Tolerable Error Rate Research Articles

Symmetric extendibility for a class of qudit states

The concept of symmetric extendibility has recently drawn attention in the context of tolerable error rates in quantum cryptography, where it can be used to decide whether quantum states shared between two parties can be purified by means of entanglement purification with one-way classical communication only. Unfortunately, at present there exists no simple general criterion to decide whether a state possesses a symmetric extension or not. In this paper, we derive criteria for symmetric extendibility within subclasses of all two-qudit states. Using these criteria, we can completely solve the problem for a two-parameter family of two-qudit states, which includes the isotropic states as a subclass.

Symmetric extendibility for qudits and tolerable error rates in quantum cryptography

Symmetric extendibility of quantum states has recently drawn attention in the context of quantum cryptography to judge whether quantum states shared between two distant parties can be purified by means of one-way error correction protocols. In this paper we study the symmetric extendibility in a specific class of two-qudit states, i.e., states composed of two $d$-level systems, in order to find upper bounds on tolerable error rates for a wide class of qudit-based quantum cryptographic protocols using two-way error correction. In important cases these bounds coincide with previously known lower bounds, thereby proving sharpness of these bounds in arbitrary finite-dimensional systems.

Entanglement enhances security in quantum communication

Secret sharing is a protocol in which a 'boss' wants to send a classical message secretly to two 'subordinates', such that none of the subordinates is able to know the message alone, while they can find it if they cooperate. Quantum mechanics is known to allow for such a possibility. We analyze tolerable quantum bit error rates in such secret sharing protocols in the physically relevant case when the eavesdropping is local with respect to the two channels of information transfer from the boss to the two subordinates. We find that using entangled encoding states is advantageous to legitimate users of the protocol. We therefore find that entanglement is useful for secure quantum communication. We also find that bound entangled states with positive partial transpose are not useful as a local eavesdropping resource. Moreover, we provide a criterion for security in secret sharing--a parallel of the Csiszar-Koerner criterion in single-receiver classical cryptography.

The Influence of the Detection Paradigm in Recording Auditory Steady-State Responses

The purpose of this study was to evaluate the risks of uncontrolled use of an objective detection criterion in recording auditory steady-state responses (ASSRs). The influence of decisions such as when to accept a response and stop the recording was assessed by analyzing the number of false- and true-detected responses. A large sample of 500 multiple-stimulus ASSR recordings of normal-hearing and hearing-impaired adults and babies was processed offline. Three types of detection paradigms were evaluated. A first type had a fixed recording length with significance testing after the last sweep. A second type allowed a variable recording length and implied sequential application of the statistical decision criterion. The recording was stopped after significance was reached for y consecutive sweeps. The third type was analogous to the second, with the additional requirement of a minimum of eight recorded sweeps. Furthermore, the effect of significance level and averaging procedure were assessed. Error rates were calculated for the different detection paradigms at eight control frequencies. At the signal frequencies, detection rates and recording times were determined, keeping the error rates fixed. Moreover, ASSR thresholds were compared for a selection of detection paradigms. When a variable recording length was allowed and a significance level of p = 0.05 was applied, the error rate increased to unacceptable levels because of the effect of repeated testing. The error rate decreased as the required number of consecutive significant sweeps increased and approximated 5% only when eight consecutive significant sweeps were required (with a maximum of 32 recorded sweeps). With an error rate of 5%, the highest detection rate was associated with a fixed recording length of 32 sweeps combined with weighted averaging. A substantial decrease in detection rate was noted when less than 24 sweeps were recorded per intensity. All paradigms with a variable recording length had rather comparable detection rates and recording times. With an error rate of only 1%, small responses could not be distinguished from the noise. The reduction in recording time using a variable instead of a fixed recording length was very limited when a conventional multiple-stimulus approach was used. Test duration would be reduced considerably when the test set-up would allow an independent presentation and recording of the eight signals and responses. Differences in overall detection rate had a small effect on the ASSR thresholds. The error rate, detection rate, and recording time can improve or deteriorate significantly, even with small adaptations of the detection protocol. When a variable recording length is allowed, the acceptance criterion of the statistical test needs to be adjusted to ensure a tolerable error rate. However, most commercial devices do not offer this option. Then, it is advisable to use a fixed recording length and to judge the significance of the responses at the end of the recording. Although response detection is objective, the measurement protocol has to be well-considered and a critical approach is required when interpreting the responses.

