Maximum Success Probability Research Articles

Quantum teleportation is a reversal of quantum measurement

We introduce a generalized concept of quantum teleportation in the framework of quantum measurement and reversing operation. Our framework makes it possible to find an optimal protocol for quantum teleportation enabling a faithful transfer of unknown quantum states with maximum success probability up to the fundamental limit of the no-cloning theorem. Moreover, an optimized protocol in this generalized approach allows us to overcome noise in quantum channel beyond the reach of existing teleportation protocols without requiring extra qubit resources. Our proposed framework is applicable to multipartite quantum communications and primitive functionalities in scalable quantum architectures.

Lagrange Multiplier Optimization of the Probabilistic Caching Policy in Noise-Limited Network

Caching is a powerful technique that reduces the peak traffic loading by pre-storing popular contents in caching helpers during off-peak hours. In this work, the problem of probabilistic caching is revisited, in which users are allowed to request multiple contents sequentially. A novel algorithm based on the method of Lagrange multipliers is proposed to produce a policy that guarantees to yield a locally maximal content delivery success probability (CDSP) of the most demanding user, who requests the largest number of consecutive contents. Due to the non-convex nature of the problem, this algorithm may be trapped into an insignificant local maximum. We further propose an enhanced version of the algorithm based on the idea of simulated annealing, which enables the algorithm to statistically escape from a local maximum. Simulation results show that the proposed enhanced algorithm can attain a 45% CDSP improvement over the state-of-the-art when hundreds of contents are involved, and is significantly less sensitive to initial values. Moreover, to increase the overall system throughput, we propose an alternative metric of maximizing the weighted CDSP, instead of considering only the CDSP of the most demanding user. For this new metric, an algorithm adapted from the proposed algorithm is introduced, for which similar conclusions can be drawn.

Generic aspects of the resource theory of quantum coherence

The class of incoherent operations induces a pre-order on the set of quantum pure states, defined by the possibility of converting one state into the other by transformations within the class. We prove that if two $n$-dimensional pure states are chosen independently according to the natural uniform distribution, then the probability that they are comparable vanishes as $n\rightarrow\infty$. We also study the maximal success probability of incoherent conversions and find an explicit formula for its large-$n$ asymptotic distribution. Our analysis is based on the observation that the extreme values (largest and smallest components) of a random point uniformly sampled from the unit simplex are distributed asymptotically as certain explicit homogeneous Markov chains.

Distillability for non-full-rank coherent states in the probabilistic framework

We adequately characterize the distillability of quantum coherence under the maximally incoherent operations (MIO) in the probabilistic distillation’s framework. In particular, we prove that every non-full-rank coherent state exhibits a nonzero probability in the task of probabilistic deterministic distillation. Moreover, we find that the maximal coherence, a computable coherence monotone under strictly incoherent operations (SIO), is a coherence monotone under incoherent operations (IO) and add the proof that the maximal coherence fulfills strong monotonicity under SIO. It is suggested that the maximal success probability of distillation from all coherent states whose density matrix does not contain any rank-one submatrix is less than 1 under IO and equals 0 under SIO. Finally, we present an explicit example for probabilistic distillation under IO and show that a class of non-full rank 3-dimensional states possesses the probabilistic distillability.

Probabilistic coherence distillation with assisted setting

We consider the distillation of quantum coherence in the one-shot setting. The protocol is based on the probabilistic coherence distillation assisted by another party. In this context, coherent states including pure states and mixed states can be transformed into maximally coherent pure state with some probability and the maximal probability is defined as the maximal success probability of assistance. Then we show an upper bound for the maximal success probability of assistance for transforming d-dimensional mixed state to d-dimensional maximally coherent pure state. This upper bound is reached by all mixed states in two- and three-dimensional system and all incoherent states. A lower bound of the maximal success probability of assistance for the full-rank quantum states is also proposed. We also show an upper bound for the maximal success probability of assistance for transforming d-dimensional mixed state to $$m\ (m\le d)$$ -dimensional maximally coherent pure state in general case.

Optimal abort rules for additive multi-attempt missions

Mission aborts can be executed in many real-world systems when the specified malfunction/deterioration conditions are met and, therefore, a risk of a system's loss in the case of mission continuation becomes too high. After mission aborting, a rescue or recovery procedure is usually initiated. Previous results reported in the literature dealt with the setting when only one attempt to complete a mission is allowed. However, missions with a possibility of multiple attempts can occur in different real-world settings when accomplishing a mission is really important and the cost-related and the time-wise restrictions for this are not very severe. In this paper, we consider the case when a part of the mission task that was accomplished in the earlier attempts can be saved (additively) and not discarded. The probabilistic model for this case is developed and the tradeoff between the overall mission success probability and the system loss probability is studied. The problem of achieving the maximal mission success probability for the given level of system survivability is solved. A detailed example illustrating application of the suggested model is presented. It is shown that, unlike the single attempt case, aborting the mission when multiple attempts are allowed, can be beneficial even when the mission completion is the only concern and no constraint is imposed on the system survival probability.

