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The states in the three-qubit GHZ SLOCC class can exhibit diverse entanglement patterns, as they may have no entanglement in any reduced subsystems, or show entanglement across one, two, or all three bipartite cuts. Significant research has…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
We consider the task of decentralized minimization of the sum of smooth strongly convex functions stored across the nodes of a network. For this problem, lower bounds on the number of gradient computations and the number of communication…
Dense coding with non-maximally entangled states has been investigated in many different scenarios. We revisit this problem for protocols adopting the standard encoding scheme. In this case, the set of possible classical messages cannot be…
The impossibility of deterministic and error-free discrimination among nonorthogonal quantum states lies at the core of quantum theory and constitutes a primitive for secure quantum communication. Demanding determinism leads to errors,…
We study the maximum-confidence (MC) measurement strategy for discriminating among nonorthogonal symmetric qudit states. Restricting to linearly dependent and equally likely pure states, we find the optimal positive operator valued measure…
We derive an optimal bound for arbitrary entanglement manipulation based on the transmission of a pulse in coherent states over a lossy channel followed by local operations and unlimited classical communication (LOCC). This stands on a…
We introduce a new entanglement measure based on optimal entanglement witness. First of all, we show that the entanglement measure satisfies some necessary properties, including zero entanglements for all separable states, convexity,…
Given n-copies of unknown bipartite (possiblly mixed) state, our task is to test whether the state is a pure state of not. Allowed to use the global operations, optimal one-sided error test is the projection onto the symmetric subspace,…
A key concept of quantum information theory is that accessing information encoded in a quantum system requires us to discriminate between several possible states the system could be in. A natural generalization of this problem, namely,…
We develop and analyze a set of new sequential simulation-optimization algorithms for large-scale multi-dimensional discrete optimization via simulation problems with a convexity structure. The "large-scale" notion refers to that the…
It is a central fact in quantum mechanics that non-orthogonal states cannot be distinguished perfectly. This property ensures the security of quantum key distribution. It is therefore an important task in quantum communication to design and…
Now, the known ensembles of orthogonal states which are distinguishable by local operators and classical communication (LOCC) satisfy the condition that the sum of Schmidit numbers of the orthogonal states is not bigger than the dimensions…
Post-selection strategies that discard low-confidence computational results can significantly improve the effective fidelity of quantum error correction at the cost of reduced acceptance rates, which can be particularly useful for offline…
One of the key ingredients of many LOCC protocols in quantum information is a multiparticle (locally) maximally entangled quantum state, aka a critical state, that possesses local symmetries. We show how to design critical states with…
We study differentially private (DP) stochastic optimization (SO) with loss functions whose worst-case Lipschitz parameter over all data may be extremely large or infinite. To date, the vast majority of work on DP SO assumes that the loss…
We construct the protocols to achieve probabilistic and deterministic entanglement transformations for bipartite pure states by means of local operations and classical communication. A new condition on pure contraction transformations is…
We study differentially private (DP) algorithms for stochastic convex optimization (SCO). In this problem the goal is to approximately minimize the population loss given i.i.d. samples from a distribution over convex and Lipschitz loss…
We explore the intersection of studies in quantum error correction and quantum local operations and classical communication (LOCC). We consider one-way LOCC measurement protocols as quantum channels and investigate their error correction…
It is shown that local distinguishability of orthogonal mixed states can be completely characterized by local distinguishability of their supports irrespective of entanglement and mixedness of the states. This leads to two kinds of upper…