Bounding fault-tolerant thresholds for purification and quantum computation

In this paper, we place bounds on when it is impossible to purify a noisy two-qubit state if all the gates used in the purification protocol are subject to adversarial, local, independent noise. It is found that the gate operations must be subject to less than 5.3% error. An existing proof that purification is equivalent to error correction is used to show that this bound can also be applied to concatenated error correcting codes in the presence of noisy gates, and hence gives a limit to the tolerable error rate for a fault-tolerant quantum computer formed by concatenation. This is shown to apply also to the case where error detection and postselection, as proposed by Knill, is used to enhance the threshold. We demonstrate the trade-off between gate and environmentally induced faulty rotations and qubit loss errors.

Long-range coupling and scalable architecture for superconducting flux qubits

Constructing a fault-tolerant quantum computer is a daunting task. Given any design, it is possible to determine the maximum error rate of each type of component that can be tolerated while still permitting arbitrarily large-scale quantum computation. It is an under-appreciated fact that including an appropriately designed mechanism enabling long-range qubit coupling or transport substantially increases the maximum tolerable error rates of all components. With this thought in mind, we take the superconducting flux qubit coupling mechanism described in Plourde et al. (Phys. Rev. B, 70, 140501(R) (2004)) and extend it to allow approximately 500~MHz coupling of square flux qubits, 50 µm a side, at a distance of up to several mm. This mechanism is then used as the basis of two scalable architectures for flux qubits taking into account crosstalk and fault-tolerant considerations such as permitting a universal set of logical gates, parallelism, measurement and initialization, and data mobility.PACS No.: 03.67.Lx

Cryptographic robustness of a quantum cryptography system using phase-time coding

A cryptographic analysis is presented of a new quantum key distribution protocol using phase-time coding. An upper bound is obtained for the error rate that guarantees secure key distribution. It is shown that the maximum tolerable error rate for this protocol depends on the counting rate in the control time slot. When no counts are detected in the control time slot, the protocol guarantees secure key distribution if the bit error rate in the sifted key does not exceed 50%. This protocol partially discriminates between errors due to system defects (e.g., imbalance of a fiber-optic interferometer) and eavesdropping. In the absence of eavesdropping, the counts detected in the control time slot are not caused by interferometer imbalance, which reduces the requirements for interferometer stability.

Long-range coupling and scalable architecture for superconducting flux qubits

Constructing a fault-tolerant quantum computer is a daunting task. Given any design, it is possible to determine the maximum error rate of each type of component that can be tolerated while still permitting arbitrarily large-scale quantum computation. It is an underappreciated fact that including an appropriately designed mechanism enabling long-range qubit coupling or transport substantially increases the maximum tolerable error rates of all components. With this thought in mind, we take the superconducting flux qubit coupling mechanism described by Plourde et al. [Phys. Rev. B 70, 140501(R) (2004)] and extend it to allow approximately $500\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$ coupling of square flux qubits, $50\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ a side, at a distance of up to several millimeters. This mechanism is then used as the basis of two scalable architectures for flux qubits taking into account cross-talk and fault-tolerant considerations such as permitting a universal set of logical gates, parallelism, measurement and initialization, and data mobility.

Optimized power allocation for iterative multiuser detection for a SC-CDMA uplink

Abstract. This paper deals with optimization of the received power profile for iterative parallel and successive interference cancellation (PIC/SIC) in coded CDMA systems. For practical implementation additional constraints should be applied. This paper focuses on the maximum tolerable bit error rate. It will be shown that optimized power profile can considerably gain the overall system performance. Due to unequal required receive powers an allocation to certain users can be done with respect to their individual power constraints. This is important especially in near-far scenarios. Beside these constraints also the maximum number of iterations is implemented due to limiting the computational complexity in the receiver.