Techniques for extending unicast CR networks to multi‐source multi‐destination over Rayleigh fading channels

In this work, the authors propose a novel technique to extend the scope of cognitive radio (CR) networks to multiple source–destination pairs. To accomplish this, a simplified feasible path set is formed and then three types of criteria or methods are employed to reach a solution for the best path for each pair. This set is defined by non-intersecting paths which do not share any relay nodes. This not only solves the problem at hand but also greatly reduces the complexity which leads to a fast solution. The first method uses the maximum probability of success as a means for selecting the best path. In the second method, a fast and simple technique is used by choosing the minimum number of overall hops for path selection. The element with the minimum overall transmission time is selected for data transmission in the third technique. Finally, the proposed methods are compared through simulation to a unicast single user case in terms of throughput and packet delivery rate. The simulation results show that the first method has the best performance while the second method is slightly worse but faster.

Quantum random access codes and incompatibility of measurements

It is one of the peculiar features of quantum physics that some sets of measurements are incompatible in the sense that they cannot be performed simultaneously. Incompatibility is an important quantum resource as it enables Bell nonlocality and steering. Here we show that incompatibility is crucial also in certain communication tasks; we prove that quantum random access code performs better than its classical counterpart only when incompatible quantum measurements are used in the decoding task. As a consequence, evaluating the average success probability for quantum random access code provides a semi-device-independent test for the detection of quantum incompatibility. We further demonstrate that any incompatible pair of projective measurements gives an advantage over all classical strategies. Finally, we establish a connection between the maximal average success probability for quantum random access code and earlier quantities introduced to assess incompatibility.

Volume of the set of LOCC-convertible quantum states

The class of quantum operations known as local operations and classical communication (LOCC) induces a partial ordering on quantum states. We present the results of systematic numerical computations related to the volume (with respect to the unitarily invariant measure) of the set of LOCC-convertible bipartite pure states, where the ordering is characterised by an algebraic relation known as majorization. The numerical results, which exploit a tridiagonal model of random matrices, provide quantitative evidence that the proportion of LOCC-convertible pairs vanishes in the limit of large dimensions, and therefore support a previous conjecture by Nielsen. In particular, we show that the problem is equivalent to the persistence of a non-Markovian stochastic process and the proportion of LOCC-convertible pairs decays algebraically with a nontrivial persistence exponent. We extend this analysis by investigating the distribution of the maximal success probability of LOCC-conversions. We show a dichotomy in behaviour between balanced and unbalanced bipartitions. In the latter case the asymptotics is somehow surprising: in the limit of large dimensions, for the overwhelming majority of pairs of states a perfect LOCC-conversion is not possible; nevertheless, for most states there exist local strategies that succeed in achieving the conversion with a probability arbitrarily close to one. We present strong evidence of a universal scaling limit for the maximal probability of successful LOCC-conversions and we suggest a connection with the typical fluctuations of the smallest eigenvalue of Wishart random matrices.

Quantifying the resource content of quantum channels: An operational approach

We propose a general method to operationally quantify the resourcefulness of quantum channels via channel discrimination, an important information processing task. A main result is that the maximum success probability of distinguishing a given channel from the set of free channels by free probe states is exactly characterized by the resource generating power, i.e. the maximum amount of resource produced by the action of the channel, given by the trace distance to the set of free states. We apply this framework to the resource theory of quantum coherence, as an informative example. The general results can also be easily applied to other resource theories such as entanglement, magic states, and asymmetry.

Probabilistic exact universal quantum circuits for transforming unitary operations

This paper addresses the problem of designing universal quantum circuits to transform $k$ uses of a $d$-dimensional unitary input-operation into a unitary output-operation in a probabilistic heralded manner. Three classes of protocols are considered, parallel circuits, where the input-operations can be simultaneously, adaptive circuits, where sequential uses of the input-operations are allowed, and general protocols, where the use of the input-operations may be performed without a definite causal order. For these three classes, we develop a systematic semidefinite programming approach that finds a circuit which obtains the desired transformation with the maximal success probability. We then analyse in detail three particular transformations; unitary transposition, unitary complex conjugation, and unitary inversion. For unitary transposition and unitary inverse, we prove that for any fixed dimension $d$, adaptive circuits have an exponential improvement in terms of uses $k$ when compared to parallel ones. For unitary complex conjugation and unitary inversion we prove that if the number of uses $k$ is strictly smaller than $d-1$, the probability of success is necessarily zero. We also discuss the advantage of indefinite causal order protocols over causal ones and introduce the concept of delayed input-state quantum circuits.

