Probabilistic Cloning Research Articles

Photon-phonon quantum cloning in optomechanical system

Quantum cloning is an essential operation in quantum information and quantum computing. Similar to the ‘copy’ operation in classical computing, the cloning of flying bits for further processing from the solid-state quantum bits in storage is an operation frequently used in quantum information processing. Here we propose a high-fidelity and controllable quantum cloning scheme between solid bits and flying bits. In order to overcome the obstacles from the no-cloning theorem and the weak phonon-photon interaction, we introduce a hybrid optomechanical system that performs both the probabilistic cloning and deterministic cloning closed to the theoretical optimal limit with the help of designed driving pulse in the presence of dissipation. In addition, our scheme allows a highly tunable switching between two cloning methods, namely the probabilistic and deterministic cloning, by simply changing the input laser pulse. This provides a promising platform for experimental executability.

DAP: Efficient Detection Against Probabilistic Cloning Attacks in Anonymous RFID Systems

Radio frequency identification (RFID) systems have achieved wide applications in various scenarios, such as warehouse management, logistic tracking, smart transportation, etc. Despite the enormous benefits from the RFID systems, the security issues are still of great concern, such as the cloning attacks. In this article, we focus on the detection of probabilistic cloning attacks for the anonymous RFID systems, in which each cloned genuine tag suffers attacks from its clone tags with a certain probability. We propose an efficient detection protocol against the probabilistic cloning attacks in anonymous RFID systems named DAP, which can detect the probabilistic cloning attacks with the required detection reliability <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> if at least one tag is attacked with the probability no less than the threshold <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$P_T$</tex-math></inline-formula> . The proposed DAP protocol fully utilizes the inconsistency and unreconcilable collision caused by the probabilistic cloning attacks to effectively detect the probabilistic cloning attacks.The parameters are theoretically analyzed to maximize the detection efficiency. The extensive simulations are conducted and the results demonstrate the effectiveness of the proposed DAP protocol.

Nowhere to Hide: Efficiently Identifying Probabilistic Cloning Attacks in Large-Scale RFID Systems

Radio-Frequency Identification (RFID) is an emerging technology which has been widely applied in various scenarios, such as tracking, object monitoring, and social networks, etc. Cloning attacks can severely disturb the RFID systems, such as missed detection for the missing tags. Although there are some techniques with physical architecture design or complicated encryption and cryptography proposed to prevent the tags from being cloned, it is difficult to definitely avoid the cloning attack. Therefore, cloning attack detection and identification are critical for the RFID systems. Prior works rely on that each clone tag will reply to the reader when its corresponding genuine tag is queried. In this article, we consider a more general attack model, in which each clone tag replies to the reader's query with a predefined probability, i.e., attack probability. We concentrate on identifying the tags being attacked with the probability no less than a threshold $P_{t}$ with the required identification reliability $\alpha $ . We first propose a basic protocol to Identify the Probabilistic Cloning Attacks with required identification reliability for the large-scale RFID systems called IPCA. Then we propose two enhanced protocols called MS-IPCA and S-IPCA respectively to improve the identification efficiency. We theoretically analyze the parameters of the proposed IPCA, MS-IPCA and S-IPCA protocols to maximize the identification efficiency. Finally we conduct extensive simulations to validate the effectiveness of the proposed protocols.

Geometrical analysis of probabilistic quantum cloning and identification of N states

Creating n perfect clones from m copies of one of N prior known quantum states with minimum failure probability is a long-standing problem. We present a general geometrical form of the sufficient and necessary condition of probabilistic cloning of N known quantum states. With only one equality, we delineate in a parameter space the feasible set for probabilistic cloning of N known quantum states with prior probabilities and the surface for the optimal probabilistic cloning. The results are also applicable to the identification of those N quantum states. We provide a complete process of optimal identification of N given states and illustrate it with examples of three states. We further discover the relationship between probabilistic identification and the convexity of the feasible set. In addition, we discuss the differences in parameter selection when N = 2 and N ⩾ 3, plus provide a rigorous proof of some specific conclusions of this probabilistic quantum cloning problem when N = 2.

