GHZ state quantum channel. Only when the channel is noisy and the sender is allowed to gain some control authority can the tradeoff between the control power and the classical capacity be activated, and the overall control power for transmitting classical information will be enhanced by reducing the classical capacity of the high-dimensional quantum channel. This noise induced characteristic is very different from that of transmitting quantum information, and it may provide new ideas and methods to develop the resource theory of quantum channels.

Detecting positive quantum capacities of quantum channels

AbstractDetermining whether a noisy quantum channel can be used to reliably transmit quantum information is a challenging problem in quantum information theory. This is because it requires computation of the channel’s coherent information for an unbounded number of copies of the channel. In this paper, we devise an elementary perturbative technique to solve this problem in a wide variety of circumstances. Our analysis reveals that a channel’s ability to transmit information is intimately connected to the relative sizes of its input, output, and environment spaces. We exploit this link to develop easy tests which can be used to detect positivity of quantum channel capacities simply by comparing the channels’ input, output, and environment dimensions. Several noteworthy examples, such as the depolarizing and transpose-depolarizing channels (including the Werner-Holevo channel), dephasing channels, generalized Pauli channels, multi-level amplitude damping channels, and (conjugate) diagonal unitary covariant channels, serve to aptly exhibit the utility of our method. Notably, in all these examples, the coherent information of a single copy of the channel turns out to be positive.

Charged lithium adsorption on pristine and defective silicene: a theoretical study

We investigated by first principle calculations the adsorption of Li q (q = −1, 0 or +1) on a silicene single layer. Pristine and three different defective silicene configurations with and without Li doping were studied: single vacancy (SV), double vacancy (DV) and Stone–Wales (STW). Structural studies and the adsorption energies of various sites were obtained and compared in order to understand the stability of the Li on the surface. Moreover, electronic structure and charge density difference analysis were performed before and after adsorption at the most stables sites, which showed the presence of a magnetic moment in the undoped SV system, the displacement of the Fermi level produced by Li doping and a charge transfer from Li to the surface. Additionally, quantum capacity (QC) and charge density studies were performed on these systems. This analysis showed that the generation of defects and doping improves the QC of silicene in positive bias, because of the existence of 3p orbital in the zone of the defect. Consequently, the innovative calculations performed in this work of charged lithium doping on silicene can be used for future comparison with experimental studies of this Li-ion battery anode material candidate.

Information flow and error scaling for fully quantum control

The optimally designed control of quantum systems is playing an increasingly important role to engineer novel and more efficient quantum technologies. Here, in the scenario represented by controlling an arbitrary quantum system via the interaction with an another optimally initialized auxiliary quantum system, we show that the quantum channel capacity sets the scaling behaviour of the optimal control error. Specifically, we prove that the minimum control error is ensured by maximizing the quantum capacity of the channel mapping the initial control state into the target state of the controlled system, i.e., optimizing the quantum information flow from the controller to the system to be controlled. Analytical results, supported by numerical evidences, are provided when the systems and the controller are either qubits or single Bosonic modes and can be applied to a very large class of platforms for controllable quantum devices.

The transmission efficiency analysis for quantum secure direct communications over noisy channels

The concept of quantum secure direct communication (QSDC) is to distribute secure message directly between distant users securely, which is an important branch of quantum information science. The purpose of QSDC is to investigate the large capacity of quantum channels and fast speed of information transmission. However, the fidelity of qubits and the efficiency of QSDC will inevitably be affected by the channel noise and the decoherence of the quantum system. In this work, we focus on the performance of QSDC under different noisy channels, and investigate the evolution of quantum states. By numerically studying the performance for two QSDC protocols, we show the efficiency of information transmission over different noisy channel models.

