The scenario of remote state preparation with a shared correlated quantum state and one bit of forward communication [B. Dakić et al., Nat. Phys. 8, 666 (2012)] is considered. Optimization of the transmission efficiency is extended to include general encoding and decoding strategies. The importance of the use of linear fidelity is recognized. It is shown that separable states cannot exceed the efficiency of entangled states by means of “local operations plus classical communication” actions limited to 1 bit of forward communication. It is proven however that such a surprising phenomena may naturally occur when the decoding agent has limited resources in the sense that either (i) has to use decoding which is insensitive to the change of the coordinate system in the plane in question (which is the natural choice if the receiver does not know the latter) or (ii) is forced to use bistochastic operations which may be imposed by physically inconvenient local thermodynamical conditions.
The scenario of remote state preparation with a shared correlated quantum state and one bit of forward communication [B. Dakić et al., Nat. Phys. 8, 666 (2012)] is considered. Optimization of the transmission efficiency is extended to include general encoding and decoding strategies. The importance of the use of linear fidelity is recognized. It is shown that separable states cannot exceed the efficiency of entangled states by means of “local operations plus classical communication” actions limited to 1 bit of forward communication. It is proven however that such a surprising phenomena may naturally occur when the decoding agent has limited resources in the sense that either (i) has to use decoding which is insensitive to the change of the coordinate system in the plane in question (which is the natural choice if the receiver does not know the latter) or (ii) is forced to use bistochastic operations which may be imposed by physically inconvenient local thermodynamical conditions.
Transmission efficiency (TE) of remote state preparation (RSP) with a shared quantum state and one bit of classical communication is considered. Following Daki\ifmmode \acute{c}\else \'{c}\fi{} et al. [Nat. Phys. 8, 666 (2012)], the encoding and decoding operators of the protocol are restricted to the physically relevant classes of projective measurements and unitary operators, respectively. It is shown that contrary to the previous arguments, the quadratic fidelity as well as the linear fidelity could be a valid figure of merit to quantify the TE of RSP. Then, the TE of the protocol in terms of both linear and quadratic fidelities is evaluated in a fully optimized scenario which includes the maximization over the encoding parameters as well as a meaningful maximization over the decoding parameters. The results show that, in this scenario, the TE scales with the sum of the two largest eigenvalues of the squared correlation matrix of the resource state that is zero only for product states. This approach successfully quantifies the performance of the protocol in terms of the resource state parameters and provides a means to compare the usefulness of any two resource states for RSP.
We investigate dense coding by imposing various locality restrictions to our decoder by employing the resource theory of asymmetry framework. In this task, the sender Alice and the receiver Bob share an entangled state. She encodes the classical information into it using a symmetric preserving encoder and sends the encoded state to Bob through a noiseless quantum channel. The decoder is limited to a measurement to satisfy a certain locality condition on the bipartite system composed of the receiving system and the preshared entanglement half. Our contributions are summarized as follows: First, we derive an achievable transmission rate for this task dependently of conditions of encoder and decoder. Surprisingly, we show that the obtained rate cannot be improved even when the decoder is relaxed to local measurements, two-way LOCCs, separable measurements, or partial transpose positive (PPT) measurements for the bipartite system. Moreover, depending on the class of allowed measurements with a locality condition, we relax the class of encoding operations to super-quantum encoders in the framework of general probability theory (GPT). That is, when our decoder is restricted to a separable measurement, theoretically, a positive operation is allowed as an encoding operation. Surprisingly, even under this type of super-quantum relaxation, the transmission rate cannot be improved. This fact highlights the universal validity of our analysis beyond quantum theory.
Entanglement-assisted classical communication and transmission of a quantum system are the two quantum resources for information processing. Many information tasks can be performed using either quantum resource. However, this equivalence is not always present since entanglement-assisted classical communication is sometimes known to be the better performing resource. Here, we show not only the opposite phenomenon, that there exist tasks for which transmission of a quantum system is a more powerful resource than entanglement-assisted classical communication, but also that such phenomena can have a surprisingly strong dependence on the dimension of Hilbert space. We introduce a family of communication complexity problems parametrized by the dimension of Hilbert space and study the performance of each quantum resource. Under an additional assumption of a linear strategy for the receiving party, we find that for low dimensions the two resources perform equally well, whereas for dimension seven and above the equivalence is suddenly broken and transmission of a quantum system becomes more powerful than entanglement-assisted classical communication. Moreover, we find that transmission of a quantum system may even outperform classical communication assisted by the stronger-than-quantum correlations obtained from the principle of macroscopic locality.
