We present a scheme to efficiently simulate, with a classical computer, the dynamics of multipartite quantum systems on which the amount of entanglement (or of correlations in the case of mixed-state dynamics) is conveniently restricted. The evolution of a pure state of n qubits can be simulated by using computational resources that grow linearly in n and exponentially in the entanglement. We show that a pure-state quantum computation can only yield an exponential speed-up with respect to classical computations if the entanglement increases with the size n of the computation, and gives a lower bound on the required growth.
We investigate the phase enhancement of quantum states subject to non-linear phase shifts. The optimal phase estimation of even entangled coherent states (ECSs) is shown to be better than that of NOON states and of odd ECS states with the same average particle number <n> and non-linearity exponent k. We investigate the creation of approximate ECSs (AECSs) from a squeezed vacuum with current optical technology methods and find that a pure AECS is even slightly better than an even ECS for large <n>. We also examine simple but physically relevant cases of loss in the non-linear interferometer arm…
Recently it has been shown that projected entangled-pair states can be considered as a (physically motivated) resource state for measurement-based quantum computation. Here we elaborate on how to construct a deterministic measurement-based quantum computation model on projected entangled-pair states. In particular, we use this scheme to build a 4-level many-body model for universal quantum computation on qubits. We also derive a 3-local parent Hamiltonian for this model, whose ground state is non-degenerate.
Bell inequalities (BIs) derived in terms of quantum probability statistics are extended to general bipartite-entangled states of arbitrary spins with parallel polarization. The original formula of Bell for the two-spin singlet is slightly modified in the parallel configuration, while, the inequality for- mulated by Clauser-Horne-Shimony-Holt remains not changed. The violation of BIs indeed resulted from the quantum non-local correlation for spin-1=2 case. However, the inequalities are always satisfied for the spin-1 entangled states regardless of parallel or antiparallel polarizations of two s…
We propose a scheme for efficient cluster state quantum computation by using imperfect polarization-entangled photon-pair sources, linear optical elements and inefficient non-photon-number-resolving detectors. The efficiency threshold for loss tolerance in our scheme requires the product of source and detector efficiencies should be >1/2 - the best known figure. This figure applies to uncorrelated loss. We further find that the loss threshold is unaffected by correlated loss in the photon pair source. Our approach sheds new light on efficient linear optical quantum computation with imperfect e…
We demonstrate how to discriminate two non-orthogonal, entangled quantum state which are slightly different from each other by using pseudo-Hermitian system. The positive definite metric operator which makes the pseudo-Hermitian systems fully consistent quantum theory is used for such a state discrimination. We further show that non-orthogonal states can evolve through a suitably constructed pseudo-Hermitian Hamiltonian to orthogonal states. Such evolution ceases at exceptional points of the pseudo-Hermitian system.
In this work, we study the quantum Fisher information (QFI) per particle of an open (particles can enter and leave the system) and dissipative (far from thermodynamical equilibrium) steady state system of two qubits in noisy channels. We concentrate on two noisy channels these are dephasing and non-dephasing channels. We will show that under certain conditions QFI per particle is slightly greater than 1 for both systems. This means that both systems can be slightly entangled.
We develop an octonionic representation of the payoff function for three player, two strategy, maximally entangled quantum games in order to obtain computationally friendly version of this function. This computational capability is then exploited to analyze and potentially classify the Nash equilibria in the quantum games.
