Broadcasting quantum and classical information is a basic task in quantum information processing, and is also a useful model in the study of quantum correlations including quantum discord. We establish a full operational characterization of two-sided quantum discord in terms of bilocal broadcasting of quantum correlations. Moreover, we show that both the optimal fidelity of unilocal broadcasting of the correlations in an arbitrary bipartite quantum state and that of broadcasting an arbitrary set of quantum states can be formulized as semidefinite programs (SDPs), which are efficiently computable. We also analyze some properties of these SDPs and evaluate the broadcasting fidelities for some cases of interest.
Broadcasting quantum and classical information is a basic task in quantum information processing, and is also a useful model in the study of quantum correlations including quantum discord. We establish a full operational characterization of two-sided quantum discord in terms of bilocal broadcasting of quantum correlations. Moreover, we show that both the optimal fidelity of unilocal broadcasting of the correlations in an arbitrary bipartite quantum state and that of broadcasting an arbitrary set of quantum states can be formulized as semidefinite programs (SDPs), which are efficiently computable. We also analyze some properties of these SDPs and evaluate the broadcasting fidelities for some cases of interest.
Quantum broadcasting is central to quantum information processing and characterizes the correlations within quantum states. Nonetheless, traditional quantum broadcasting encounters inherent limitations dictated by the principles of quantum mechanics. In a previous study, Parzygnat et al. [Phys. Rev. Lett. 132, 110203 (2024)] introduced a canonical broadcasting quantum map that goes beyond the quantum no-broadcasting theorem through a virtual process. In this work, we generalize the concept of virtual broadcasting to unilocal broadcasting by incorporating a reference system and introduce protocols that can be approximated using physical operations with minimal cost. First, we propose a universal unilocal protocol enabling multiple parties to share the correlations of a target bipartite state, which is encoded in the expectation value for any observable. Second, we formalize the simulation cost of a virtual quantum broadcasting protocol into a semidefinite programming problem. Notably, we propose a specific protocol with optimal simulation cost for the two-broadcasting scenario, revealing an explicit relationship between simulation cost and the quantum system's dimension. Moreover, we establish upper and lower bounds on the simulation cost of the virtual n-broadcasting protocol and demonstrate the convergence of the lower bound to the upper bound as the quantum system's dimension increases.
The no-broadcasting theorem, a fundamental limitation on the communication of quantum information, holds that a physical process cannot broadcast copies of an unknown quantum state to two or more receivers. Recent work has explored ways of circumventing this limitation using "virtual" implementations of non-physical processes using measurement and data-processing on statistical samples of the unknown input. However, the statistical fluctuations of this data degrades the virtual copies so much that the protocol effectively depletes, rather than proliferate, the sample size -- thereby rendering it worse than the "naive" approach of splitting the given sample and sending a subsample to each receiver. In this work, we circumvent this flaw by allowing a small amount of systematic bias in the broadcast data, resulting in approximate virtual copies. We provide efficient semidefinite programs (SDP's) to determine the minimum sample size required to keep the approximation error below a desired threshold and vice versa. For reasonably small error values, we find approximate virtual broadcasting to be viable with sample sizes smaller than naive sample-splitting would demand. Along the way, we prove several symmetry-based simplifications to the problem, allowing optimal approximate broadcasting to be characterized in terms of the simple class of depolarizing channels.
