Quantum coherence (QCh) is considered to be a key ingredient in quantum resource theories and also plays a pivotal role in the design and implementation of various information processing tasks. Consequently, it becomes important for us to create more number coherent quantum states between two labs from a given coherent state shared initially. We call this process as \textbf{Broadcasting of Quantum Coherence (QCh)}. In this work we extensively study the problem of broadcasting of QCh. In order to have a holistic view of broadcasting, we start with a most general representation two qubit mixed state in terms of Bloch vectors. As a cloning transformation we have used universal symmetric optimal Buzek-Hillery (BH) cloner locally as well as non locally. Remarkably, we find that in either of the case it is impossible to do optimal broadcasting of QCh. Further we show in case of non optimal broadcasting it is impossible to increase QCh of the state by both local and non local cloning operations. In non optimal case, apart from general result we consider examples like, a) Werner like states (WLS) and b) Bell diagonal states (BDS) and obtain ranges for broadcasting in terms of input state parameters.
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.
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 …
We prove generic versions of the no-cloning and no-broadcasting theorems, applicable to essentially {\em any} non-classical finite-dimensional probabilistic model that satisfies a no-signaling criterion. This includes quantum theory as well as models supporting ``super-quantum'' correlations that violate the Bell inequalities to a larger extent than quantum theory. The proof of our no-broadcasting theorem is significantly more natural and more self-contained than others we have seen: we show that a set of states is broadcastable if, and only if, it is contained in a simplex whose vertices are …
We prove new quantitative limitations on any approximate simultaneous cloning or broadcasting of mixed states. The results are based on information-theoretic (entropic) considerations and generalize the well known no-cloning and no-broadcasting theorems. We also observe and exploit the fact that the universal cloning machine on the symmetric subspace of $n$ qudits and symmetrized partial trace channels are dual to each other. This duality manifests itself both in the algebraic sense of adjointness of quantum channels and in the operational sense that a universal cloning machine can be used as …
Due to the axioms of quantum mechanics, perfect cloning of an unknown quantum state is impossible. But since imperfect cloning is still possible, a question arises: "Is there an optimal quantum cloning machine?" Buzek and Hillery answer to this question and construct their famous B-H quantum cloning machine. The B-H machine clones state of an arbitrary single qubit in optimal manner and hence it is universal. Generalizing this machine for two-qubit system is straightforward, but this procedure does not preserve quantum correlation existing in bipartite state in optimal manner and also, during …
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 introduce entanglement measures to describe entanglement in a three-particle system and apply it to studying broadcasting of entanglement in three-particle GHZ state. We show that entanglement of three-qubit GHZ state can be partially broadcasted with the help of local or non-local copying processes. It is found that non-local cloning is much more efficient than local cloning for the broadcasting of entanglement.
In this work, we extensively study the problem of broadcasting of entanglement as state dependent versus state independent cloners. We start by re-conceptualizing the idea of state dependent quantum cloning machine (SD-QCM), and in that process, we introduce different types of SD-QCMs, namely, orthogonal and non-orthogonal cloners. We derive the conditions for which the fidelity of these cloners will become independent of the input state. We note that such a construction allows us to maximize the cloning fidelity at the cost of having partial information of the input state. In the discussion o…
We discuss disentanglement of pure bipartite quantum states within the framework of the schemes developed for entanglement splitting and broadcasting of entanglement.
Quantum mechanical properties like entanglement, discord and coherence act as fundamental resources in various quantum information processing tasks. Consequently, generating more resources from a few, typically termed as broadcasting is a task of utmost significance. One such strategy of broadcasting is through the application of cloning machines. In this article, broadcasting of quantum resources beyond $2 \otimes 2$ systems is investigated. In particular, in $2\otimes3$ dimension, a class of states not useful for broadcasting of entanglement is characterized for a choice of optimal universal…
The N to M (M>N) universal quantum broadcasting of mixed states are proposed for qubits system. The broadcasting of mixed states is universal and optimal in the sense that the shrinking factor is independent of input state and achieves the upper bound. The quantum broadcasting of mixed qubits is a generalization of the universal quantum cloning machine for identical pure input states. A new pure state decompositions of the identical mixed qubits are obtained.