Transition probabilities in generalized quantum search Hamiltonian evolutions

A relevant problem in quantum computing concerns how fast a source state can be driven into a target state according to Schrödinger’s quantum mechanical evolution specified by a suitable driving Hamiltonian. In this paper, we study in detail the computational aspects necessary to calculate the transition probability from a source state to a target state in a continuous time quantum search problem defined by a multiparameter generalized time-independent Hamiltonian. In particular, quantifying the performance of a quantum search in terms of speed (minimum search time) and fidelity (maximum success probability), we consider a variety of special cases that emerge from the generalized Hamiltonian. In the context of optimal quantum search, we find it is possible to outperform, in terms of minimum search time, the well-known Farhi–Gutmann analog quantum search algorithm. In the context of nearly optimal quantum search, instead, we show it is possible to identify sub-optimal search algorithms capable of outperforming optimal search algorithms if only a sufficiently high success probability is sought. Finally, we briefly discuss the relevance of a tradeoff between speed and fidelity with emphasis on issues of both theoretical and practical importance to quantum information processing.

Ambient Backscatter-Assisted Wireless-Powered Relaying

Internet-of-Things (IoT) features with low-power communications among a massive number of ubiquitously-deployed and energy-constrained electronics, e.g., sensors and actuators. To cope with the demand, wireless-powered cooperative relaying emerges as a promising communication paradigm to extend data transmission coverage and solve energy scarcity for the IoT devices. In this paper, we propose a novel hybrid relaying strategy by combining wireless-powered communication and ambient backscattering functions to improve the applicability and performance of data transfer. In particular, the hybrid relay can harvest energy from radio frequency (RF) signals and use the energy for active transmission. Alternatively, the hybrid relay can choose to perform ambient backscattering of incident RF signals for passive transmission. For the operation of the hybrid relaying, selecting a proper mode based on the network environment is the key to better relaying performance. To address this issue, we design mode selection protocols to coordinate between the active and passive relaying in the cases with and without instantaneous channel state information (CSI) of active transmission, respectively. In the former case, since the hybrid relay is aware of whether the two relaying modes are applicable for the current time slot based on the CSI, it selects active relaying if applicable due to higher capacity and selects passive relaying otherwise. In the latter case, the hybrid relay first explores the two relaying modes and commits to the mode that achieves more successful transmissions during the exploration period. With different mode selection protocols, we characterize the success probability and ergodic capacity of a dual-hop relaying system with the hybrid relay in the field of randomly located ambient transmitters. The analytical and the numerical results demonstrate the effectiveness of the mode selection protocols in adapting the hybrid relaying into the network environment and reveal the impacts of system parameters on the performance of the hybrid relaying. As applications of our analytical framework which is computationally tractable, we formulate optimization problems based on the derived expressions to optimize the system parameters with different objectives. The optimal solutions exhibit a tradeoff between the maximum energy efficiency and target success probability.

Reversing Unknown Quantum Transformations: Universal Quantum Circuit for Inverting General Unitary Operations.

Given a quantum gate implementing a d-dimensional unitary operation U_{d}, without any specific description but d, and permitted to use k times, we present a universal probabilistic heralded quantum circuit that implements the exact inverse U_{d}^{-1}, whose failure probability decays exponentially in k. The protocol employs an adaptive strategy, proven necessary for the exponential performance. It requires that k≥d-1, proven necessary for the exact implementation of U_{d}^{-1} with quantum circuits. Moreover, even when quantum circuits with indefinite causal order are allowed, k≥d-1 uses are required. We then present a finite set of linear and positive semidefinite constraints characterizing universal unitary inversion protocols and formulate a convex optimization problem whose solution is the maximum success probability for given k and d. The optimal values are computed using semidefinite programing solvers for k≤3 when d=2 and k≤2 for d=3. With this numerical approach we show for the first time that indefinite causal order circuits provide an advantage over causally ordered ones in a task involving multiple uses of the same unitary operation.

Asymmetrical hyperentanglement concentration for entanglement of polarization and orbital angular momentum.

We propose two hyperentanglement concentration protocols (hyper-ECPs) for two-photon entangled states in the polarization and orbital angular momentum degrees of freedom. The two cases distilling a maximally hyperentangled state from partially entangled pure state with unknown parameters and known parameters are dissected respectively. Both of the protocols require only linear optical elements which make our protocols more feasible for current technologies. In our protocols, the remote parties perform different local operations, which will reduce everyone's operation and improve the total efficiency. Each of them has the theoretical maximum success probability in the corresponding situation. The hyper-ECPs can be exploited simply to hyperentangled Greenberger-Horne-Zeilinger states.

