Noncommuting mixed states cannot be broadcast

Physical Review A, 1999

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.

Physical Review Letters, 2009

We study the quantumness of bipartite correlations by proposing a quantity that combines a measure of total correlations -mutual information-with the notion of broadcast copies -i.e. generally non-factorized copies-of bipartite states. By analyzing how our quantity increases with the number of broadcast copies, we are able to classify classical, separable, and entangled states. This motivates the definition of the broadcast regularization of mutual information, the asymptotic minimal mutual information per broadcast copy, which we show to have many properties of an entanglement measure.

International Journal of Quantum Information, 2006

Quantum information, though not precisely defined, is a fundamental concept of quantum information theory which predicts many fascinating phenomena and provides new physical resources. A basic problem is to recognize the features of quantum systems responsible for those phenomena. One of such important features is that non-commuting quantum states cannot be broadcast: two copies cannot be obtained out of a single copy, not even reproduced marginally on separate systems. We focus on the difference of information contents between one copy and two copies which is a basic manifestation of the gap between quantum and classical information. We show that if the chosen information measure is the Holevo quantity, the difference between the information contents of one copy and two copies is zero if and only if the states can be broadcast. We propose a new approach in defining measures of quantumness of ensembles based on the difference of information contents between the original ensemble and the ensemble of duplicated states. We comment about the permanence property of quantum states and the recently introduced superbroadcasting operation. We also provide an Appendix where we discuss the status of quantum information in quantum physics, basing on the so-called isomorphism principle.

arXiv (Cornell University), 2022

Physical Review Letters

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, during a symmetric dynamics, asymmetry is created at one subsystem, then the asymmetry of the other subsystem must be reduced. We also find a quantitative relation describing the tradeoff between the subsystems. These results cannot be understood in terms of additivity of asymmetry, because, as we show here, any faithful measure of asymmetry violates both sub-additivity and super-additivity. Rather, it is understood as a consequence of an information-disturbance principle, which is a quantum phenomenon. Our result also implies that if a bounded-size quantum reference frame for the symmetry group, or equivalently, a bounded-size reservoir of coherence (e.g., a clock with coherence between energy eigenstates in quantum thermodynamics) is used to implement any operation that is not symmetric, then the quantum state of the frame/reservoir is necessarily disturbed in an irreversible fashion, i.e., degraded.

Physical Review Letters, 2008

We prove that the correlations present in a multipartite quantum state have an operational quantum character as soon as the state does not simply encode a multipartite classical probability distribution, i.e. does not describe the joint state of many classical registers. Even unentangled states may exhibit such quantumness, that is pointed out by the new task of local broadcasting, i.e. of locally sharing pre-established correlations: this task is feasible if and only if correlations are classical and derive a no-local-broadcasting theorem for quantum correlations. Thus, local broadcasting is able to point out the quantumness of correlations, as standard broadcasting points out the quantum character of single system states. Further, we argue that our theorem implies the standard no-broadcasting theorem for single systems, and that our operative approach leads in a natural way to the definition of measures for quantumness of correlations.

Phys Rev a, 2006

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.

Journal of Physics A-mathematical and General, 2006

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. Further we show that there exists local state dependent cloner which gives better quality copy (in terms of average fidelity) of an entangled pair than the local universal cloner.

Physical Review Letters, 2008

We prove that the correlations present in a multipartite quantum state have an operational quantum character as soon as the state does not simply encode a multipartite classical probability distribution, i.e. does not describe the joint state of many classical registers. Even unentangled states may exhibit such quantumness, that is pointed out by the new task of local broadcasting, i.e. of locally sharing pre-established correlations: this task is feasible if and only if correlations are classical and derive a no-local-broadcasting theorem for quantum correlations. Thus, local broadcasting is able to point out the quantumness of correlations, as standard broadcasting points out the quantum character of single system states. Further, we argue that our theorem implies the standard no-broadcasting theorem for single systems, and that our operative approach leads in a natural way to the definition of measures for quantumness of correlations.

Physical Review A, 1997

We show that inseparability of quantum states can be partially broadcasted (copied, cloned) with the help of local operations, i.e. distant parties sharing an entangled pair of spin 1/2 states can generate two pairs of partially nonlocally entangled states using only local operations. This procedure can be viewed as an inversion of quantum purification procedures.