We solve the problem of the optimal cloning of pure entangled two-qubit states with a fixed degree of entanglement using local operations and classical communication. We show, that amazingly, classical communication between the parties can improve the fidelity of local cloning if and only if the initial entanglement is higher than a certain critical value. It is completely useless for weakly entangled states. We also show that bound entangled states with positive partial transpose are not useful as a resource to improve the best local cloning fidelity.
We construct a quantum machine which, by using asymmetric cloner, deals with disentangling and broadcasting entanglement in a single unitary evolution. The attainable maximum value of the scaling parameter $s$ for disentangling is identical to that obtained in previous works. The fidelity of the cloning state with respect to the input entangled state is state-dependent.
We examine the perfect cloning of non-local, orthogonal states with only local operations and classical communication. We provide a complete characterisation of the states that can be cloned under these restrictions, and their relation to distinguishability. We also consider the case of catalytic cloning, which we show provides no enhancement to the set of clonable states.
We discuss the exact cloning of orthogonal but entangled qubits under local operations and classical communication. The amount of entanglement necessary in blank copy is obtained for various cases. Surprisingly this amount is more than 1 ebit for certain set of two nonmaximal but equally entangled states of two qubits system. To clone any three two qubits Bell states at least log2 3 ebit is necessary.
We discuss (im)possibility of the exact cloning of orthogonal but genuinely entangled three qubit states aided with entangled ancila under local operation and classical communication. Whereas any two orthogonal GHZ states taken from the canonical GHZ basis, can be cloned with the help of a known GHZ state, surprisingly we find that no two W states can be cloned by using any known three qubit (possibly entangled) state as blank copy.
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 …
We investigate the conditions under which a set $\SC$ of pure bipartite quantum states on a $D\times D$ system can be locally cloned deterministically by separable operations, when at least one of the states is full Schmidt rank. We allow for the possibility of cloning using a resource state that is less than maximally entangled. Our results include that: (i) all states in $\SC$ must be full Schmidt rank and equally entangled under the $G$-concurrence measure, and (ii) the set $\SC$ can be extended to a larger clonable set generated by a finite group $G$ of order $|G|=N$, the number of states …
We consider the entanglement manipulation capabilities of the universal covariant quantum cloner or quantum processor circuit for quantum bits. We investigate its use for cloning a member of a bipartite or a genuine tripartite entangled state of quantum bits. We find that for bipartite pure entangled states a nontrivial behavior of concurrence appears, while for GHZ entangled states a possibility of the partial extraction of bipartite entanglement can be achieved.
We consider the quantum cloning of continuous variable entangled states. This is achieved by introducing two symmetric entanglement cloning machines (or e-cloners): a local e-cloner and a global e-cloner; where we look at the preservation of entanglement in the clones under the condition that the fidelity of the clones is maximized. These cloning machines are implemented using simple linear optical elements such as beam splitters and homodyne detection along with squeeze gates. We show that the global e-cloner out-performs the local e-cloner both in terms of the fidelity of the cloned states a…
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 …
It is shown that any quantum operation that perfectly clones the entanglement of all maximally-entangled qubit pairs cannot preserve separability. This ``entanglement no-cloning'' principle naturally suggests that some approximate cloning of entanglement is nevertheless allowed by quantum mechanics. We investigate a separability-preserving optimal cloning machine that duplicates all maximally-entangled states of two qubits, resulting in 0.285 bits of entanglement per clone, while a local cloning machine only yields 0.060 bits of entanglement per clone.
By amplifying photonic qubits it is possible to produce states that contain enough photons to be seen with a human eye, potentially bringing quantum effects to macroscopic scales [1]. In this paper we theoretically study quantum states obtained by amplifying one side of an entangled photon pair with different types of optical cloning machines for photonic qubits. We propose a detection scheme that involves lossy threshold detectors (such as human eye) on the amplified side and conventional photon detectors on the other side. We show that correlations obtained with such coarse-grained measureme…
We study the degree to which quantum entanglement survives when a three-qubit entangled state is copied by using local and non-local processes, respectively, and investigate iterating quantum copying for the three-qubit system. There may exist inter-three-qubit entanglement and inter-two-qubit entanglement for the three-qubit system. We show that both local and non-local copying processes degrade quantum entanglement in the three-particle system due to a residual correlation between the copied output and the copying machine. We also show that the inter-two-qubit entanglement is preserved bette…
We discuss the usefulness of quantum cloning and present examples of quantum computation tasks for which cloning offers an advantage which cannot be matched by any approach that does not resort to it. In these quantum computations, we need to distribute quantum information contained in states about which we have some partial information. To perform quantum computations, we use state-dependent probabilistic quantum cloning procedure to distribute quantum information in the middle of a quantum computation.
