We show that non-local resources cannot be used for probabilistic signalling even if one can produce exact clones with the help of a probabilistic quantum cloning machine (PQCM). We show that PQCM cannot help to distinguish two statistical mixtures at a remote location. Thus quantum theory rules out the possibility of sending superluminal signals not only deterministically but also probabilistically. We give a bound on the success probability of producing multiple clones in an entangled system.
The method of quantum cloning is divided into two main categories: approximate and probabilistic quantum cloning. The former method is used to approximate an unknown quantum state deterministically, and the latter can be used to faithfully copy the state probabilistically. So far, many approximate cloning machines have been experimentally demonstrated, but probabilistic cloning remains an experimental challenge, as it requires more complicated networks and a higher level of precision control. In this work, we designed an efficient quantum network with a limited amount of resources, and perform…
From Ref. [Phys. Rev. Lett. 80(1998)4999] one knows that the quantum states 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 the probabilistic quantum cloning (PQC) of linearly dependent states with nonnegative cloning efficiencies. We show that a linearly independent subset of the linearly dependent quantum states can be probabilistically cloned if and only if any one state in the subset can not be expressed as the linear superposition of the other…
Bipartite and tripartite EPR-Bell type systems are examined via joint quasi-probability distributions where elementary probabilities are permitted to be negative. It is shown that such distributions exist only when the no-signalling condition is satisfied. A characteristic measure, the probability mass, is introduced and, via its minimization, limits the number of quasi-distributions describing a given marginal probability distribution. The minimized probability mass is shown to be an alternative way to characterize non-local systems. Non-signalling polytopes for two, three, and four settings …
It has been recently shown that probabilistic protocols based on postselection boost the performances of phase estimation and the replication of quantum clocks. Here we demonstrate that the improvements in these two tasks have to match exactly in the macroscopic limit where the number of clones grows to infinity, preserving the equivalence between asymptotic cloning and estimation for arbitrary values of the success probability. Remarkably, the cloning fidelity depends critically on the number of rationally independent eigenvalues of the clock Hamiltonian. We also prove that probabilistic metr…
Non-signalling quantum channels -- relevant in, e.g., the study of Bell and Einstein-Podolsky-Rosen scenarios -- may be simulated via affine combinations of local operations in bipartite scenarios. Moreover, when these channels correspond to stochastic maps between classical variables, such simulation is possible even in multipartite scenarios. These two results have proven useful when studying the properties of these channels, such as their communication and information processing power, and even when defining measures of the non-classicality of physical phenomena (such as Bell non-classicali…
It is known that to imperfectly clone a phase-set of states uncorrelatedly is impossible due to the linearity and the hermitian-preservation of quantum operations deterministically shown by D'Ariano et al. In this paper we address uncorrelated cloning in probabilistic cases. We show that there exists a linear and hermitian-preserving probabilistic map to imperfectly clone a phase-set of states uncorrelatedly. It is pointed out that the existence of such a map is due to the difference between non-unit-trace output operators and normalized (unit-trace) output operators inherent to probabilistic …
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 intrig…
Recently, the nonlocal optimal probabilistic cloning (NLOPC) of two non-orthogonal qubit states has been proposed [Phys. Rev. A 86, 052332 (2012)] by means of an experimental setup based on a pair of twin photons in a maximally entangled state. Here we study the performance of the NLOPC protocol when implemented via a partially entangled state. We show that the errors introduced by the use of partial entanglement can be undone by applying a quantum state discrimination process. Since quantum state discrimination is a probabilistic process the correction succeeds with a certain probability but …
Attempts at cloning a quantum system result in the introduction of imperfections in the state of the copies. This is a consequence of the no-cloning theorem, which is a fundamental law of quantum physics and the backbone of security for quantum communications. Although such perfect copies are prohibited, a quantum state may be copied with maximal accuracy via various optimal cloning schemes. Optimal quantum cloning, which lies at the border of the physical limit imposed by the no-signalling theorem and the Heisenberg uncertainty principle, has been experimentally realized for low dimensional p…
Summoning is a task between two parties, Alice and Bob, with distributed networks of agents in space-time. Bob gives Alice a random quantum state, known to him but not her, at some point. She is required to return the state at some later point, belonging to a subset defined by communications received from Bob at other points. Many results about summoning, including the impossibility of unrestricted summoning tasks and the necessary conditions for specific types of summoning tasks to be possible, follow directly from the quantum no-cloning theorem and the relativistic no-superluminal-signalling…
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 cl…
Many-party correlations between measurement outcomes in general probabilistic theories are given by conditional probability distributions obeying the non-signalling condition. We show that any such distribution can be obtained from classical or quantum theory, by relaxing positivity constraints on either the mixed state shared by the parties, or the local functions which generate measurement outcomes. Our results apply to generic non-signalling correlations, but in particular they yield two distinct quasi-classical models for quantum correlations.
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 det…
Probabilistically creating n perfect clones from m copies for one of N priori known quantum states with minimum failure probability is a long-standing problem. We provide a rigorous proof for the geometric approach to this probabilistic quantum cloning problem when N = 2. Then, we give the general geometric form of the sufficient and necessary condition of probabilistic cloning for N known quantum states. By this general geometric approach, we realize the optimal probabilistic quantum cloning of N known quantum states with priori probabilities. The results are also applicable to the identifica…
In this paper, we study the entanglement and quantum discord of the output modes in the unified $1\rightarrow 2$ state-dependent cloning and probabilistic quantum cloning. The tripartite entanglement among the output modes and the quantum cloning machine is also considered. We find that the roles of the quantum correlations including the bipartite and tripartite entanglement and quantum discord strongly depend on the quantum cloning machines as well as the cloned state. In particular, it is found that this quantum cloning scheme can be realizable even without any quantum correlation.