Variational estimation of capacity bounds for quantum channels

We propose a framework to variationally obtain detectable capacity bounds for quantum channels. The proposal of this framework is motivated by the difficulty of estimating the von Neumann entropy of an unknown quantum state. Instead of estimating the von Neumann entropy at the channel output, we propose to estimate the state purity---which can be measured by a single measurement setting---followed by bounding the von Neumann entropy from above and below. This procedure leads to new upper and lower bounds on various communication rates of quantum channels for some fixed input states. Then, by utilizing the variational method to find optimal input states we obtain lower bounds on (i) the quantum capacity of arbitrary channels, (ii) the entanglement-assisted classical capacity of arbitrary channels, and (iii) the classical capacity of covariant channels. Corresponding to these lower bounds, we also obtain upper bounds on (i) $N$-shot coherent information, (ii) the entanglement-assisted classical capacity, and (iii) the $N$-shot Holevo capacity of arbitrary quantum channels. All these bounds can be estimated by a single measurement setting without needing a full process tomography or any further a priori knowledge, e.g., preferred basis of the channel.

Bounding the quantum capacity with flagged extensions

In this article we consider flagged extensions of convex combination of quantum channels, and find general sufficient conditions for the degradability of the flagged extension. An immediate application is a bound on the quantum Q and private P capacities of any channel being a mixture of a unitary map and another channel, with the probability associated to the unitary component being larger than 1/2. We then specialize our sufficient conditions to flagged Pauli channels, obtaining a family of upper bounds on quantum and private capacities of Pauli channels. In particular, we establish new state-of-the-art upper bounds on the quantum and private capacities of the depolarizing channel, BB84 channel and generalized amplitude damping channel. Moreover, the flagged construction can be naturally applied to tensor powers of channels with less restricting degradability conditions, suggesting that better upper bounds could be found by considering a larger number of channel uses.

On capacity of quantum channels generated by irreducible projective unitary representations of finite groups

We study mixed unitary quantum channels generated by irreducible projective unitary representations of finite groups. Under some assumptions on the probability distribution determining a mixture the classical capacity of the channel is found. Examples illustrating the techniques are given.

Secure delegated quantum computation based on Z-rotation encryption

Quantum computing on encrypted data allows a client who has limited quantum capacity to delegate his or her private computation to an untrusted quantum server, while the input and output are encrypted by the quantum one-time pad and only the client can correctly decrypt them. Generally, the client is required to have ability to prepare some single qubits and perform some basic gates. In this work, we consider a further restricted situation where the client can only prepare one single qubit and perform one basic gate. Specifically, we show that as long as the client can prepare a fixed qubit and perform a fixed phase gate P, then he or she can still achieve the secure delegated quantum computation. Besides, our protocol can provide a more rigorous security for any quantum computation. For example, even if some encryption keys about the computation are leaked, it can still guarantee the privacy of the input and output. Finally, our protocol experimentally has a great significance in reducing the device complexity of the client's side.

Influence of sand and dust turbulent atmosphere on performance of free space quantum communication

Quantum communication is a frontier hotspot of current research, and it has ideal information security. In order to enable quantum systems in arid and desertified areas to work almost under all-weather condition, it is necessary to study the attenuation of free-space quantum signal transmission and the influence of the turbulence atmosphere carrying sand and dust on communication performance. Using Mie scattering theory, multiple scattering simulation method, and atmospheric turbulence theory, the attenuation of optical wave transmission in sand and dust turbulent atmospheric channels with different visibility, and the influence of multiple scattering and turbulence on attenuation are studied. The results show that the effect of multiple scattering increases with the decrease of visibility, the turbulence effect gradually strengthens with the increase of distance. According to the quantum amplitude damped channel model, the effects of multiple scattering and turbulence in the sand and dust turbulent atmosphere with different visibility on the quantum channel capacity, fidelity and bit error rate are analyzed. The results show that as the visibility decreases, the multiple scattering effect increases, resulting in the decrease of attenuation and bit error rate, but an increase in channel capacity, fidelity and the boundaries of security key rate. The existence of turbulence in the dust atmosphere will increase the attenuation and bit error rate, but reduce the channel capacity, fidelity and security key rate. It can be seen that the influence of multiple scattering and turbulence on the communication performance, when the visibility of the sand and dust atmosphere are both low, cannot be ignored. In practical applications, the relevant parameters of quantum communication should be adaptively adjusted according to the visibility and turbulence intensity to improve the probability, efficiency and reliability of quantum communication.