Recently Galvão and Hardy have shown that quantum cloning can improve the performance of some quantum computation tasks. However such performance enhancement is possible only if quantum correlations survive the cloning process. We investigate preservation of the quantum correlations in the process of non--local cloning of entangled pairs of two--level systems. We consider different kinds of quantum cloning machines and compare their effectiveness in the cloning of non--maximally entangled pure states. A mean entanglement is introduced in order to obtain a quantitative evaluation of an average …
We propose a protocol where one can exploit dual quantum and classical channels to achieve perfect ``cloning'' and ``orthogonal-complementing'' of an unknown state with a minimal assistance from a state preparer (without revealing what the input state is). The first stage of the protocol requires usual teleportation and in the second stage, the preparer disentangles the left-over entangled states by a single particle measurement process and communicates a number of classical bits (1-cbit per copy) to different parties so that perfect copies and complement copies are produced. We discuss our pr…
The efficacies of maximally and that of non-maximally entangled mixed states as teleportation channels have been studied. A new class of non-maximally entangled mixed states have been proposed also. Their advantages as quantum teleportation channels over existing non-maximally entangled mixed states have been verified. The mixed states can also be generated using quantum cloning machines. We have also studied how one can utilize the mixed entangled states obtained as output from a state independent quantum cloning machine in teleportation and dense coding. Mixed states can also be used in secr…
We consider a generalisation of Ekert's entanglement-based quantum cryptographic protocol where qubits are replaced by qu$N$its (i.e., N-dimensional systems). In order to study its robustness against optimal incoherent attacks, we derive the information gained by a potential eavesdropper during a cloning-based individual attack. In doing so, we generalize Cerf's formalism for cloning machines and establish the form of the most general cloning machine that respects all the symmetries of the problem. We obtain an upper bound on the error rate that guarantees the confidentiality of quNit generali…
We have found a quantum cloning machine that optimally duplicates the entanglement of a pair of $d$-dimensional quantum systems. It maximizes the entanglement of formation contained in the two copies of any maximally-entangled input state, while preserving the separability of unentangled input states. Moreover, it cannot increase the entanglement of formation of all isotropic states. For large $d$, the entanglement of formation of each clone tends to one half the entanglement of the input state, which corresponds to a classical behavior. Finally, we investigate a local entanglement cloner, whi…
The dynamics of a general two qubits system in noninetrial frame is investigated analytically, where it is assumed that both of its subsystems are differently accelerated. Two classes of initial travelling states are considered:self transposed and a generic pure states. The entanglement contained in all possible generated entangled channels between the qubits and their Anti-qubits is quantified. The usefulness of the travelling channels as quantum channels to perform quantum teleportation is investigated. For the self transposed classes, we show that the generalized Werner state is the most ro…
We investigate quantum teleportation through dissipative channels and calculate teleportation fidelity as a function of damping rates. It is found that the average fidelity of teleportation and the range of states to be teleported depend on the type and rate of the damping in the channel. Using the fully entangled fraction, we derive two bounds on the damping rates of the channels: one is to beat the classical limit and the second is to guarantee the non-existence of any other copy with better fidelity. Effect of the initially distributed maximally entangled state on the process is presented; …
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.