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 study broadcasting of entanglement where we use universal quantum cloners (in general less optimal) to perform local cloning operations. We show that there is a lower bound on the fidelity of the universal quantum cloners that can be used for broadcasting. We prove that an entanglement is optimally broadcast only when optimal quantum cloners are used for local copying. We also show that broadcasting of entanglement into more than two entangled pairs is forbidden using only local operations.
In this work, we extensively study the problem of broadcasting of quantum correlations. This includes broadcasting of quantum entanglement as well as correlations that go beyond the notion of entanglement. It is quite well known from the "No-Broadcasting theorem" that perfect broadcasting of quantum correlation is not possible. However it does not rule out the possibility of partial broadcasting of correlations where we can get lesser correlated states from a given correlated state. In order to have a holistic view of broadcasting, we investigate this problem by starting with most general repr…
We analyze various eavesdropping strategies on a quantum cryptographic channel. We present the optimal strategy for an eavesdropper restricted to a two-dimensional probe, interacting on-line with each transmitted signal. The link between safety of the transmission and the violation of Bell's inequality is discussed. We also use a quantum copying machine for eavesdropping and for broadcasting quantum information.
Coherence, being at the heart of interference phenomena, is found to be an useful resource in quantum information theory. Here we want to understand quantum coherence under the combination of two fundamentally dual processes, viz., cloning and deleting. We found the role of quantum cloning and deletion machines with the consumption and generation of quantum coherence. We establish cloning as a cohering process and deletion as a decohering process. Fidelity of the process will be shown to have connection with coherence generation and consumption of the processes.
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…
Coherence and entanglement are the two most crucial resources for various quantum information processing tasks. Here, we study the interplay of coherence and entanglement under the action of different three qubit quantum cloning operations. Considering certain well-known quantum cloning machines (input state independent and dependent), we provide examples of coherent and incoherent operations performed by them. We show that both the output entanglement and coherence could vanish under incoherent cloning operations. Coherent cloning operations on the other hand, could be used to construct a uni…
It is well known that it is impossible to clone an arbitrary quantum state. However, this inability does not lead directly to no-cloning of quantum coherence. Here, we show that it is impossible to clone the coherence of an arbitrary quantum state which is a stronger statement than the 'no-cloning of quantum state'. In particular, with ancillary system as machine state, we show that it is impossible to clone the coherence of states whose coherence is greater than the coherence of the known states on which the transformations are defined. Also, we characterize the class of states for which cohe…
Symmetries of both closed and open-system dynamics imply many significant constraints. These generally have instantiations in both classical and quantum dynamics (Noether's theorem, for instance, applies to both sorts of dynamics). We here provide an example of such a constraint which has no counterpart for a classical system, that is, a uniquely quantum consequence of symmetric dynamics. Specifically, we demonstrate the impossibility of broadcasting asymmetry (symmetry-breaking) relative to a continuous symmetry group, for bounded-size quantum systems. The no-go theorem states that if two ini…
"Broadcasting", namely distributing information over many users, suffers in-principle limitations when the information is quantum. This poses a critical issue in quantum information theory, for distributed processing and networked communications. For pure states ideal broadcasting coincides with the so-called "quantum cloning", describing an hypothetical ideal device capable of producing from a finite number N of copies of a state (drawn from a set) a larger number M>N of output copies of the same state. Since such a transformation is not isometric, it cannot be achieved by any physical machin…
We investigate the multiphoton states generated by high-gain optical parametric amplification of a single injected photon, polarization encoded as a ''qubit''. The experiment configuration exploits the optimal phase-covariant cloning in the high gain regime. The interference fringe pattern showing the non local transfer of coherence between the injected qubit and the mesoscopic amplified output field involving up to 4000 photons has been investigated. A probabilistic new method to extract full information about the multiparticle output wavefunction has been implemented.
