arXiv subjects

Seiseki Akibue

Publications and source records attributed to Seiseki Akibue.

24 records · Page 2Linked to original sources

arXiv2022

Quadratic improvement on accuracy of approximating pure quantum states and unitary gates by probabilistic implementation

Pure quantum states are often approximately encoded as classical bit strings such as those representing probability amplitudes and those describing circuits that generate the quantum states. The crucial quantity is the minimum length of classical bit strings from which the original pure states are approximately reconstructible. We derive asymptotically tight bounds on the minimum bit length required for probabilistic encodings with which one can approximately reconstruct the original pure state as an ensemble of the quantum states encoded in classical strings. We also show that such a probabilistic encoding asymptotically halves the bit length required for "deterministic" ones. This is based on the fact that the accuracy of approximating pure states by using a given subset of pure states can be increased quadratically if we use ensembles of pure states in the subset. Moreover, we show that a similar fact holds when we consider the approximation of unitary gates by using a given subset of unitary gates. This improves the reduction rate of the circuit size by using probabilistic circuit synthesis compared to previous results. This also demonstrates that the reduction is possible even for low-accuracy circuit synthesis, which might improve the accuracy of various NISQ algorithms.

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arXiv2018

Perfect discrimination of non-orthogonal quantum states with posterior classical partial information

The indistinguishability of non-orthogonal pure states lies at the heart of quantum information processing. Although the indistinguishability reflects the impossibility of measuring complementary physical quantities by a single measurement, we demonstrate that the distinguishability can be perfectly retrieved simply with the help of posterior classical partial information. We demonstrate this by showing an ensemble of non-orthogonal pure states such that a state randomly sampled from the ensemble can be perfectly identified by a single measurement with help of the post-processing of the measurement outcomes and additional partial information about the sampled state, i.e., the label of subensemble from which the state is sampled. When an ensemble consists of two subensembles, we show that the perfect distinguishability of the ensemble with the help of the post-processing can be restated as a matrix-decomposition problem. Furthermore, we give the analytical solution for the problem when both subensembles consist of two states.

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arXiv2018

Bipartite discrimination of independently prepared quantum states as a counterexample to a parallel repetition conjecture

For distinguishing quantum states sampled from a fixed ensemble, the gap in bipartite and single-party distinguishability can be interpreted as a nonlocality of the ensemble. In this paper, we consider bipartite state discrimination in a composite system consisting of $N$ subsystems, where each subsystem is shared between two parties and the state of each subsystem is randomly sampled from a particular ensemble comprising the Bell states. We show that the success probability of perfectly identifying the state converges to $1$ as $N\rightarrow\infty$ if the entropy of the probability distribution associated with the ensemble is less than $1$, even if the success probability is less than $1$ for any finite $N$. In other words, the nonlocality of the $N$-fold ensemble asymptotically disappears if the probability distribution associated with each ensemble is concentrated. Furthermore, we show that the disappearance of the nonlocality can be regarded as a remarkable counterexample of a fundamental open question in theoretical computer science, called a parallel repetition conjecture of interactive games with two classically communicating players. Measurements for the discrimination task include a projective measurement of one party represented by stabilizer states, which enable the other party to perfectly distinguish states that are sampled with high probability.

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arXiv2017

Entanglement-assisted classical communication can simulate classical communication without causal order

Phenomena induced by the existence of entanglement, such as nonlocal correlations, exhibit characteristic properties of quantum mechanics distinguishing from classical theories. When entanglement is accompanied by classical communication, it enhances the power of quantum operations jointly performed by two spatially separated parties. Such a power has been analyzed by the gap between the performances of joint quantum operations implementable by local operations at each party connected by classical communication with and without the assistance of entanglement. In this work, we present a new formulation for joint quantum operations connected by classical communication beyond special relativistic causal order but without entanglement and still within quantum mechanics. Using the formulation, we show that entanglement assisting classical communication necessary for implementing a class of joint quantum operations called separable maps can be interpreted to simulate "classical communication" not respecting causal order. Our results reveal a new counter-intuitive aspect of entanglement related to spacetime.

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arXiv2016

Network coding for distributed quantum computation over cluster and butterfly networks

To apply network coding for quantum computation, we study the distributed implementation of unitary operations over all separated input and output nodes of quantum networks. We consider a setting of networks where quantum communication between nodes is restricted to sending just a qubit, but classical communication is unrestricted. We analyze which N-qubit unitary operations are implementable over cluster networks by investigating transformations of a given cluster network into quantum circuits. We show that any two-qubit unitary operation is implementable over the butterfly network and the grail network, which are fundamental primitive networks for classical network coding. We also analyze probabilistic implementations of unitary operations over cluster networks.

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arXiv2014

Two-party LOCC convertibility of quadpartite states and Kraus-Cirac number of two-qubit unitaries

Nonlocal properties (globalness) of a non-separable unitary determine how the unitary affects the entanglement properties of a quantum state. We apply a given two-qubit unitary on a quadpartite system including two reference systems and analyze its "LOCC partial invertibility" under two-party LOCC. A decomposition given by Kraus and Cirac for two-qubit unitaries shows that the globalness is completely characterized by three parameters. Our analysis shows that the number of non-zero parameters (the Kraus-Cirac number) has an operational significance when converting entanglement properties of multipartite states. All two-qubit unitaries have the Kraus-Cirac number at most 3, while those with at most 1 or 2 are equivalent, up to local unitaries, to a controlled-unitary or matchgate, respectively. The presented operational framework distinguishes the untaries with the Kraus-Cirac number 2 and 3, which was not possible by the known measure of the operator Schmidt decomposition. We also analyze how the Kraus-Cirac number changes when two or more two-qubit unitaries are applied sequentially.

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