A general formalism of the problem of perfect state transfer is presented. We show that there are infinitely many Hamiltonians which may provide solution to this problem. In a first attempt to give a classification of them we investigate their possible forms and the related dynamics during the transfer. Finally, we show how the present formalism can be used for the engineering of perfect quantum wires of various topologies and coupling configurations.
The difficulty of an optimization task in quantum information science depends on the proper mathematical expression of the physical target. Here we demonstrate the power of optimization functionals targeting an arbitrary perfect two-qubit entangler, creating a maximally-entangled state out of some initial product state. For two quantum information platforms of current interest, nitrogen vacancy centers in diamond and superconducting Josephson junctions, we show that an arbitrary perfect entangler can be reached faster and with higher fidelity than specific two-qubit gates or local equivalence …
We exploit a ferromagnetic chain of interacting $d$-level ($d>2$) particles for arbitrary perfect transfer of quantum states with $(d-1)$ levels. The presence of one extra degree of freedom in the Hilbert space of particles, which is not used in encoding, allows to achieve perfect transfer even in a uniform chain through a repeated measurement procedure with consecutive single site measurements. Apart from the first iteration, for which the time of evolution grows linearly with the size of the chain, in all other iterations, the evolution times are short and does not scale with the length. The…
Optimal control theory is a powerful tool for improving figures of merit in quantum information tasks. Finding the solution to any optimal control problem via numerical optimization depends crucially on the choice of the optimization functional. Here, we derive a functional that targets the full set of two-qubit perfect entanglers, gates capable of creating a maximally-entangled state out of some initial product state. The functional depends on easily-computable local invariants and uniquely determines when a gate evolves into a perfect entangler. Optimization with our functional is most usefu…
We propose a class of qubit networks that admit perfect state transfer of any two-dimensional quantum state in a fixed period of time. We further show that such networks can distribute arbitrary entangled states between two distant parties, and can, by using such systems in parallel, transmit the higher dimensional systems states across the network. Unlike many other schemes for quantum computation and communication, these networks do not require qubit couplings to be switched on and off. When restricted to $N$-qubit spin networks of identical qubit couplings, we show that $2\log_3 N$ is the m…
A famously hard graph problem with a broad range of applications is computing the number of perfect matchings, that is the number of unique and complete pairings of the vertices of a graph. We propose a method to estimate the number of perfect matchings of undirected graphs based on the relation between Gaussian Boson Sampling and graph theory. The probability of measuring zero or one photons in each output mode is directly related to the hafnian of the adjacency matrix, and thus to the number of perfect matchings of a graph. We present encodings of the adjacency matrix of a graph into a Gauss…
Spin chains have been proposed as wires to transport information between distributed registers in a quantum information processor. Unfortunately, the challenges in manufacturing linear chains with engineered couplings has hindered experimental implementations. Here we present strategies to achieve perfect quantum information transport in arbitrary spin networks. Our proposal is based on the weak coupling limit for pure state transport, where information is transferred between two end-spins that are only weakly coupled to the rest of the network. This regime allows disregarding the complex, int…
Future quantum computers are likely to be expensive and affordable outright by few, motivating client/server models for outsourced computation. However, the applications for quantum computing will often involve sensitive data, and the client would like to keep her data secret, both from eavesdroppers and the server itself. Homomorphic encryption is an approach for encrypted, outsourced quantum computation, where the client's data remains secret, even during execution of the computation. We present a scheme for the homomorphic encryption of arbitrary quantum states of light with no more than a …
The notion of perfect correlations between arbitrary observables, or more generally arbitrary POVMs, is introduced in the standard formulation of quantum mechanics, and characterized by several well-established statistical conditions. The transitivity of perfect correlations is proved to generally hold, and applied to a simple articulation for the failure of Hardy's nonlocality proof for maximally entangled states. The notion of perfect correlations between observables and POVMs is used for defining the notion of a precise measurement of a given observable in a given state. A longstanding misc…
We find analytic models that can perfectly transfer, without state initializati$ or remote collaboration, arbitrary functions in two- and three-dimensional interacting bosonic and fermionic networks. We elaborate on a possible implementation of state transfer through bosonic or fermionic atoms trapped in optical lattices. A significant finding is that the state of a spin qubit can be perfectly transferred through a fermionic system. Families of Hamiltonians, both linear and nonlinear, are described which are related to the linear Boson model and that enable the perfect transfer of arbitrary fu…
We show a perfect state transfer of an arbitrary unknown two-qubit state can be achieved via a discrete-time quantum walk with various settings of coin flippings, and extend this method to distribution of an arbitrary unknown multi-qubit entangled state between every pair of sites in the multi-dimensional network. Furthermore, we study the routing of quantum information on this network in a quantum walk architecture, which can be used as quantum information processors to communicate between separated qubits.