Use of confidence intervals to demonstrate performance against forest management standards

The objective of continuous improvement embedded in forest management standards relies on the capacity of management to respond appropriately to evidence of performance provided by monitoring. This evidence is rarely unequivocal. Under a null hypothesis of no effect, two kinds of errors in interpretation are possible—inferring an effect where none exists (Type I error) and inferring no effect when in fact one exists (Type II error). If the monitoring relates to possible improvement in growth or yield then a Type I error leads to false optimism and a Type II error to false pessimism. If monitoring concerns a potential environmental or social impact, a Type I error implies alarmism and a Type II error a false sense of security. Explicit consideration of statistical power in designing and interpreting monitoring data is an effective buffer against these errors. However, strict application of statistical power may be impractical. In particular, the requirement to specify tolerable error rates and effect sizes will be difficult in many circumstances where the perspectives of managers, auditors or stakeholders are contested or perceived to be arbitrary or vague. We advocate the use of confidence intervals as an alternative to power calculations. Confidence intervals offer an accessible approach to communicating performance under a standard and the extent to which a monitoring program is able to distinguish compliance from non-compliance. We illustrate these arguments and tools through a hypothetical example involving a proposed change in silviculture where the magnitude of gains in yield and environmental impacts are unclear.

Asymptotic correctability of Bell-diagonal qudit states and lower bounds on tolerable error probabilities in quantum cryptography

The concept of asymptotic correctability of Bell-diagonal quantum states is generalized to elementary quantum systems of higher dimensions. Based on these results basic properties of quantum state purification protocols are investigated which are capable of purifying tensor products of Bell-diagonal states and which are based on B-steps of the Gottesman-Lo-type with the subsequent application of a Calderbank–Shor–Steane quantum code. Consequences for maximum tolerable error rates of quantum cryptographic protocols are discussed.

Optimal Transmit Power in Wireless Sensor Networks

Power conservation is one of the most important issues in wireless ad hoc and sensor networks, where nodes are likely to rely on limited battery power. Transmitting at unnecessarily high power not only reduces the lifetime of the nodes and the network, but also introduces excessive interference. It is in the network designer's best interest to have each node transmit at the lowest possible power while preserving network connectivity. In this paper, we investigate the optimal common transmit power, defined as the minimum transmit power used by all nodes necessary to guarantee network connectivity. This is desirable in sensor networks where nodes are relatively simple and it is difficult to modify the transmit power after deployment. The optimal transmit power derived in this paper is subject to the specific routing and medium access control (MAC) protocols considered; however, the approach can be extended to other routing and MAC protocols as well. In deriving the optimal transmit power, we distinguish ourselves from a conventional graph-theoretic approach by taking realistic physical layer characteristics into consideration. In fact, connectivity in this paper is defined in terms of a quality of service (QoS) constraint given by the maximum tolerable bit error rate (BER) at the end of a multihop route with an average number of hops

Error tolerance of two-basis quantum-key-distribution protocols using qudits and two-way classical communication

We investigate the error tolerance of quantum cryptographic protocols using $d$-level systems. In particular, we focus on prepare-and-measure schemes that use two mutually unbiased bases and a key-distillation procedure with two-way classical communication. For arbitrary quantum channels, we obtain a sufficient condition for secret-key distillation which, in the case of isotropic quantum channels, yields an analytic expression for the maximally tolerable error rate of the cryptographic protocols under consideration. The difference between the tolerable error rate and its theoretical upper bound tends slowly to zero for sufficiently large dimensions of the information carriers.

Modified Bennett-Brassard 1984 quantum key distribution protocol with two-way classical communications

The quantum key distribution protocol without public announcement of bases is equipped with a two-way classical communication symmetric entanglement purification protocol. This modified key distribution protocol is unconditionally secure and has a higher tolerable error rate of 20%, which is higher than previous scheme without public announcement of bases.

Scalable quantum computing in the presence of large detected-error rates

The theoretically tolerable erasure error rate for scalable quantum computing is shown to be well above 0.1, given standard scalability assumptions. This bound is obtained by implementing computations with generic stabilizer code teleportation steps that combine the necessary operations with error correction. An interesting consequence of the technique is that the only errors that affect the maximum tolerable error rate are storage and Bell measurement errors. If storage errors are negligible, then any detected Bell measurement error below 1/2 is permissible. For practical computation with high detected error rates, the implementation overheads need to be improved.

Experimental realization of entanglement concentration and a quantum repeater.