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…
Quantum mechanics put restriction on performing some task which we can do classically. One such restriction is that we cannot copy an arbitrary quantum state. This is known as No-cloning theorem. Although quantum mechanics forbid us to construct a perfect cloner, there is no restriction to construct an imperfect cloner. Therefore, we have constructed and studied a special kind of quantum cloning machine named as Hybrid quantum cloning machine which is nothing but a different combination of pre-existing quantum cloning machines. We showed that this hybrid quantum cloning machine sometime gives …
We propose a bio-inspired sequential quantum protocol for the cloning and preservation of the statistics associated to quantum observables of a given system. It combines the cloning of a set of commuting observables, permitted by the no-cloning and no-broadcasting theorems, with a controllable propagation of the initial state coherences to the subsequent generations. The protocol mimics the scenario in which an individual in an unknown quantum state copies and propagates its quantum information into an environment of blank qubits. Finally, we propose a realistic experimental implementation of …
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…
Any physical transformation that equally distributes quantum information over a large number M of users can be approximated by a classical broadcasting of measurement outcomes. The accuracy of the approximation is at least of the order 1/M. In particular, quantum cloning of pure and mixed states can be approximated via quantum state estimation. As an example, for optimal qubit cloning with 10 output copies, a single user has error probability p > 0.45 in distinguishing classical from quantum output--a value close to the error probability of the random guess.
It is well known that classical information can be cloned, but non-orthogonal quantum states cannot be cloned, and non-commuting quantum states cannot be broadcast. We conceive a scenario in which the object we want to broadcast is the statistical distinguishability, as quantified by quantum Fisher information, about a signal parameter encoded in quantum states. We show that quantum Fisher information cannot be cloned, whilst it might be broadcast even when the input states are non-commuting. This situation interpolates between cloning of classical information and no-broadcasting of quantum in…
Quantum theory can be regarded as a non-commutative generalization of classical probability. From this point of view, one expects quantum dynamics to be analogous to classical conditional probabilities. In this paper, a variant of the well-known isomorphism between completely positive maps and bipartite density operators is derived, which makes this connection much more explicit. The new isomorphism is given an operational interpretation in terms of statistical correlations between ensemble preparation procedures and outcomes of measurements. Finally, the isomorphism is applied to elucidate th…
We show that there does not exist any universal quantum cloning machine that can broadcast an arbitrary mixed qubit with a constant fidelity. Based on this result, we investigate the dependent quantum cloner in the sense that some parameter of the input qubit $ρ_s(θ,ω,λ)$ is regarded as constant in the fidelity. For the case of constant $ω$, we establish the $1\to2$ optimal symmetric dependent cloner with a fidelity 1/2. It is also shown that the $1\to M$ optimal quantum cloning machine for pure qubits is also optimal for mixed qubits, when $λ$ is the unique parameter in the fidelity. For gene…
We show that all Macroscopic Quantum Superpositions (MQS) based on phase-covariant quantum cloning are characterized by an anomalous high resilence to the de-coherence processes. The analysis supports the results of recent MQS experiments and leads to conceive a useful conjecture regarding the realization of complex decoherence - free structures for quantum information, such as the quantum computer.
We show that the quantum states generated by universal optimal quantum cloning of a single photon represent an universal set of quantum superpositions resilient to decoherence. We adopt Bures distance as a tool to investigate the persistence ofquantum coherence of these quantum states. According to this analysis, the process of universal cloning realizes a class of quantum superpositions that exhibits a covariance property in lossy configuration over the complete set of polarization states in the Bloch sphere.
We show that, given a general mixed state for a quantum system, there are no physical means for {\it broadcasting\/} that state onto two separate quantum systems, even when the state need only be reproduced marginally on the separate systems. This result generalizes and extends the standard no-cloning theorem for pure states.
We study generating joint measurements by operating on the input quantum state with a broadcasting channel followed by local measurements on the two outputs of the broadcasting channel. Although, due to perfect broadcasting or cloning being impossible, this scheme cannot generate perfect joint observables for all pairs of quantum observables, we study for what intended joint observables and local measurements this procedure can be carried out. For local sharp observables this is always possible as long as the intended joint observable is dominated by the tensor product of the local sharp obser…
Limits on Broadcasting Genuine Multipartite Entanglement in Quantum Networks
S. N. Bose National Centre for Basic Sciences（S.N. 玻色基础科学国家中心）；Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）；Indian Institute of Technology Indore（印度理工学院印多尔分校）
The high resilience to de-coherence shown by a recently discovered Macroscopic Quantum Superposition (MQS) generated by a quantum injected optical parametric amplifier (QI-OPA) and involving a number of photons in excess of 5x10^4 motivates the present theoretical and numerical investigation. The results are analyzed in comparison with the properties of the MQS based on coherent states and NOON states, in the perspective of the comprehensive theory of the subject by W.H.Zurek. In that perspective the concepts of "pointer state", "einselection" are applied to the new scheme.