Though the no-cloning theorem [1] prohibits exact replication of arbitrary quantum states, there are many instances in quantum information processing and entanglement measurement in which a weaker form of cloning may be useful. Here, I provide a construction for generating an "entangled clone" for a particular but rather expansive and rich class of states. Given a stabilizer code or free fermion Hamiltonian, this construction generates an exact entangled clone of the original ground state, in the sense that the entanglement between the original and the exact copy can be tuned to be arbitrarily…
Complementarity have been an intriguing feature of physical systems for a long time. In this work we establish a new kind of complimentary relations in the frame work of quantum information processing tasks. In broadcasting of entanglement we create many pairs of less entangled states from a given entangled state both by local and non local cloning operations. These entangled states can be used in various information processing tasks like teleportation and superdense coding. Since these states are less entangled states it is quite intuitive that these states are not going to be as powerful res…
We study an initially inverted three-level atom in the lambda configuration embedded in a waveguide, interacting with a propagating single-photon pulse. Depending on the temporal shape of the pulse, the system behaves either as an optimal universal cloning machine, or as a highly efficient deterministic source of maximally entangled photon pairs. This quantum transistor operates over a wide range of frequencies, and can be implemented with today's solid-state technologies.
In this work, we exhaustively investigate $1 \rightarrow 2$ local and nonlocal broadcasting of entanglement as well as correlations beyond entanglement (geometric discord) using asymmetric Pauli cloners with most general two qubit state as the resource. We exemplify asymmetric broadcasting of entanglement using Maximally Entangled Mixed States. We demonstrate the variation of broadcasting range with the amount of entanglement present in the resource state as well as with the asymmetry in the cloner. We show that it is impossible to optimally broadcast geometric discord with the help of these a…
We pose the question whether the asymptotic equivalence between quantum cloning and quantum state estimation, valid at single-copy level, still holds when all the copies are examined jointly. For an N-to-M cloner, we consider the overall fidelity between the state of the M output systems and the state of M ideal copies, and we ask whether the optimal fidelity is attained by a measure-and- prepare protocol in the limit of large M. In order to gain intuition into the general problem, we analyze two concrete examples: i) cloning qubit states on the equator of the Bloch sphere and ii) cloning two-…
Recently, Li. \emph{et. al.} [Int. J. Theor. Phys., 48, 2777 (2009)] derived a necessary and sufficient condition for LOCC cloning of a set of bipartite orthogonal partially but equally entangled state. We demonstrates that, the result is based on a wrong observation regarding a set of non-maximally entangled states with equal entanglement. We also provide a simple example in favor of our comment.
We propose an experiment where a photon is first cloned by stimulated parametric down-conversion, making many (imperfect) copies, and then the cloning transformation is inverted, regenerating the original photon while destroying the copies. Focusing on the case where the initial photon is entangled with another photon, we study the conditions under which entanglement can be proven in the final state. The proposed experiment would provide a clear demonstration that quantum information is preserved in quantum cloning. It would furthermore allow a definitive experimental proof for micro-macro ent…
Impossibility of cloning and deleting of unknown states are important restrictions on processing of information in the quantum world. On the other hand, a known quantum state can always be cloned or deleted. However if we restrict the class of allowed operations, there will arise restrictions on the ability of cloning and deleting machines. We have shown that cloning and deleting of known states is in general not possible by local operations. This impossibility hints at quantum correlation in the state. We propose dual measures of quantum correlation based on the dual restrictions of no local …
In this work, we extensively study the problem of broadcasting of entanglement. In the first part of the work, we reconceptualize the idea of state dependent quantum cloning machine, and in that process we introduce different types of state dependent cloners like static and dynamic state dependent cloners. We derive the conditions under which we can make these cloners independent of the input state. In the broadcasting part, as our resource initial state, we start with general two qubit state and consider specific examples like, non maximally entangled state (NME), Werner like state (WS), and …
In this Letter we analyze the (im)possibility of the exact cloning of orthogonal three-qubit CAT states under local operation and classical communication(LOCC) with the help of a restricted entangled state. We also classify the three-qubit CAT states that can(not) be cloned under LOCC restrictions and extend the results to the n-qubit case.
We consider bipartite entangled states that cannot outperform separable states in any linear interferometer. Then, we show that these states can still be more useful metrologically than separable states if several copies of the state are provided or an ancilla is added to the quantum system. We present a general method to find the local Hamiltonian for which a given quantum state performs the best compared to separable states. We obtain analytically the optimal Hamiltonian for some quantum states with a high symmetry. We show that all bipartite entangled pure states outperform separable states…
Quantum teleportation (QT) is a fundamentally remarkable communication protocol that also finds many important applications for quantum informatics. Given a quantum entangled resource, it is crucial to know to what extent one can accomplish the QT. This is usually assessed in terms of output fidelity, which can also be regarded as an operational measure of entanglement. In the case of multipartite communication when each communicator possesses a part of $N$-partite entangled state, not all pairs of communicators can achieve a high fidelity due to monogamy property of quantum entanglement. We h…
We derive a new inequality for entanglement for a mixed four-partite state. Employing this inequality, we present a one-shot lower bound for entanglement cost and prove that entanglement cost is strictly larger than zero for any entangled state. We demonstrate that irreversibility occurs in the process of formation for all non-distillable entangled states. In this way we solve a long standing problem, of how "real" is entanglement of bound entangled states. Using the new inequality we also prove impossibility of local-cloning of a known entangled state.
