Consider a set of $N$ systems and an arbitrary interaction Hamiltonian $H$ that couples them. We investigate the use of local operations and classical communication (LOCC), together with the Hamiltonian $H$, to simulate a unitary evolution of the $N$ systems according to some other Hamiltonian $H'$. First, we show that the most general simulation using $H$ and LOCC can be also achieved, with the same time efficiency, by just interspersing the evolution of $H$ with local unitary manipulations of each system and a corresponding local ancilla (in a so-called LU+anc protocol). Thus, the ability to make local measurements and to communicate classical information does not help in non--local Hamiltonian simulation. Second, we show that both for the case of two $d$-level systems ($d>2$), or for that of a setting with more than two systems ($N>2$), LU+anc protocols are more powerful than LU protocols. Therefore local ancillas are a useful resource for non--local Hamiltonian simulation. Third, we use results of majorization theory to explicitly solve the problem of optimal simulation of two-qubit Hamiltonians using LU (equivalently, LU+anc, LO or LOCC).
The need for Hamiltonians with many-body interactions arises in various applications of quantum computing. However, interactions beyond two-body are difficult to realize experimentally. Perturbative gadgets were introduced to obtain arbitrary many-body effective interactions using Hamiltonians with two-body interactions only. Although valid for arbitrary $k$-body interactions, their use is limited to small $k$ because the strength of interaction is $k$'th order in perturbation theory. In this paper we develop a nonperturbative technique for obtaining effective $k$-body interactions using Hamil…
Nonlocal gate operation is based on sharing an ancillary pair of qubits in perfect entanglement. When the ancillary pair are partially entangled, the efficiency of the gate operation drops. Using general transformations, we devise probabilistic nonlocal gates, which perform the nonlocal operation conclusively when the ancillary pair are only partially entangled. We show that a controlled purification protocol can be implemented by the probabilistic nonlocal operation.
We propose a protocol for local implementation of two consecutive nonlocal operations by three parters. It consumes one shared GHZ state in this protocol. We also demonstrate that these resources are sufficient and necessary to locally implement two consecutive CNOT operations.
We develop a geometric approach to quantify the capability of creating entanglement for a general physical interaction acting on two qubits. We use the entanglement measure proposed by us for $N$-qubit pure states (PRA \textbf{77}, 062334 (2008)). Our procedure reproduces the earlier results (PRL \textbf{87}, 137901 (2001)). The geometric method has the distinct advantage that it gives an experimental way to monitor the process of optimizing entanglement production.
We investigate the local implementation of nonlocal operations with the block matrix form, and propose a protocol for any diagonal or offdiagonal block operation. This method can be directly generalized to the two-party multiqubit case and the multiparty case. Especially, in the multiparty cases, any diagonal block operation can be locally implemented using the same resources as the multiparty control-U operation discussed in Ref. [Eisert et al., Phys. Rev. A 62, 052317(2000)]. Although in the bipartite case, this kind of operations can be transformed to control-U operation using local operati…
Entangling and disentangling capacities are the key manifestation of the nonlocal content of a quantum operation. A lot of effort has been put recently into investigating (dis)entangling capacities of unitary operations, but very little is known about capacities of non-unitary operations. Here we investigate (dis)entangling capacities of unital CPTP maps acting on two qubits.
For manipulations of multipartite quantum systems, it was well known that all local operations assisted by classical communication (LOCC) constitute a proper subset of the class of separable operations. Recently, Gheorghiu and Griffiths found that LOCC and general separable operations are equally powerful for transformations between bipartite pure states. In this letter we extend this comparison to mixed states and show that in general separable operations are strictly stronger than LOCC when transforming a mixed state to a pure entangled state. A remarkable consequence of our finding is the e…
We develop the probabilistic implementation of a nonlocal gate $\exp{[iξ{σ_{n_A}}σ_{n_B}]}$ and $ξ\in[0,\frac\pi4]$, by using a single non-maximally entangled state. We prove that, nonlocal gates can be implemented with a fidelity greater than 79.3% and a consumption of less than 0.969 ebits and 2 classical bits, when $ξ\leq0.353$. This provides a higher bound for the feasible operation compared to the former techniques \cite{Cirac,Groisman,Bennett-1}. Besides, gates with $ξ\geq0.353$ can be implemented with the probability 79.3% and a consumption of 0.969 ebits, which is the same efficiency a…
We show that any Bell local state, with a hidden nonlocality that can be revealed by local filtering, is more, or equally, entangled than nonlocal states. More precisely, it can be deterministically transformed into a nonlocal state, by local operations and classical communication. For such a state, there is a clear anomaly of nonlocality, for any measures of entanglement and nonlocality. Moreover, we prove that the hidden nonlocality of any bipartite state more, or equally, entangled than nonlocal states, can be revealed by local operations and the sending of two one-bit messages, one in each…