远程两态概率量子克隆

远程两态概率量子克隆

Sequential state discrimination with quantum correlation

The sequential unambiguous state discrimination (SSD) of two states prepared in arbitrary prior probabilities is studied, and compared with three strategies that allow classical communication. The deviation from equal probabilities contributes to the success in all the tasks considered. When one considers at least one of the parties succeeds, the protocol with probabilistic cloning is superior to others, which is not observed in the special case with equal prior probabilities. We also investigate the roles of quantum correlations in SSD, and show that the procedure requires discords but rejects entanglement. The left and right discords correspond to the part of information extracted by the first observer and the part left to his successor respectively. Their relative difference is extended by the imbalance of prior probabilities.

Probabilistic quantum cloning of a subset of linearly dependent states

It is well known that a quantum state, secretly chosen from a certain set, can be probabilistically cloned with positive cloning efficiencies if and only if all the states in the set are linearly independent. In this paper, we focus on probabilistic quantum cloning of a subset of linearly dependent states. We show that a linearly-independent subset of linearly-dependent quantum states {|Ψ1⟩,|Ψ2⟩,…,|Ψ n ⟩} can be probabilistically cloned if and only if any state in the subset cannot be expressed as a linear superposition of the other states in the set {|Ψ1⟩,|Ψ2⟩,…,|Ψ n ⟩}. The optimal cloning efficiencies are also investigated.

Probabilistic Cloning of Three Real States with Optimal Success Probabilities

We investigate the probabilistic quantum cloning (PQC) of three real states with average probability distribution. To get the analytic forms of the optimal success probabilities we assume that the three states have only two pairwise inner products. Based on the optimal success probabilities, we derive the explicit form of 1 →2 PQC for cloning three real states. The unitary operation needed in the PQC process is worked out too. The optimal success probabilities are also generalized to the M→N PQC case.

Surpassing the no-cloning limit with a heralded hybrid linear amplifier for coherent states

The no-cloning theorem states that an unknown quantum state cannot be cloned exactly and deterministically due to the linearity of quantum mechanics. Associated with this theorem is the quantitative no-cloning limit that sets an upper bound to the quality of the generated clones. However, this limit can be circumvented by abandoning determinism and using probabilistic methods. Here, we report an experimental demonstration of probabilistic cloning of arbitrary coherent states that clearly surpasses the no-cloning limit. Our scheme is based on a hybrid linear amplifier that combines an ideal deterministic linear amplifier with a heralded measurement-based noiseless amplifier. We demonstrate the production of up to five clones with the fidelity of each clone clearly exceeding the corresponding no-cloning limit. Moreover, since successful cloning events are heralded, our scheme has the potential to be adopted in quantum repeater, teleportation and computing applications.

Probabilistic Cloning of two Single-Atom States via Thermal Cavity

We propose a cavity QED scheme for implementing the 1 → 2 probabilistic quantum cloning (PQC) of two single-atom states. In our scheme, after the to-be-cloned atom and the assistant atom passing through the first cavity, a measurement is carried out on the assistant atom. Based on the measurement outcome we can judge whether the PQC should be continued. If the cloning fails, the other operations are omitted. This makes our scheme economical. If the PQC is continued (with the optimal probability) according to the measurement outcome, two more cavities and some unitary operations are used for achieving the PQC in a deterministic way. Our scheme is insensitive to the decays of the cavities and the atoms.

Optimal probabilistic cloning of two linearly independent states with arbitrary probability distribution

We investigate the probabilistic quantum cloning (PQC) of two states with arbitrary probability distribution. The optimal success probabilities are worked out for $$1\rightarrow 2$$1 2 PQC of the t...

No-signaling bounds for quantum cloning and metrology

The impossibility of superluminal communication is a fundamental principle of physics. Here we show that this principle underpins the performance of several fundamental tasks in quantum information processing and quantum metrology. In particular, we derive tight no-signaling bounds for probabilistic cloning and super-replication that coincide with the corresponding optimal achievable fidelities and rates known. In the context of quantum metrology, we derive the Heisenberg limit from the no-signaling principle for certain scenarios including reference frame alignment and maximum likelihood state estimation. We elaborate on the equivalence of assymptotic phase-covariant cloning and phase estimation for different figures of merit.

Probabilistic cloning of a single-atom state via cavity QED

We propose a scheme for probabilistically cloning a two-level state of an atom to a polarization photon via cavity QED system combined with linear optics elements. By choosing appropriate parameters, a controlled phase flip (CPF) gate between the atom and the probe photon is realized. Then we can judge that the cloning process should be continued (with the optimal probability) or interrupted by detecting the probe photon. If the cloning can be continued, the original atom state is deterministically cloned to the cloning photon by performing two more CPF gates and three single-qubit unitary operations. Otherwise, if the detection shows that the cloning should be interrupted, the cloning photon and the relevant operations are omitted.