We consider the optimal cloning of quantum coherent states with single-clone and joint fidelity as figures of merit. Both optimal fidelities are attained for phase space translation covariant cloners. Remarkably, the joint fidelity is maximized by a Gaussian cloner, whereas the single-clone fidelity can be enhanced by non-Gaussian operations: a symmetric non-Gaussian 1-to-2 cloner can achieve a single-clone fidelity of approximately 0.6826, perceivably higher than the optimal fidelity of 2/3 in a Gaussian setting. This optimal cloner can be realized by means of an optical parametric amplifier …
The usefulness of the genuinely entangled six qubit state that was recently introduced by Borras et al. is investigated for the quantum teleportation of an arbitrary three qubit state and for quantum state sharing (QSTS) of an arbitrary two qubit state. For QSTS, we explicitly devise two protocols and construct sixteen orthogonal measurement basis which can lock an arbitrary two qubit information between two parties.
We study the process of quantum telecloning of $d$-dimensional pure quantum states using partially entangled pure states as quantum channel. This process efficiently mixes optimal universal symmetric cloning with quantum teleportation. It is shown that it is possible to implement universal symmetric telecloning in a probabilistic way using unambiguous state discrimination and quantum state separation schemes. It is also shown that other strategies, such as minimum error discrimination, lead to a decrease in the fidelity of the copies and that certain partially entangled pure states with maxima…
We propose entangled (M+1)-mode quantum states as a multiuser quantum channel for continuous-variable communication. Arbitrary quantum states can be sent via this channel simultaneously to M remote and separated locations with equal minimum excess noise in each output mode. For a set of coherent-state inputs, the channel realizes optimum symmetric 1-to-M cloning at a distance (``telecloning''). It also provides the optimal cloning of coherent states without the need of amplifying the state of interest. The generation of the multiuser quantum channel requires no more than two 10\log_{10}[(\sqrt…
Encrypted Cloning, Absolute Maximal Entanglement and Quantum Secret Sharing
National University of Singapore（新加坡国立大学）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；Department of Physics, National University of Singapore（新加坡国立大学物理系）；Quantum Bridge Technologies Inc.（量子桥技术有限公司）；University of Toronto（多伦多大学）；Department of Electrical and Computer Engineering, University of Toronto（多伦多大学电气与计算机工程系）
We present a review of the problem of finding out whether a quantum state of two or more parties is entangled or separable. After a formal definition of entangled states, we present a few criteria for identifying entangled states and introduce some entanglement measures. We also provide a classification of entangled states with respect to their usefulness in quantum dense coding, and present some aspects of multipartite entanglement.
Suppose we are given an entangled pair and then one can ask how well we can produce two entangled pairs starting from a given entangled pair using only local operations. To give response of the above asked question, we study broadcasting of entanglement using state dependent quantum cloning machine as a local copier. We show that the length of the interval for probability-amplitude-squared for broadcasting of entanglement using state dependent cloner can be made larger than the length of the interval for probability-amplitude-squared for broadcasting entanglement using state independent cloner…
We investigate an entangled deformation of the deterministic quantum cloning process, called enscription, that can be applied to (certain) sets of distinct quantum states which are not necessarily orthogonal, called texts. Some basic theorems on enscribable texts are given, and a relationship to probabilistic quantum cloning is demonstrated.