Remote state preparation is the variant of quantum state teleportation in which the sender knows the quantum state to be communicated. The original paper introducing teleportation established minimal requirements for classical communication and entanglement but the corresponding limits for remote state preparation have remained unknown until now: previous work has shown, however, that it not only requires less classical communication but also gives rise to a tradeoff between these two resources in the appropriate setting. We discuss this problem from first principles, including the various choices one may follow in the definitions of the actual resources. Our main result is a general method of remote state preparation for arbitrary states of many qubits, at a cost of 1 bit of classical communication and 1 bit of entanglement per qubit sent. In this "universal" formulation, these ebit and cbit requirements are shown to be simultaneously optimal by exhibiting a dichotomy. Our protocol then yields the exact tradeoff curve for memoryless sources of pure states (including the case of incomplete knowledge of the ensemble probabilities), based on the recently established quantum-classical tradeoff for visible quantum data compression. A variation of that method allows us to solve the even more general problem of preparing entangled states between sender and receiver (i.e., purifications of mixed state ensembles). The paper includes an extensive discussion of our results, including the impact of the choice of model on the resources, the topic of obliviousness, and an application to private quantum channels and quantum data hiding.
Quantum entanglement plays a central role in many quantum communication protocols. It allows distant particles to share correlations beyond the limits of classical interactions. Entanglement is essential for superdense coding, quantum teleportation, and secure cryptographic key distribution in quantum communication. It is also a pillar for developing quantum networks, where the management and distribution of entanglement are crucial for connecting distant nodes. Although perfect entanglement is a sought-after ideal, experimental imperatives, including entanglement distribution over long distances, often limit the quality of entangled states. An important question is whether weaker entanglement still offers advantages. First, we study more general tasks than dense coding to show that simpler measurements, combined with entanglement, allow advantageous and sometimes even optimal qubit communication protocols to be obtained. We also demonstrate that simple measurements can generate quantum correlations that cannot be modelled by two classical communication bits and can constitute an optimal protocol with quantum resources. We implement a novel Bell-type inequality tailored for certifying full network non-locality (FNN) to develop certification methods guaranteeing security on an entanglement-based network. Our experiment uses two pairs of polarised entangled photons in a network configuration with three nodes, briefly referred to as a bilocal network scenario. Finally, we show that weakly entangled states can improve communication over a qubit channel using only separate (local) measurements on isotropic non-steerable two-qubit states, without interference, of individual photons, across two communication tasks: secret sharing and its stochastic variant.
Suppose two distant observers Alice and Bob share a pure bipartite quantum state. By applying local operations and communicating with each other using a classical channel, Alice and Bob can manipulate it into some other states. Previous investigations of entanglement manipulations have been largely limited to a small number of strategies and their average outcomes. Here we consider a general entanglement manipulation strategy, and go beyond the average property. For a pure entangled state shared between two separated persons Alice and Bob, we show that the mathematical interchange symmetry of the Schmidt decomposition can be promoted into a physical symmetry between the actions of Alice and Bob. Consequently, the most general (multistep two-way-communications) strategy of entanglement manipulation of a pure state is, in fact, equivalent to a strategy involving only a single (generalized) measurement by Alice followed by one-way communications of its result to Bob. We also prove that strategies with one-way communications are generally more powerful than those without communications. In summary, one-way communications is necessary and sufficient for entanglement manipulations of a pure bipartite state. The supremum probability of obtaining a maximally entangled state (of any dimension) from an arbitrary state is determined, and a strategy for achieving this probability is constructed explicitly. One important question is whether collective manipulations in quantum mechanics can greatly enhance the probability of large deviations from the average behavior. We answer this question in the negative by showing that, given n pairs of identical partly entangled pure states $(|\ensuremath{\Psi}〉)$ with entropy of entanglement $E(|\ensuremath{\Psi}〉),$ the probability of getting nK $[K>E(|\ensuremath{\Psi}〉)]$ singlets out of entanglement concentration tends to zero as n tends to infinity.