Mission success evaluation of repairable phased-mission systems with spare parts

Mission success is an important criterion to measure the performance of phased-mission systems, which is the ability of systems to finish the work successfully. Activating the spare parts takes little time, which can reduce the maintenance time while performing the mission. Moreover, adding the spare parts also can ensure the mission to complete with higher success probability. This paper puts forward an integrated modeling method to evaluate the mission success probability for repairable phased-mission systems with spare parts. Some illustrative examples are introduced to verify the flexibility and effectiveness of the proposed approach with different cases. Based on the state analysis of the component group, the risk ranking of component groups or mission phases is discussed to improve the mission success probability effectively. After analyzing the effect of spare parts on mission success probability, the optimal spare parts allocation method is proposed to obtain a cost-effective solution with the maximum mission success probability.

Parametrization of quantum states based on the quantum state discrimination problem

A discrimination problem consists of N linearly independent pure quantum states $$\Phi =\{|\phi _i\rangle \}$$ and the corresponding occurrence probabilities $$\eta =\{\eta _i\}$$ . With any such problem, we associate, up to a permutation over the probabilities $$\{\eta _i\}$$ , a unique pair of density matrices $$\varvec{\rho _{_{T}}}$$ and $$\varvec{\eta _{{p}}}$$ defined on the N-dimensional Hilbert space $$\mathcal {H}_N$$ . The first one, $$\varvec{\rho _{_{T}}}$$ , provides a new parametrization of a generic full-rank density matrix in terms of the parameters of the discrimination problem, i.e., the mutual overlaps $$\gamma _{ij}=\langle \phi _i|\phi _j\rangle $$ and the occurrence probabilities $$\{\eta _i\}$$ . The second one, on the other hand, is defined as a diagonal density matrix $$\varvec{\eta _p}$$ with the diagonal entries given by the probabilities $$\{\eta _i\}$$ with the ordering induced by the permutation p of the probabilities. $$\varvec{\rho _{_{T}}}$$ and $$\varvec{\eta _{{p}}}$$ capture information about the quantum and classical versions of the discrimination problem, respectively. In this sense, when the set $$\Phi $$ can be discriminated unambiguously with probability one, i.e., when the states to be discriminated are mutually orthogonal and can be distinguished by a classical observer, then $$\varvec{\rho _{_{T}}} \rightarrow \varvec{\eta _{{p}}}$$ . Moreover, if the set lacks its independency and cannot be discriminated anymore, the distinguishability of the pair, measured by the fidelity $$F(\varvec{\rho _{_{T}}}, \varvec{\eta _{{p}}})$$ , becomes minimum. This enables one to associate with each discrimination problem a measure of discriminability defined by the fidelity $$F(\varvec{\rho _{_{T}}}, \varvec{\eta _{{p}}})$$ . This quantity, though distinct from the maximum probability of success, has the advantage of being easy to calculate, and in this respect, it can find useful applications in estimating the extent to which the set is discriminable.

Probabilistic Distillation of Quantum Coherence.

The ability to distill quantum coherence is pivotal for optimizing the performance of quantum technologies; however, such a task cannot always be accomplished with certainty. Here we develop a general framework of probabilistic distillation of quantum coherence in a one-shot setting, establishing fundamental limitations for different classes of free operations. We first provide a geometric interpretation for the maximal success probability, showing that under maximally incoherent operations (MIO) and dephasing-covariant incoherent operations (DIO) the problem can be simplified into efficiently computable semidefinite programs. Exploiting these results, we find that DIO and its subset of strictly incoherent operations have equal power in the probabilistic distillation of coherence from pure input states, while MIO are strictly stronger. We then prove a fundamental no-go result: Distilling coherence from any full-rank state is impossible even probabilistically. We further find that in some conditions the maximal success probability can vanish suddenly beyond a certain threshold in the distillation fidelity. Finally, we consider probabilistic coherence distillation assisted by a catalyst and demonstrate, with specific examples, its superiority to the unassisted and deterministic cases.

Almost all quantum channels are equidistant

In this work, we analyze properties of generic quantum channels in the case of large system size. We use random matrix theory and free probability to show that the distance between two independent random channels converges to a constant value as the dimension of the system grows larger. As a measure of the distance we use the diamond norm. In the case of a flat Hilbert-Schmidt distribution on quantum channels, we obtain that the distance converges to 12+2π, giving also an estimate for the maximum success probability for distinguishing the channels. We also consider the problem of distinguishing two random unitary rotations.

Optimal discrimination of optical coherent states cannot always be realized by interfering with coherent light, photon counting, and feedback

It is well known that a minimum error quantum measurement for arbitrary binary optical coherent states can be realized by a receiver that comprises interfering with a coherent reference light, photon counting, and feedback control. We show that, for ternary optical coherent states, a minimum error measurement cannot always be realized by such a receiver. The problem of finding an upper bound on the maximum success probability of such a receiver can be formulated as a convex programming. We derive its dual problem and numerically find the upper bound. At least for ternary phase-shift keyed coherent states, this bound does not reach that of a minimum error measurement.