Quantum control requires full knowledge of the system many-body Hamiltonian. In many cases this information is not directly available due to restricted access to the system. Here we show how to indirectly estimate all the coupling strengths in a spin chain by measuring one spin at the end of the chain. We also discuss the efficiency of this "quantum inverse problem" and give a numerical example.
The characterization of an unknown quantum system requires the Hamiltonian identification. The full access to the system, however, is usually restricted, hindering the direct retrieval of relevant parameters, and a reliable indirect estimation is usually required. In this work, the algorithm proposed by Burgarth et al. [Phys. Rev. A 79, 020305 (2009)], which allows estimating the coupling strengths in a linear chain by addressing only one end site, is further investigated. The scheme is numerically studied for states with chain structure, exploring its applicability against observational error…
Neural-Network Quantum State (NQS) has attracted significant interests as a powerful wave-function ansatz to model quantum phenomena. In particular, a variant of NQS based on the restricted Boltzmann machine (RBM) has been adapted to model the ground state of spin lattices and the electronic structures of small molecules in quantum devices. Despite these progresses, significant challenges remain with the RBM-NQS based quantum simulations. In this work, we present a state-preparation protocol to generate a specific set of complex-valued RBM-NQS, that we name the unitary-coupled RBM-NQS, in quan…
Unitary-accessible coherence-erasure distance: Exact qubit solution and a tight qutrit bound
Changchun University of Technology（长春工业大学）；Yanbian University（延边大学）；Capital Normal University（首都师范大学）；Max-Planck-Institute for Mathematics in the Sciences（马克斯·普朗克科学促进部数理研究所）
Quantum communication leads to strong correlations, that can outperform classical ones. Complementary to previous works in this area, we investigate correlations in prepare-and-measure scenarios assuming a bound on the information content of the quantum communication, rather than on its Hilbert-space dimension. Specifically, we explore the extent of classical and quantum correlations given an upper bound on the one-shot accessible information. We provide a characterisation of the set of classical correlations and show that quantum correlations are stronger than classical ones. We also show tha…
In 2013, Boneh and Zhandry introduced the notion of indistinguishability (IND) in chosen plaintext (CPA) and chosen ciphertext (CCA) attacks by a quantum adversary which is given superposition access to an oracle for encryption and decryption queries but is restricted to classical queries in the challenge phase. In this paper we define IND-CPA and IND-CCA notions for symmetric encryption schemes where the adversary has full quantum superposition access to the oracle, and give constructions that achieve these security notions. Our results are formulated in the concrete security framework.
In the general setting of quantum controls, it is unrealistic to control all of the degrees of freedom of a quantum system. We consider a scenario where our direct access is restricted to a small subsystem $S$ that is constantly interacting with the rest of the system $E$. What we investigate here is the fundamental structure of the Hilbert space that is caused solely by the restrictedness of the direct control. We clarify the intrinsic space structure of the entire system and that of the operations which could be activated through $S$. The structures hereby revealed would help us make quantum…
We consider a communication scenario where classical information is encoded in an ensemble of quantum states that admit a power series expansion in a cost parameter and with the vanishing cost converge to a single zero-cost state. For a given measurement scheme, we derive an approximate expression for mutual information in the leading order of the cost parameter. The general results are applied to selected problems in optical communication, where coherent states of light are used as input symbols and the cost is quantified as the average number of photons per symbol. We show that for an arbitr…
We study measures of quantum information when the space spanned by the set of accessible observables is not closed under products, i.e., we consider systems where an observer may be able to measure the expectation values of two operators, $\langle O_1 \rangle$ and $\langle O_2 \rangle$, but may not have access to $\langle O_1 O_2 \rangle$. This problem is relevant for the study of localized quantum information in gravity since the set of approximately-local operators in a region may not be closed under arbitrary products. While we cannot naturally associate a density matrix with a state in thi…
For numerous applications of quantum theory it is desirable to be able to apply arbitrary unitary operations on a given quantum system. However, in particular situations only a subset of unitary operations is easily accessible. This raises the question of what additional unitary gates should be added to a given gate-set in order to attain physical universality, i.e., to be able to perform arbitrary unitary transformation on the relevant Hilbert space. In this work, we study this problem for three paradigmatic cases of naturally occurring restricted gate-sets: (A) particle-number preserving bos…
During the early history of unitary quantum theory the Kato's exceptional points (EPs, a.k.a. non-Hermitian degeneracies) of Hamiltonians $H(λ)$ did not play any significant role, mainly due to the Stone theorem which firmly connected the unitarity with the Hermiticity. During the recent wave of optimism people started believing that the corridors of a unitary access to the EPs could be opened leading, say, to a new picture of quantum phase transitions via an {\it ad hoc} weakening of the Hermiticty (replaced by the quasi-Hermiticity). Subsequently, the pessimism prevailed (the paths of access…