Capacities of Gaussian Quantum Channels With Passive Environment Assistance

Passive environment assisted communication takes place via a quantum channel modeled as a unitary interaction between the information carrying system and an environment, where the latter is controlled by a passive helper, who can set its initial state such as to assist sender and receiver, but not help actively by adjusting her behaviour depending on the message. Here we investigate the information transmission capabilities in this framework by considering Gaussian unitaries acting on Bosonic systems. We consider both quantum communication and classical communication with helper, as well as classical communication with free classical coordination between sender and helper (conferencing encoders). Concerning quantum communication, we prove general coding theorems with and without energy constraints, yielding multi-letter (regularized) expressions. In the search for cases where the capacity formula is computable, we look for Gaussian unitaries that are universally degradable or anti-degradable. However, we show that no Gaussian unitary yields either a degradable or anti-degradable channel for all environment states. On the other hand, restricting to Gaussian environment states, results in universally degradable unitaries, for which we thus can give single-letter quantum capacity formulas. Concerning classical communication, we prove a general coding theorem for the classical capacity under and energy constraint, given by a multi-letter expression. Furthermore, we derive an uncertainty-type relation between the classical capacities of the sender and the helper, helped respectively by the other party, showing a lower bound on the sum of the two capacities. Then, this is used to lower bound the classical information transmission rate in the scenario of classical communication between sender and helper.

Communication Over Quantum Channels With Parameter Estimation

Communication over a random-parameter quantum channel when the decoder is required to reconstruct the parameter sequence is considered. We study scenarios that include either strictly-causal, causal, or non-causal channel side information (CSI) available at the encoder, and also when CSI is not available. This model can be viewed as a form of quantum metrology, and as the quantum counterpart of the classical rate-and-state channel with state estimation at the decoder. Regularized formulas for the capacity-distortion regions are derived. In the special case of measurement channels, single-letter characterizations are derived for the strictly-causal and causal settings. Furthermore, in the more general case of entanglement-breaking channels, a single-letter characterization is derived when CSI is not available. As a consequence, we obtain regularized formulas for the capacity of random-parameter quantum channels with CSI, generalizing previous results by Boche <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , 2016, on classical-quantum channels. Bosonic dirty paper coding is introduced as a consequence, where we demonstrate that the optimal coefficient is not necessarily that of minimum mean-square error estimation as in the classical setting.

Experimental Space-Division Multiplexed Polarization-Entanglement Distribution through 12 Paths of a Multicore Fiber

The development and wide application of quantum technologies highly depend on the capacity of the communication channels distributing entanglement. Space-division multiplexing (SDM) enhanced channel capacities in classical telecommunication and bears the potential to transfer the idea to quantum communication using current infrastructure. Here, we demonstrate an SDM of polarization-entangled photons over a 411m long 19-core multicore fiber distributing polarization-entangled photon pairs through up to 12 channels simultaneously. The quality of the multiplexed transfer is evidenced by high polarization visibility and CHSH Bell inequality violation for each pair of opposite cores. Our distribution scheme shows high stability over 24 hours without any active polarization stabilization and can be effortlessly adapted to a higher number of channels. This technique increases the quantum-channel capacity and allows the reliable implementation of quantum networks of multiple users based on a single entangled-photon pair source.

Mechanisms of electrical conductivity, quantum capacity and negative capacitance effects in InSe nanohybrid

Mechanisms of electrical conductivity, quantum capacity and negative capacitance effects in InSe nanohybrid