One of the most striking features of quantum theory is the existence of entangled states, responsible for Einstein's so called "spooky action at a distance". These states emerge from the mathematical formalism of quantum theory, but to date we do not have a clear idea of which physical principles give rise to entanglement. Why does quantum theory have entangled states? Would any theory superseding classical theory have entangled states, or is quantum theory special? We demonstrate that without entanglement, non-classical degrees of freedom cannot reversibly interact. We present two postulates,…
In classical information theory one can, in principle, produce a perfect copy of any input state. In quantum information theory, the no cloning theorem prohibits exact copying of nonorthogonal states. Moreover, if we wish to copy multiparticle entangled states and can perform only local operations and classical communication (LOCC), then further restrictions apply. We investigate the problem of copying orthogonal, entangled quantum states with an entangled blank state under the restriction to LOCC. Throughout, the subsystems have finite dimension D. We show that if all of the states to be copi…
We introduce a simple sufficient criterion, which allows one to tell whether a subspace of a bipartite or multipartite Hilbert space is entangled. The main ingredient of our criterion is a bound on the minimal entanglement of a subspace in terms of entanglement of vectors spanning that subspace expressed for geometrical measures of entanglement. The criterion is applicable to both completely and genuinely entangled subspaces. We explore its usefulness in several important scenarios. Further, an entanglement criterion for mixed states following directly from the condition is stated. As an auxil…
We propose a particular encoding for bipartite entangled states derived from multipartite cluster-type entangled coherent states (CTECSs). We investigate the effects of amplitude damping on the entanglement content of this bipartite state, as well as its usefulness as a quantum channel for teleportation. We find interesting relationships among the amplitude of the coherent states constituting the CTECSs, the number of subsystems forming the logical qubits (redundancy), and the extent to which amplitude damping affects the entanglement of the channel. For instance, in the sense of sudden death …
National University of Singapore（新加坡国立大学）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；Stony Brook University（石溪大学）
A quantum telecloning process combining quantum teleportation and optimal quantum cloning from one input to M outputs is presented. The scheme relies on the establishment of particular multiparticle entangled states, which function as multiuser quantum information channels. The entanglement structure of these states is analyzed and shown to be crucial for this type of information processing.
A Macro-state consisting of N= 3.5 x 10^4 photons in a quantum superposition and entangled with a far apart single-photon state (Micro-state) is generated. Precisely, an entangled photon pair is created by a nonlinear optical process, then one photon of the pair is injected into an optical parametric amplifier (OPA) operating for any input polarization state, i.e. into a phase-covariant cloning machine. Such transformation establishes a connection between the single photon and the multi particle fields. We then demonstrate the non-separability of the bipartite system by adopting a local filter…
It is known that beyond $2 \otimes 2$ and $2 \otimes 3$ dimensional quantum systems, Peres-Hordecki criterion is no longer sufficient as an entanglement detection criterion as there are entangled states with both positive and negative partial transpose (PPT and NPT). Further, it is also true that all PPT entangled states are bound entangled states. However, in the class of NPT states, there can exist bound entangled states as well as free entangled states. All free/useful/distillable entanglement is a part of the class of NPT entangled states. In this article, we ask the question that given an…
The bound entangled state carries noisy entanglement and it is very hard to distill but the usefulness of bound entangled states has been depicted in different applications. This article represents a comparative dynamical study of an open quantum system for one of the bound entangled states proposed by Bennett et al. The study is conducted under the influence of Heisenberg, bi-linear bi-quadratic and Dzyaloshinskii-Moriya (DM) interaction. During the study, an auxiliary qutrit interacts with one of the qutrits of the selected two qutrit bound entangled state through different interactions. The…
We propose a generalization of quantum teleportation: the so-called many-to-many quantum communication of the information of a d-level system from N spatially separated senders to M>N receivers situated at different locations. We extend the concept of asymmetric telecloning from qubits to d-dimensional systems. We investigate the broadcasting of entanglement by using local 1->2 optimal universal asymmetric Pauli machines and show that the maximal fidelities of the two final entangled states are obtained when symmetric machines are applied. Cloning of entanglement is studied using a nonlocal op…
We propose a scheme for broadcasting entanglement at a distance based on linear optics. We show that an initial polarization entangled state can be simultaneously split and transmitted to a pair of observers situated at different locations with the help of two conditional Bell-state analyzers based on two beam splitters characterized by the same reflectivity R. In particular for R=1/3 the final states coincide with the output states obtained by the broadcasting protocol proposed by Buzek et al. [Phys. Rev. A 55, 3327 (1997)]. Further we present a different protocol called telecloning of entang…