We present a method to show that low-energy states of quantum many-body interacting systems in one spatial dimension are nonlocal. We assign a Bell inequality to the Hamiltonian of the system in a natural way and we efficiently find its classical bound using dynamic programming. The Bell inequality is such that its quantum value for a given state, and for appropriate observables, corresponds to the energy of the state. Thus, the presence of nonlocal correlations can be certified for states of low enough energy. The method can also be used to optimize certain Bell inequalities: in the translati…
We address nonlocality of a class of fully inseparable three-mode Gaussian states generated either by bilinear three-mode Hamiltonians or by a sequence of bilinear two-mode Hamiltonians. Two different tests revealing strong nonlocality are considered, in which the dichotomic Bell operator is represented by displaced parity and by pseudospin operator respectively. Three-mode states are also considered as a conditional source of two-mode non Gaussian states, whose nonlocal properties are analyzed. We found that the non Gaussian character of the conditional states allows violation of Bell's inequ…
In the previous paper, it has been proved that elastic scattering processes of two quantum particles are always accompanied with nonlocal processes. Furthermore, it is found that setting an additional Hamiltonian after the originally scattering one can help to describe the two type of processes in a united frame. Here we discuss the contribution of this additional Hamiltonian to irreversible process in isolated quantum systems. The use of the Hamiltonian can induce the non-Markovian Langevin equation, showing a complex memory effect, and thus revealing the irreversible essence of isolated syst…
We propose a simple setup for the conversion of multipartite entangled states in a quantum network with restricted access. The scheme uses nonlocal operations to enable the preparation of states that are inequivalent under local operations and classical communication, but most importantly does not require full access to the states. It is based on a flexible linear optical conversion gate that uses photons, which are ideally suited for distributed quantum computation and quantum communication in extended networks. In order to show the basic working principles of the gate, we focus on converting…
Quantum separable operations are defined as those that cannot produce entanglement from separable states, and it is known that they strictly surpass local operations and classical communication (LOCC) in a number of tasks, which is sometimes referred to as "quantum nonlocality without entanglement." Here we consider a task with such a gap regarding the trade-off between state discrimination and preservation of entanglement. We show that this task along with the gap has an analogue in a purely classical setup, indicating that the quantum properties are not essential in the existence of a nonzer…
The realism-based nonlocality (RBN) is a recently introduced measure that differs from the well-known Bell's nonlocality. For bipartite states, the RBN concerns how much an element of reality associated with a given observable is affected upon local measurements on a subsystem. Here, we present an analytical proof for the unitary invariance of the RBN and that it presents a monotonous behavior upon the action of unital and non-unital local quantum noise. We illustrate our results by employing the two-qubits Werner state and thermal quantum correlated states. We show how the RBN is limited by t…
Superselection rules severely alter the possible operations that can be implemented on a distributed quantum system. Whereas the restriction to local operations imposed by a bipartite setting gives rise to the notion of entanglement as a nonlocal resource, the superselection rule associated with particle number conservation leads to a new resource, the \emph{superselection induced variance} of local particle number. We show that, in the case of pure quantum states, one can quantify the nonlocal properties by only two additive measures, and that all states with the same measures can be asymptot…
We analyze optimal schemes and also propose some practical schemes for the nonlocal conversion from two shared Bell pairs to four-qubit entangled states in optical quantum networks. In the analysis, we consider two-qubit operations as nonlocal operations and minimize the number of access to ancillary qubits as possible. First, we consider two-qubit unitary operations without using ancillary qubits and derive a necessary and sufficient condition for convertible states. Second, we consider nonlocal optical systems composed of passive linear optics and postselection. For the passive linear optica…
A multipartner secure direct communication protocol is presented, using quantum nonlocality. Security of this protocol is based on `High fidelity implies low entropy'. When the entanglement was successfully distributed, anyone of the multipartner can send message secretly by using local operation and reliable public channel. Since message transfered only by using local operation and public channel after entanglement successfully distributed, so this protocol can protect the communication against destroying-travel-qubit-type attack.
We analyze the new equation of motion for the damped oscillator. It differs from the standard one by a damping term which is nonlocal in time and hence it gives rise to a system with memory. Both classical and quantum analysis is performed. The characteristic feature of this nonlocal system is that it breaks local composition low for the classical Hamiltonian dynamics and the corresponding quantum propagator.
We consider supersymmetric quantum mechanical models with both local and nonlocal potentials. We present a nonlocal deformation of exactly solvable local models. Its energy eigenfunctions and eigenvalues are determined exactly. We observe that both our model Hamiltonian and its supersymmetric partner may have normalizable zero-energy ground states, in contrast to local models with nonperiodic or periodic potentials.