We report an experimental realization of entanglement concentration using two polarization-entangled photon pairs produced by pulsed parametric down-conversion. In the meantime, our setup also provides a proof-in-principle demonstration of a quantum repeater. The quality of our procedure is verified by observing a violation of Bell's inequality by more than 5 standard deviations. The high experimental accuracy achieved in the experiment implies that the requirement of tolerable error rate in multistage realization of quantum repeaters can be fulfilled, hence providing a useful toolbox for quantum communication over large distances.

Experimental entanglement purification of arbitrary unknown states.

Distribution of entangled states between distant locations is essential for quantum communication over large distances. But owing to unavoidable decoherence in the quantum communication channel, the quality of entangled states generally decreases exponentially with the channel length. Entanglement purification--a way to extract a subset of states of high entanglement and high purity from a large set of less entangled states--is thus needed to overcome decoherence. Besides its important application in quantum communication, entanglement purification also plays a crucial role in error correction for quantum computation, because it can significantly increase the quality of logic operations between different qubits. Here we demonstrate entanglement purification for general mixed states of polarization-entangled photons using only linear optics. Typically, one photon pair of fidelity 92% could be obtained from two pairs, each of fidelity 75%. In our experiments, decoherence is overcome to the extent that the technique would achieve tolerable error rates for quantum repeaters in long-distance quantum communication. Our results also imply that the requirement of high-accuracy logic operations in fault-tolerant quantum computation can be considerably relaxed.

The stochastic evolution of catalysts in spatially resolved molecular systems.

A fully stochastic chemical modelling technique is derived which describes the influence of spatial separation and discrete population size on the evolutionary stability of coupled amplification in biopolymers. The model is analytically tractable for an infinite-dimensional space (simplex geometry), which also provides insight into evolution in normal Euclidean space. The results are compared with stochastic simulations describing the co-evolution of combinatorial families of molecular sequences both in the simplex geometry and in lower (one, two and three) space dimensions. They demonstrate analytically the generic limits which exploitation place on co-evolving multi-component amplification systems. In particular, there is an optimal diffusion (or migration) coefficient for cooperative amplification and minimal and maximal threshold values for stable cooperation. Over a bounded range of diffusion rates, the model also exhibits stable limit cycles. Furthermore, the co-operatively coupled system has a maximum tolerable error rate at intermediate rates of diffusion. A tractable model is thereby established which demonstrates that spatial effects can stabilize catalytic biological information. The analytic behaviour in infinite-dimensional simplex space is seen to provide a reasonable guide to the spatial dependence of the error threshold in physical space. Nanoscale possibilities for the evolution of catalysis on the basis of the model are outlined. We denote the modelling technique by PRESS, Probability Reduced Evolution of Spatially-discrete Species.

A slotted CDMA protocol with BER scheduling for wireless multimedia networks

In future wireless multimedia networks, there will be a mixture of different traffic classes which have their own maximum tolerable bit error rate (BER) requirements. In this paper, a novel medium access control (MAC) protocol called wireless multimedia access control protocol with BER scheduling (in short form, WISPER) for CDMA-based systems is proposed. WISPER utilizes the novel idea of scheduling the transmission of multimedia packets according to their BER requirements. The scheduler assigns priorities to the packets, and performs an iterative procedure to determine a good accommodation of the highest-priority packets in the slots of a frame so that packets with equal or similar BER requirements are transmitted in the same slots. The proposed WISPER protocol has been validated using a software emulator on the cellular environment. Performance evaluation results based on the implementation are also included.

VLSI Design of Digital Cellular Neural Networks for Image Processing

Biologically inspired analog VLSI systems have attracted more and more studies. For system consistency and for quick application of neural systems, we have established digital models for neuron operations such that the cell operations can be implemented with simple digital adders and multipliers. To provide fast data transfer and minimum reconfiguration for various sizes of networks, the architecture is designed for low hardware complexity and high mask flexibility, and is perfectly suited for VLSI array implementation. The parallel computation model derived here is used to realize parallel array processor architectures for digital neural networks. Some image processing operations have been simulated. The tolerable error rate compared to the analog model and the competent speed performance make this applicable to digital systems and suitable for 2-D signal processing.