We show how to perfectly transfer, without state initialization and remote collaboration, arbitrary functions in interacting boson lattices. We describe a possible implementation of state transfer through bosonic atoms trapped in optical lattices or polaritons in on-chip coupled cavities. Significantly, a family of Hamiltonians, both linear and nonlinear, is found which are related to the Bose-Hubbard model and that enable the perfect transfer of arbitrary functions. It is shown that the state transfer between two sites in two-dimensional lattices can result in quantum interference due to the …
Perfect state transfer (PST) is discussed in the context of passive quantum networks with logical bus topology, where many logical nodes communicate using the same shared media, without any external control. The conditions under which, a number of point-to-point PST links may serve as building blocks for the design of such multi-node networks are investigated. The implications of our results are discussed in the context of various Hamiltonians that act on the entire network, and are capable of providing PST between the logical nodes of a prescribed set in a deterministic manner.
It is shown how to perfectly transfer an arbitrary qudit state in interacting boson networks. By defining a family of Hamiltonians related to Bose-Hubbard model, we describe a possible method for state transfer through bosonic atoms trapped in these networks with different kinds of coupling strengths between them. Particularly, by taking the underlying networks of so called group schemes as interacting boson networks, we show how choose suitable coupling strengths between the nodes, in order that an arbitrary qudit state be transferred from one node to its antipode, perfectly. In fact, by empl…
Polarization of light is harnessed in an abundance of classical and quantum applications. Characterizing polarization in a classical sense is done resoundingly successfully using the Stokes parameters, and numerous proposals offer new quantum counterparts of this characterization. The latter often rely on distance measures from completely polarized or unpolarized light. We here show that the accepted class of perfectly polarized quantum states of light is severely lacking in terms of both pure states and mixed states. By appealing to symmetry and geometry arguments we determine all of the stat…
I show a scheme which allows a perfect transfer of an unknown single-qubit atomic state from one atom to another by letting two atoms interact simultaneously with a cavity QED. During the interaction between atom and cavity, the cavity is only virtually excited and accordingly the scheme is insensitive to the cavity field states and cavity decay. Based on this scheme, a network for transfer of an arbitrary single-qubit atomic state between atoms is engineered. Then the scheme is generalized to perfectly transfer an arbitrary 2-qubit atomic state and accordingly a network for transfer of an arb…
Remote state preparation (RSP) is the act of preparing a quantum state at a remote location without actually transmitting the state itself. Using at most two classical bits and a single shared maximally entangled state, one can in theory remotely prepare any qubit state with certainty and with perfect fidelity. However, in any experimental implementation the average fidelity between the target and output states cannot be perfect. In order for an RSP experiment to demonstrate genuine quantum advantages, it must surpass the optimal threshold of a comparable classical protocol. Here we study the …
Let $s_1,s_2,\ldots s_n$ be states of a general probability theory, and $\mathcal A$ be the set of all subsets of indices $H \subset [n]\equiv\{1,2,\ldots n\}$ such that the states $(s_j)_{j\in H}$ are jointly perfectly distinguishable. All subsets with a single element are of course in $\mathcal A$, and since smaller collections are easier to distinguish, if $H\in \mathcal A$ and $L \subset H$ then $L\in \mathcal A$; in other words, $\mathcal A$ is a so-called $\textit{independence system}$ on the set of indices $[n]$. In this paper it is shown that every independence system on $[n]$ can be r…
We investigate quantum state transfer in XY spin chains and propose a recursive procedure to construct the nonuniform couplings of these chains with arbitrary length to achieve perfect state transfer(PST). We show that this method is capable of finding all possible coupling schemes for PST. These schemes, without external control fields, only involve preengineered couplings but not dynamical control of them, so they can be simply realized experimentally. The analytical solutions provide all information for coupling design.
A significant hurdle towards realization of practical and scalable quantum computing is to protect the quantum states from inherent noises during the computation. In physical implementation of quantum circuits, a long-distance interaction between two qubits is undesirable since, it can be interpreted as a noise. Therefore, multiple quantum technologies and quantum error correcting codes strongly require the interacting qubits to be arranged in a nearest neighbor (NN) fashion. The current literature on converting a given quantum circuit to an NN-arranged one mainly considered chained qubit topo…
