The ideal realization of quantum teleportation relies on having access to a maximally entangled state; however, in practice, such an ideal state is typically not available and one can instead only realize an approxima...
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The ideal realization of quantum teleportation relies on having access to a maximally entangled state; however, in practice, such an ideal state is typically not available and one can instead only realize an approximate teleportation. With this in mind, we present a method to quantify the performance of approximate teleportation when using an arbitrary resource state. More specifically, after framing the task of approximate teleportation as an optimization of a simulation error over one-way local operations and classical communication (LOCC) channels, we establish a semidefinite relaxation of this optimization task by instead optimizing over the larger set of 2-PPT-extendible channels (where PPT denotes positive partial transpose). The main analytical calculations in our paper consist of exploiting the unitary covariance symmetry of the identity channel to establish a significant reduction of the computational cost of this latter optimization. Next, by exploiting known connections between approximate teleportation and quantum error correction, we also apply these concepts to establish bounds on the performance of approximate quantum error correction over a given quantum channel. Finally, we evaluate our bounds for various examples of resource states and channels.
Electrolyte-insulator-semiconductor (EIS)-based sensors are a novel class of electronic chips designed for biochemical sensing that offer a direct electronic readout, making them part of a new generation of sensing te...
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Quantum protocols including quantum key distribution and blind quantum computing often require the preparation of quantum states of known dimensions. Here, we show that, rather surprisingly, hidden multi-dimensional m...
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This paper studies an event-tniggered control problem for nonlinear systems subject to both external disturbancoes and dy namic *** is assumed that the system satisfies a global sector bound *** avold infnitely fast s...
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This paper studies an event-tniggered control problem for nonlinear systems subject to both external disturbancoes and dy namic *** is assumed that the system satisfies a global sector bound *** avold infnitely fast samplng,a novel eventriggred sampling mechanism is propoeed,which use8 not only the measuned system state but also an estimation of the inluence of the *** the propoeed design,the intersampling intervals an be lower bounded by a poeitive constant,and it is independent of botb external disturbances and dynamie ***,the doeedl loop event-tniggered system i proved to be input-torstate stable with repect to the extemal *** smalgain techmigues are;used for the stability analysis of the dloeeil-bop system.
We present a quantum algorithm for simulating a family of Markovian master equations that can be realized through a probabilistic application of unitary channels and state preparation. Our approach employs a second-or...
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We present a quantum algorithm for simulating a family of Markovian master equations that can be realized through a probabilistic application of unitary channels and state preparation. Our approach employs a second-order product formula for the Lindblad master equation, achieved by decomposing the dynamics into dissipative and Hamiltonian components and replacing the dissipative segments with randomly compiled, easily implementable elements. The sampling approach eliminates the need for ancillary qubits to simulate the dissipation process and reduces the gate complexity in terms of the number of jump operators. We provide a rigorous performance analysis of the algorithm. We also extend the algorithm to time-dependent Lindblad equations, generalize the family of Markovian master equations it can be applied to, and explore applications beyond the Markovian noise model. A new error bound, in terms of the diamond norm, for second-order product formulas for time-dependent Liouvillians is provided that might be of independent interest.
The analysis of dissipatively coupled oscillators is challenging and highly relevant in power grids. Standard mathematical methods are not applicable, due to the lack of network symmetry induced by dissipative couplin...
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Identification over quantum broadcast channels is considered. As opposed to the information transmission task, the decoder only identifies whether a message of his choosing was sent or not. This relaxation allows for ...
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Parametrized artificial neural networks (ANNs) can be very expressive ansatzes for variational algorithms, reaching state-of-the-art energies on many quantum many-body Hamiltonians. Nevertheless, the training of the A...
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Parametrized artificial neural networks (ANNs) can be very expressive ansatzes for variational algorithms, reaching state-of-the-art energies on many quantum many-body Hamiltonians. Nevertheless, the training of the ANN can be slow and stymied by the presence of local minima in the parameter landscape. One approach to mitigate this issue is to use parallel tempering methods, and in this work, we focus on the role played by the temperature distribution of the parallel tempering replicas. Using an adaptive method that adjusts the temperatures in order to equate the exchange probability between neighboring replicas, we show that this temperature optimization can significantly increase the success rate of the variational algorithm with negligible computational cost by eliminating bottlenecks in the replicas' random walk. We demonstrate this using two different neural networks, a restricted Boltzmann machine and a feedforward network, which we use to study a toy problem based on a permutation invariant Hamiltonian with a pernicious local minimum and the J1−J2 model on a rectangular lattice.
This paper establishes single-letter formulas for the exact entanglement cost of simulating quantum channels under free quantum operations that completely preserve positivity of the partial transpose (PPT). First, we ...
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This paper establishes single-letter formulas for the exact entanglement cost of simulating quantum channels under free quantum operations that completely preserve positivity of the partial transpose (PPT). First, we introduce the κ-entanglement measure for point-to-point quantum channels, based on the idea of the κ entanglement of bipartite states, and we establish several fundamental properties for it, including amortization collapse, monotonicity under PPT superchannels, additivity, normalization, faithfulness, and nonconvexity. Second, we introduce and solve the exact entanglement cost for simulating quantum channels in both the parallel and sequential settings, along with the assistance of free PPT-preserving operations. In particular, we establish that the entanglement cost in both cases is given by the same single-letter formula, the κ-entanglement measure of a quantum channel. We further show that this cost is equal to the largest κ entanglement that can be shared or generated by the sender and receiver of the channel. This formula is calculable by a semidefinite program, thus allowing for an efficiently computable solution for general quantum channels. Noting that the sequential regime is more powerful than the parallel regime, another notable implication of our result is that both regimes have the same power for exact quantum channel simulation, when PPT superchannels are free. For several basic Gaussian quantum channels, we show that the exact entanglement cost is given by the Holevo-Werner formula [Holevo and Werner, Phys. Rev. A 63, 032312 (2001)], giving an operational meaning of the Holevo-Werner quantity for these channels.
While monotone operator theory is often studied on Hilbert spaces, many interesting problems in machine learning and optimization arise naturally in finite-dimensional vector spaces endowed with non-Euclidean norms, s...
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