It is often argued that entanglement is at the root of the speedup for quantum compared to classical computation, and that one needs a sufficient amount of entanglement for this speedup to be manifest. In measurement-based quantum computing (MBQC), the need for a highly entangled initial state is particularly obvious. Defying this intuition, we show that quantum states can be too entangled to be useful for the purpose of computation. We prove that this phenomenon occurs for a dramatic majority of all states: the fraction of useful n-qubit pure states is less than exp(-n^2). Computational unive…
Telecloning and its reverse process, referred to as remote information concentration(RIC), have attracted considerable interest because of their potential applications in quantum-information processing. We here present a general scheme for RIC in d-level systems (qudits), in which the quantum information initially distributed in many spatially separated qudits can be remotely and deterministically concentrated to a single qudit via an entangled channel without performing any global operations. We show that the entangled channel of RIC can be different types of entangled states, including mixed…
In the seminal paper [Metger and Vidick, Quantum '21], they proposed a computational self-testing protocol for Bell states in a single quantum device. Their protocol relies on the fact that the target states are stabilizer states, and hence it is highly non-trivial to reveal whether the other class of quantum states, non-stabilizer states, can be self-tested within their framework. Among non-stabilizer states, magic states are indispensable resources for universal quantum computation. In this letter, we show that a magic state for the CCZ gate can be self-tested while that for the T gate canno…
In blind quantum computation (BQC), a client delegates her quantum computation to a server with universal quantum computers who learns nothing about the client's private information. In measurement-based BQC model, entangled states are generally used to realize quantum computing. However, to generate a large-scale entangled state in experiment becomes a challenge issue. In circuit-based BQC model, single-qubit gates can be realized precisely, but entangled gates are probabilistically successful. This remains a challenge to realize entangled gates with a deterministic method in some systems. To…
Braid theories are applied to quantum computation processes, where to each crossing in the Braid diagram a unitary Yang-Baxter operator R is associated, representing either a Braiding matrix or a universal quantum gate. By operating with Braid operators on the computational basis of n-QUBITS states, orthonormal entangled states are obtained, referred here as general Bell states. The 3-QUBITS Bell states are explicitly developed and the present methods are generalized to any n-QUBITS system. The quantum properties of the general Bell states are analyzed and these properties are related to concu…
We investigate performances of pure continuous variable states in discriminating thermal and identity channels by comparing their M-copy error probability bounds. This offers us a simplified mathematical analysis for quantum target detection with slightly modified features: the object -- if it is present -- perfectly reflects the signal beam irradiating it, while thermal noise photons are returned to the receiver in its absence. This model facilitates us to obtain analytic results on error-probability bounds i.e., the quantum Chernoff bound and the lower bound constructed from the Bhattacharya…
Measurement-based quantum computation (MQC) is a leading paradigm for building a quantum computer. Cluster states being used in this context act as one-way quantum computers. Here, we consider Z-states as a type of highly entangled states like cluster states, which can be used for one-way or measurement based quantum computation. We define Z-state basis as a set of orthonormal states which are as equally entangled as the cluster states. We design new quantum circuits to non-destructively discriminate these highly entangled Z-states. The proposed quantum circuits can be generalized for N-qubit …
We show that using a slightly modified XX model for a spin-1/2 chain, one can transmit almost perfectly a maximally entangled two-qubit state from one end of the chain to the other one. This is accomplished without external fields or modulation of the coupling constants among the qubits. We also show that this strategy works for any size of the chain and is relatively robust to imperfections in the coupling constants among the qubits belonging to the chain. Actually, under certain scenarios of small disorder, we obtain better results than those predicted by the optimal ordered and noiseless ca…
This is a pedagogical paper, where bispinors solutions to the four-dimensional massless Dirac equation are considered in relativistic quantum mechanics and in quantum computation, taking advantage of the common mathematical description of four dimensional spaces. First, Weyl and massless Majorana bispinors are shown to be unitary equivalent, closing a gap in the literature regarding their equivalence. A discrepancy in the number of linearly independent solutions reported in the literature is also addressed. Then, it is shown that Weyl bispinors are algebraically equivalent to two-qubit direct …
Entanglement between the constituents of a quantum system is an essential resource in the implementation of many quantum processes and algorithms. Indeed, universal quantum computation is possible by measuring individual qubits comprising highly entangled cluster states. In this work it is shown that the unique gapped ground state of non-interacting fermions hopping on a specially prepared lattice is equivalent to a cluster state, where the entanglement between qubits results solely by fermionic indistinguishability and antisymmetry. A deterministic strategy for universal measurement-based qua…