Probabilistic cloning of three nonorthogonal states

We study the probabilistic cloning of three nonorthogonal states with equal success probabilities. For simplicity, we assume that the three states belong to a special set. Analytical form of the maximal success probability for $$M\rightarrow N$$M?N probabilistic cloning is calculated. With the maximal success probability, we deduce the explicit form of $$M\rightarrow N$$M?N probabilistic quantum cloning machine. In the case of $$1\rightarrow 2$$1?2 cloning, we get the unambiguous form of the unitary operation. It is demonstrated that the upper bound for probabilistic quantum cloning machine in (Qiu in J Phys A 35:6931, 2002) can be reached only if the three states are equidistant.

Quantum correlations support probabilistic pure state cloning

Abstract The probabilistic scheme for making two copies of two nonorthogonal pure states requires two auxiliary systems, one for copying and one for attempting to project onto the suitable subspace. The process is performed by means of a unitary-reduction scheme which allows having a success probability of cloning different from zero. The scheme becomes optimal when the probability of success is maximized. In this case, a bipartite state remains as a free degree which does not affect the probability. We find bipartite states for which the unitarity does not introduce entanglement, but does introduce quantum discord between some involved subsystems.

Nonlocal optimal probabilistic cloning of qubit states via twin photons

Here we propose a feasible experimental setup for implementing optimal probabilistic cloning of two arbitrary nonorthogonal qubit states. This proposal is based on linear optics together with a pair of entangled twin photons generated via spontaneous parametric down-conversion. The states to be cloned are encoded in the polarization degree of freedom of one of the photons while two perfect clones are generated and encoded in the polarization and the spatial degree of freedom of the resting photon. Therefore, the clones are produced nonlocally. The proposed implementation requires the application of recovery unitary operations onto the photon hosting the clones which are conditional on measurements performed on the other photon in a process akin to quantum teleportation.

Optical scheme for realization of optimal unambiguous state discrimination of the JS limit

We exploit optimal probabilistic cloning to rederive the JS limit. Dependent on the formulation given by the optimal probabilistic cloning, the explicit transformation of a measure of the JS limit is presented. Based on linear optical devices, we propose an experimentally feasible scheme to implement the JS limit measure of a general pair of two nonorthogonal quantum states. The success probability of the proposed scheme is unity.

Probabilistic cloning of coherent states without a phase reference

We present a probabilistic cloning scheme operating independently of any phase reference. The scheme is based solely on a phase-randomized displacement and photon counting, omitting the need for non-classical resources and non-linear materials. In an experimental implementation, we employ the scheme to clone coherent states from a phase covariant alphabet and demonstrate that the cloner is capable of outperforming the hitherto best-performing deterministic scheme. An analysis of the covariances between the output states shows that uncorrelated clones can be approached asymptotically. An intriguing feature is that the trade-off between success rate and achieved fidelity can be optimized even after the cloning procedure.

Multicopy quantum state discrimination

In this paper, we study the problem of multicopy quantum two-state discrimination. By exploring the quantum hypothesis testing, i.e., the probabilistic quantum cloning, we derive the upper bounds of the minimal error discrimination (MED) and the optimal unambiguous discrimination (OUD), which coincides with the Helstrom theorem and the JS limit. Furthermore, when prior probabilities are unknown, we derive the minimax MED and the minimax OUD. Based on the optimal N→M probabilistic quantum cloning, we present the optimal strategies of collective measurements of the MED and the OUD. When the number of the copies is infinite, regardless of whether prior probabilities are known or not, the success probabilities of the MED and the OUD go to 100%, in accordance with the quantum measurement hypothesis that unknown quantum state can be determined if and only if infinite identical quantum state copies are given.

Local cloning of multipartite entangled states

No cloning theorem is a very fundamental issue in quantum mechanics. But the issue is much more involved if we consider quantum state shared among two or more than two parties and allow only local operation and classical communication. In the context of the fact that no known bipartite entangled state can be cloned by local operation and classical communication (LOCC) without assistance of extra entangled state, the cloning of unknown orthogonal entangled state becomes meaningful when there is some supply of free entanglement. With restriction on supply of free entanglement, various cases have been studied. In this paper, we try to give an overview of the subject and results that have been obtained across the literature along with a new result on probabilistic LOCC cloning of four Bell states.