International Journal of Quantum Information最新文献

We present a comprehensive characterization of the interconnections between single-mode, phase-insensitive Gaussian Bosonic Channels resulting from channel concatenation. This characterization enables us to identify, in the parameter space of these maps, two distinct regions: low-ground and high-ground. In the low-ground region, the information capacities are smaller than a designated reference value, while in the high-ground region, they are provably greater. As a direct consequence, we systematically outline an explicit set of upper bounds for the quantum and private capacity of these maps, which combine known upper bounds and composition rules, improving upon existing results.

For the continuous Wigner function and for certain discrete Wigner functions, permuting the values of the Wigner function in accordance with a symplectic linear transformation is equivalent to performing a certain unitary transformation on the state. That is, performing this unitary transformation is simply a matter of moving Wigner-function values around in phase space. This result holds in particular for the simplest discrete Wigner function defined on a $d\times d$ phase space when the Hilbert-space dimension $d$ is odd. It does not hold for a $d\times d$ phase space if the dimension is even. Here we show, though, that a generalized version of this correspondence does apply in the case of a two-qubit phase space. In this case, a symplectic linear permutation of the points of the phase space, together with a certain reinterpretation of the Wigner function, is equivalent to a unitary transformation.

We present a criterion to establish the local continuity of the relative entropy of resource, i.e. the relative entropy distance to the set of free states, in any quantum resource theory. Several basic corollaries of this criterion are presented. Applications to the relative entropy of entanglement in multipartite quantum systems are considered. It is shown, in particular, that local continuity of any relative entropy of multipartite entanglement follows from local continuity of the quantum mutual information.

The pretty good measurement is a fundamental analytical tool in quantum information theory, giving a method for inferring the classical label that identifies a quantum state chosen probabilistically from an ensemble. Identifying and constructing the pretty good measurement for the class of bosonic Gaussian states is of immediate practical relevance in quantum information processing tasks. Holevo recently showed that the pretty good measurement for a bosonic Gaussian ensemble is a bosonic Gaussian measurement that attains the accessible information of the ensemble [IEEE Trans. Inf. Theory66(9) (2020) 5634]. In this paper, we provide an alternate proof of Gaussianity of the pretty good measurement for a Gaussian ensemble of multimode bosonic states, with a focus on establishing an explicit and efficiently computable Gaussian description of the measurement. We also compute an explicit form of the mean square error of the pretty good measurement, which is relevant when using it for parameter estimation.

Generalizing the pretty good measurement is a quantum instrument, called the pretty good instrument. We prove that the post-measurement state of the pretty good instrument is a faithful Gaussian state if the input state is a faithful Gaussian state whose covariance matrix satisfies a certain condition. Combined with our previous finding for the pretty good measurement and provided that the same condition holds, it follows that the expected output state is a faithful Gaussian state as well. In this case, we compute an explicit Gaussian description of the post-measurement and expected output states. Our findings imply that the pretty good instrument for bosonic Gaussian ensembles is no longer merely an analytical tool, but that it can also be implemented experimentally in quantum optics laboratories.

This paper reviews Holevo’s contributions to quantum information theory during the 20 century. At that time, he mainly studied three topics, classical-quantum channel coding, quantum estimation with Craméro–Rao approach and quantum estimation with the group covariant approach. This paper addresses these three topics.

We study the symbols of linear operators generated by a finite unitary group. Under some assumptions, it is shown that the operator can be restored from its symbol. We also introduce symbols of mixed unitary quantum channels generated by finite unitary groups. An example illustrating the technique is given.

We study the long distance $(0,1)$-excitation state restoring in the linear open chain governed by the XX-Hamiltonian. We show that restoring the 1-order coherence matrix results in restoring the 1-excitation block of the 0-order coherence matrix, so that only one 0-excitation element of the density matrix remains unrestored. Such restoring also scales the concurrence between any two qubits of the transferred state, the scaling factor is defined by the Hamiltonian and doesn’t depend on the initial sender’s state. Sender–Receiver entanglement is also studied via the PPT criterion.

This paper focuses on the construction of a general parametric model that can be implemented executing multiple swap tests over few qubits and applying a suitable measurement protocol. The model turns out to be equivalent to a two-layer feedforward neural network which can be realized combining small quantum modules. The advantages and the perspectives of the proposed quantum method are discussed.

Quantum information and quantum foundations are becoming popular topics for advanced undergraduate courses. Many of the fundamental concepts and applications in these two fields, such as delayed choice experiments and quantum encryption, are comprehensible to undergraduates with basic knowledge of quantum mechanics. In this paper, we show that the quantum eraser, usually used to study the duality between wave and particle properties, can also serve as a generic platform for quantum key distribution. We present a pedagogical example of an algorithm to securely share random keys using the quantum eraser platform and propose its implementation with quantum circuits.

This work proposes a $d$-dimensional quantum multi-secret sharing scheme with a cheat-detection mechanism. The dealer creates multiple secrets and distributes the shares of these secrets using multi-access structures and a monotone span program. The dealer detects the cheating of each participant using the black box’s cheat-detection mechanism. To detect the participants’ deceit, the dealer distributes secret shares’ shadows derived from a randomly invertible matrix $X$ to the participants, stored in the black box. The black box identifies the participant’s deceitful behavior during the secret recovery phase. Only honest participants authenticated by the black box acquire their secret shares to recover the multiple secrets. After the black box cheating verification, the participants reconstruct the secrets by utilizing the unitary operations and quantum Fourier transform. The proposed protocol is reliable in preventing attacks from eavesdroppers and participants. The scheme’s efficiency is demonstrated in different noise environments: dit-flip noise, $d$-phase-flip noise and amplitude-damping noise, indicating its robustness in practical scenarios. The proposed protocol provides greater versatility, security and practicality.