Measurement based quantum computation requires the generation of a cluster state (quantum resource) prior to starting a computation. Generation of this entangled state can be difficult with many schemes already proposed. We present an abstract scheme which can create 2D cluster states as a universal resource for quantum computing. We find a linear scaling of grid size with cluster depth. The scheme is also capable of creating more exotic topologies including 3D structures and the unit cell for topological error correction. We note its relevance to the cavity QED scheme in [30] although it coul…
Recently, Boyer et al. presented a novel semiquantum key distribution protocol [M. Boyer, D. Kenigsberg, and T. Mor, Phys. Rev. Lett. 99, 140501 (2007)], in which quantum Alice shares a secret key with classical Bob. Li et al. proposed two semiquantum secret sharing protocols [Q. Li, W. H. Chan, and D. Y. Long, Phys. Rev. A 82, 022303 (2010)] by using maximally entangled Greenberger-Horne-Zeilinger states. In this paper, we present a semiquantum secret sharing protocol by using two-particle entangled states in which quantum Alice shares a secret key with two classical parties, Bob and Charlie.…
We study the classical simulation complexity in both the weak and strong senses, of matchgate (MG) computations supplemented with all combinations of settings involving inclusion of intermediate adaptive or nonadaptive computational basis measurements, product state or magic and general entangled state inputs, and single- or multi-line outputs. We find a striking parallel to known results for Clifford circuits, after some rebranding of resources. We also give bounds on the amount of classical simulation effort required in case of limited access intermediate measurements and entangled inputs. I…
We study classical simulation of quantum computation, taking the Gottesman-Knill theorem as a starting point. We show how each Clifford circuit can be reduced to an equivalent, manifestly simulatable circuit (normal form). This provides a simple proof of the Gottesman-Knill theorem without resorting to stabilizer techniques. The normal form highlights why Clifford circuits have such limited computational power in spite of their high entangling power. At the same time, the normal form shows how the classical simulation of Clifford circuits fits into the standard way of embedding classical compu…
Cluster state quantum computation for many-level systems
量子计算的簇态模型[Phys. Rev. Lett. 86，5188]概述了一个方案，允许人们使用测量一个大的纠缠量子系统在什么是所谓的集群状态进行量子计算。该模型本身和许多致力于它的工作涉及使用纠缠量子比特。在本文中，我们考虑的问题，而不是使用纠缠量子点。我们提出了一个完整的框架，簇态量子计算使用qudits，它不仅包含了原来的量子比特模型的功能，但也包含了新的自适应计算的想法：通过改变经典计算，有助于纠正错误的模型中固有的，可以改变实现的量子计算。这个特性是通过使用qudits时出现的额外自由度而产生的。最后，对于素数维，我们给出了一个非常明确的描述模型，利用相互无偏的基础。
We study the construction of both universal quantum computation and multi-partite entangled states in the topological diagrammatical approach to quantum teleportation. Our results show that the teleportation-based quantum circuit model admits a space-time topological interpretation which makes the construction of both quantum gates and four-partite entangled states more intuitive and simpler. Our results state a deeper link between the space-time non-locality and the quantum non-locality which are the two-fold character of the topological diagrammatical representation.
The macro-objectivation problem derives from the fact that the Schrodinger equation is linear and thus requires that a macroscopic system interacting with an entangled state must be entangled as well. However, such a requirement entails that the Schrodinger equation must also be solvable in the macroscopic world in the same way as it is solvable in the microscopic world, which itself is an assumption. In this work, the alternative assumption that the Schrodinger equation is in general an intractable problem is considered.
The notion of entanglement is the most well-known nonclassical correlation in quantum mechanics and a fundamental resource in quantum information and computation. This correlation, which is displayed by certain classes of quantum states, is of utmost importance when dealing with protocols such as quantum teleportation, cryptography, and quantum key distribution. In this paper, we exploit a classification of tripartite entanglement by introducing the concepts of entangled hypergraph and evolving entangled hypergraph as data structures suitable to model quantum protocols which use entanglement. …
We study the dissipative preparation of many-body entangled Gaussian states in bosonic lattice models which could be relevant for quantum technology applications. We assume minimal resources, represented by systems described by particle-conserving quadratic Hamiltonians, with a single localized squeezed reservoir. We show that in this way it is possible to prepare, in the steady state, the wide class of pure states which can be generated by applying a generic passive Gaussian transformation on a set of equally squeezed modes. This includes non-trivial multipartite entangled states such as clus…
We design a series of quantum circuits that generate absolute maximally entangled (AME) states to benchmark a quantum computer. A relation between graph states and AME states can be exploited to optimize the structure of the circuits and minimize their depth. Furthermore, we find that most of the provided circuits obey majorization relations for every partition of the system, and at every step of the quantum computation. The rational for our approach is to benchmark quantum computers with maximal useful entanglement, which can be used to implement multipartite quantum protocols.
We investigate the detection of entanglement in $n$-partite quantum states. We obtain practical separability criteria to identify genuinely entangled and non-separable mixed quantum states. No numerical optimization or eigenvalue evaluation is needed, and our criteria can be evaluated by simple computations involving components of the density matrix. We provide examples in which our criteria perform better than all known separability criteria. Specifically, we are able to detect genuine $n$-partite entanglement which has previously not been identified. In addition, our criteria can be used in …