Quantum mechanical properties like entanglement, discord, and coherence act as fundamental resources in various quantum information processing tasks. Consequently, the technique of generating more resources from a few, typically termed as broadcasting, serves as a promising candidate for the design of quantum networks. One way to broadcast resources could be using a cloning operation. In this article, broadcasting of quantum resources beyond $2\ensuremath{\bigotimes}2$ systems is investigated. In particular, in $2\ensuremath{\bigotimes}3$ dimensions, a class of states not useful for broadcasting of entanglement is characterized considering an optimal universal Heisenberg cloning machine. The broadcasting ranges for maximally entangled mixed states and two-parameter class of states are obtained to exemplify our protocol. A significant derivative of our protocol is that the cloning operation generates a qutrit ($3\ensuremath{\bigotimes}3$) entangled pair with positive partial transpose on one of the local sides, and an absolutely separable qubit ($2\ensuremath{\bigotimes}2$) pair on the other side of the input bipartite $2\ensuremath{\bigotimes}3$-dimensional resource state. Moving beyond entanglement, in $2\ensuremath{\bigotimes}d$ dimensions, the impossibility to optimally broadcast quantum discord and quantum coherence (l1 norm) is established. However, some significant illustrations are provided to highlight that nonoptimal broadcasting of discord and coherence is still possible.
Correlations in bipartite quantum states are fundamental objects in quantum information theory. A canonical framework for studying correlations is the entangled versus separable dichotomy in which the decompositions of separable states as convex combinations of product states play an instrumental role. In this paper, motivated by both the representation of separable states and quantum no-broadcasting considerations, we establish a constructive decomposition representation for any bipartite state. As applications, we prove the conjectures proposed by Luo [Lett. Math. Phys. 92, 143 (2010)] concerning no-unilocal broadcasting for quantum correlations and further provide a unified picture for the celebrated quantum no-broadcasting theorem for noncommuting states by Barnum et al. [Phys. Rev. Lett. 76, 2818 (1996)], and the elegant no-local-broadcasting theorem for quantum correlations by Piani et al. [Phys. Rev. Lett. 100, 090502 (2008)]. The results reveal some intrinsic relation between quantumness of correlations and noncommutativity of states, and in particular, provide a characterization for zero quantum discord introduced by Ollivier and Zurek [Phys. Rev. Lett. 88, 017901 (2001)] from the broadcasting perspective. Furthermore, it is indicated that the distinction between the decomposition for general bipartite states and that for separable states might be useful in studying entanglement versus separability.
Quantum discord, as introduced by Olliver and Zurek [Phys. Rev. Lett. 88, 017901 (2001)], is a measure of the discrepancy between two natural yet different quantum analogs of the classical mutual information. This notion characterizes and quantifies quantumness of correlations in bipartite states from a measurement perspective, and is fundamentally different from the various entanglement measures in the entanglement vs separability paradigm. The phenomenon of nonzero quantum discord is a manifestation of quantum correlations due to noncommutativity rather than due to entanglement, and has interesting and significant applications in revealing the advantage of certain quantum tasks. We will evaluate analytically the quantum discord for a large family of two-qubit states, and make a comparative study of the relationships between classical and quantum correlations in terms of the quantum discord. We furthermore compare the quantum discord with the entanglement of formation, and illustrate that the latter may be larger than the former, although for separable states, the entanglement of formation always vanishes and thus is less than the quantum discord.
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 answered this question and constructed their famous B-H quantum cloning machine. The B-H machine clones the state of an arbitrary single qubit in an optimal manner and hence it is universal. Generalizing this machine for a two-qubit system is straightforward, but during this procedure, except for product states, this machine loses its universality and becomes a state-dependent cloning machine. In this paper, we propose some classes of optimal universal local quantum state cloners for a particular class of two-qubit systems, more precisely, for a class of states with known Schmidt basis. We then extend our machine to the case that the Schmidt basis of the input state is deviated from the local computational basis of the machine. We show that more local quantum coherence existing in the input state corresponds to less fidelity between the input and output states. Also we present two classes of a state-dependent local quantum copying machine. Furthermore, we investigate local broadcasting of two aspects of quantum correlations, i.e., quantum entanglement and quantum discord, defined, respectively, within the entanglement-separability paradigm and from an information-theoretic perspective. The results show that although quantum correlation is, in general, very fragile during the broadcasting procedure, quantum discord is broadcasted more robustly than quantum entanglement.