In the presence of conservation laws, superpositions of eigenstates of the corresponding conserved quantities cannot be generated by quantum dynamics. Thus, any such coherence represents a potentially valuable resource of asymmetry, which can be used, for example, to enhance the precision of quantum metrology or to enable state transitions in quantum thermodynamics. Here we ask if such superpositions, already present in a reference system, can be broadcast to other systems, thereby distributing asymmetry indefinitely at the expense of creating correlations. We prove a no-go theorem showing tha…
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,…
Optical quantum memory is an essential element for long distance quantum communication and photonic quantum computation protocols. The practical implementation of such protocols requires an efficient quantum memory with long coherence time. Beating the no-cloning limit, for example, requires efficiencies above 50\%. An ideal optical fibre loop has a loss of 50% in 100 $μ$ s, and until now no universal quantum memory has beaten this time-efficiency limit. Here, we report results of a gradient echo memory (GEM) experiment in a cold atomic ensemble with a 1/e coherence time up to 1ms and maximum …
We investigate the basic constraint on amplifying the asymmetry in quantum states with correlated catalysts. Here a correlated catalyst is a finite-dimensional auxiliary, which exactly preserves its reduced state while allowed to become correlated to the quantum system. Interestingly, we prove that under translationally invariant operations, catalysts in pure states are useless in any state transformation, while with a correlated catalyst in a mixed state, one can enlarge the set of accessible states from an initially asymmetric state. Moreover, we show that the power of a catalyst increases w…
A way to characterize quantum nonlocality is to see difference in the figure of merit between LOCC optimal protocol and globally optimal protocol in doing certain task, e.g., state estimation, state discrimination, cloning and broadcasting. Especially, we focus on the case where $n$ tensor of unknown states. Our conclusion is that separable pure states are more non-local than entangled pure states. More specifically, the difference in the figure of the merit is exponentially small if the state is entangled, and the exponent is log of the largest Schmidt coefficient. On the other hand, in many …
Selfcomplementary quantum channels are characterized by such an interaction between the principal quantum system and the environment that leads to the same output states of both interacting systems. These maps can describe approximate quantum copy machines, as perfect copying of an unknown quantum state is not possible due to the celebrated no-cloning theorem. We provide here a parametrization of a large class of selfcomplementary channels and analyze their properties. Selfcomplementary channels preserve some residual coherences and residual entanglement. Investigating some measures of non-Mar…
Quantum technologies are developing powerful tools to generate and manipulate coherent superpositions of different energy levels. Envisaging a new generation of energy-efficient quantum devices, here we explore how coherence can be manipulated without exchanging energy with the surrounding environment. We start from the task of converting a coherent superposition of energy eigenstates into another. We identify the optimal energy-preserving operations, both in the deterministic and in the probabilistic scenario. We then design a recursive protocol, wherein a branching sequence of energy-preserv…
Thermofield dynamics (TFD) approach is a real time quantum field method for dealing with finite temperature quantum states in a purified version of usual density operator formalism at finite temperature. In the domain of quantum information, TFD represents a quite promising direction for dealing with qubits under thermal influence and can also be associated to Gaussian states. Here, we propose a generalized TFD mean expectation for the case of thermofield qubits considering the action of gate operators. We propose quantum teleportation protocols involving thermofield states, considering therma…
Coding theorems in quantum Shannon theory express the ultimate rates at which a sender can transmit information over a noisy quantum channel. More often than not, the known formulas expressing these transmission rates are intractable, requiring an optimization over an infinite number of uses of the channel. Researchers have rarely found quantum channels with a tractable classical or quantum capacity, but when such a finding occurs, it demonstrates a complete understanding of that channel's capabilities for transmitting classical or quantum information. Here, we show that the three-dimensional …