We solve the long-standing problem of making n perfect clones from m copies of one of two known pure states with minimum failure probability in the general case where the known states have arbitrary a priori probabilities. The solution emerges from a geometric formulation of the problem. This formulation also reveals a deeper connection between cloning and state discrimination. The convergence of cloning to state discrimination as the number of clones goes to infinity exhibits a phenomenon analogous to a second order symmetry breaking phase transition.
We study the relation of causal influence between input systems of a reversible evolution and its output systems, in the context of operational probabilistic theories. We analyse two different definitions that are borrowed from the literature on quantum theory -- where they are equivalent. One is the notion based on signalling, and the other one is the notion used to define the neighbourhood of a cell in a quantum cellular automaton. The latter definition, that we adopt in the general scenario, turns out to be strictly weaker than the former: it is possible for a system to have causal influenc…
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 stat…
We introduce the study of quantum protocols that probabilistically simulate quantum channels from a sender in the future to a receiver in the past. The maximum probability of simulation is determined by causality and depends on the amount and type (classical or quantum) of information that the channel can transmit. We illustrate this dependence in several examples, including ideal classical and quantum channels, measure-and-prepare channels, partial trace channels, and universal cloning channels. For the simulation of partial trace channels, we consider generalized teleportation protocols that…
The possible existence of closed timelike curves (CTCs) draws attention to fundamental questions about what is physically possible and what is not. An example is the "no cloning theorem" in quantum mechanics, which states that no physical means exists by which an unknown arbitrary quantum state can be reproduced or copied perfectly. Using the Deutsch approach, we have shown that the no-cloning theorem can be circumvented in the presence of closed timelike curves, allowing the perfect cloning of a quantum state chosen randomly from a finite alphabet of states. Further, we show that a universal …
Quantum no-cloning, the impossibility of perfectly cloning an arbitrary unknown quantum state, is one of the most fundamental limitations due to the laws of quantum mechanics, which underpin the physical security of quantum key distribution. Quantum physics does allow, however, approximate cloning with either imperfect state fidelity and/or probabilistic success. Whereas approximate quantum cloning of single-particle states has been tested previously, experimental cloning of quantum entanglement -- a highly non-classical correlation -- remained unexplored. Based on a multiphoton linear optics …
We propose a scheme to enhance the fidelity of symmetric quantum cloning machine using a weak measurement. By adjusting the intensity of weak measurement parameter $p$, we obtain the copies with different optimal fidelity. Choosing proper value of $p$, we can obtain the perfect copies for initial qubits. In this paper, we focus on $1-2$ quantum cloning for two nonorthogonal states. Sets containing more than two linear independent states are also discussed briefly. Due to weak measurements being probabilistic, we obtain high fidelity at risk of probability. If the weak measurement successes, we…
No-cloning theorem is fundamental for quantum mechanics and for quantum information science that states an unknown quantum state cannot be cloned perfectly. However, we can try to clone a quantum state approximately with the optimal fidelity, or instead, we can try to clone it perfectly with the largest probability. Thus various quantum cloning machines have been designed for different quantum information protocols. Specifically, quantum cloning machines can be designed to analyze the security of quantum key distribution protocols such as BB84 protocol, six-state protocol, B92 protocol and the…
No-cloning theorem forbids perfect cloning of an unknown quantum state. A universal quantum cloning machine (UQCM), capable of producing two copies of any input qubit with the optimal fidelity, is of fundamental interest and has applications in quantum information processing. This is enabled by delicately tailored nonclassical correlations between the input qubit and the copying qubits, which distinguish the UQCM from a classical counterpart, but whose experimental demonstrations are still lacking. We here implement the UQCM in a superconducting circuit, and investigate these correlations. The…
The possible existence of closed timelike curves (CTCs) draws attention to fundamental questions about what is physically possible and what is not. An example is the "no cloning theorem" in quantum mechanics, which states that no physical means exists by which an unknown arbitrary quantum state can be reproduced or copied perfectly. Using the Deutsch approach, we show here that this theorem can be circumvented in the presence of closed timelike curves, allowing the cloning of an unknown arbitrary quantum state chosen from a finite alphabet of states. Since the "no cloning theorem" has played a…
We present a quantum probabilistic encryption algorithm for a private-key encryption scheme based on conjugate coding of the qubit string. A probabilistic encryption algorithm is generally adopted in public-key encryption protocols. Here we consider the way it increases the unicity distance of both classical and quantum private-key encryption schemes. The security of quantum probabilistic private-key encryption schemes against two kinds of attacks is analyzed. By using the no-signalling postulate, we show that the scheme can resist attack to the key. The scheme's security against plaintext att…
Complementarity is one of the main features of quantum physics that radically departs from classical notions. Here we consider the limitations that this principle imposes due to the unpredictability of measurement outcomes of incompatible observables. For two-level systems, it is shown that any preparation violating complementarity enables the preparation of a non-signalling box violating Tsirelson's bound. Moreover, these "beyond-quantum" objects could be used to distinguish a plethora of non-orthogonal quantum states and hence enable improved cloning protocols. For higher-dimensional systems…
Perfect cloning of a known set of states with arbitrary prior probabilities is possible if we allow the cloner to sometimes fail completely. In the optimal case the probability of failure is at its minimum allowed by the laws of quantum mechanics. Here we show that it is possible to lower the failure rate below that of the perfect probabilistic cloner but the price to pay is that the clones are not perfect; the global fidelity is less than one. We determine the optimal fidelity of a cloner with a Fixed Failure Rate (FFR cloner) in the case of a pair of known states. Optimality is shown to be a…