We consider the simulation of the dynamics of one nonlocal Hamiltonian by another, allowing arbitrary local resources but no entanglement nor classical communication. We characterize notions of simulation, and proceed to focus on deterministic simulation involving one copy of the system. More specifically, two otherwise isolated systems $A$ and $B$ interact by a nonlocal Hamiltonian $H \neq H_A+H_B$. We consider the achievable space of Hamiltonians $H'$ such that the evolution $e^{-iH't}$ can be simulated by the interaction $H$ interspersed with local operations. For any dimensions of $A$ and …
We experimentally demonstrate, with an all-optical setup, a nonlocal deterministic quantum non-demolition interaction gate applicable to quantum states at nodes separated by a physical distance and connected by classical communication channels. The gate implementation, based on entangled states shared in advance, local operations, and classical communication, runs completely in parallel fashion at both the local nodes, requiring minimum resource. The nondemolition character of the gate up to the local unitary squeezing is verified by the analysis using several coherent states. A genuine quantu…
Entanglement and Bell nonlocality are used to describe quantum inseparabilities. Bell-nonlocal states form a strict subset of entangled states. A natural question arises concerning how much territory Bell nonlocality occupies entanglement for a general two-qubit entangled state. In this work, we investigate the relation between entanglement and Bell nonlocality by using lots of randomly generated two-qubit states, and give out a constraint inequality relation between the two quantum resources. For studying the upper or lower boundary of the inequality relation, we discover maximally (minimally…
An orthogonal product basis of a composite Hilbert space is genuinely nonlocal if the basis states are locally indistinguishable across every bipartition. From an operational point of view such a basis corresponds to a separable measurement that cannot be implemented by local operations and classical communication (LOCC) unless all the parties come together in a single location. In this work we classify genuinely nonlocal product bases into different categories. Our classification is based on state elimination property of the set via orthogonality-preserving measurements when all the parties a…
Departing from the usual paradigm of local operations and classical communication adopted in entanglement theory, here we study the interconversion of quantum states by means of local operations and shared randomness. A set of necessary and sufficient conditions for the existence of such a transformation between two given quantum states is given in terms of the payoff they yield in a suitable class of nonlocal games. It is shown that, as a consequence of our result, such a class of nonlocal games is able to witness quantum entanglement, however weak, and reveal nonlocality in any entangled qua…
Nonlocal quantum correlation is at the heart of bizarre nature of quantum physics. While there are various classes of nonlocal quantum correlation, steerability of a quantum state by local measurements provides unique operational features. Here, we theoretically and experimentally investigate the hidden quantum steerability. In particular, we find that there are initially unsteerable states which can reveal the steerability by using local filters on individual quantum systems. It is remarkable that a certain set of local filters are more effective on revealing steerability than Bell nonlocalit…
Ensembles containing orthogonal product states are found to be indistinguishable under local operations and classical communication (LOCC), thereby showing irreversibility in the preparation and distinguishing processes, which is commonly known as nonlocality without entanglement. On the other hand, correlations arising from incompatible measurements on entangled states lead to Bell-nonlocality. We unify these two concepts from the change in certain property incurred in the ensemble under a suitable global unitary transformation. Specifically, we prove that under controlled-NOT (CNOT) operatio…
An obstacle affecting any proposal for a topological quantum computer based on Ising anyons is that quasiparticle braiding can only implement a finite (non-universal) set of quantum operations. The computational power of this restricted set of operations (often called stabilizer operations) has been studied in quantum information theory, and it is known that no quantum-computational advantage can be obtained without the help of an additional non-stabilizer operation. Similarly, a bipartite two-qubit system based on Ising anyons cannot exhibit non-locality (in the sense of violating a Bell ineq…
We explore the link between two concepts: the level of violation of a Bell inequality by a quantum state and discrimination between two states by means of restricted classes of operations, such as local operations and classical communication (LOCC) and separable ones. For any bipartite Bell inequality, we show that its value on a given quantum state cannot exceed the classical bound by more than the maximal quantum violation shrunk by a factor related to distinguishability of this state from the separable set by means of some restricted class of operations. We then consider the general scenari…
Local Hamiltonians arise naturally in physical systems. Despite its seemingly `simple' local structure, exotic features such as nonlocal correlations and topological orders exhibit in eigenstates of these systems. Previous studies for recovering local Hamiltonians from measurements on an eigenstate $|ψ\rangle$ require information of nonlocal correlation functions. In this work, we develop an algorithm to determine local Hamiltonians from only local measurements on $|ψ\rangle$, by reformulating the task as an unconstrained optimization problem of certain target function of Hamiltonian parameter…
For two bipartite pure states, we consider the problem of unambiguous identification without classical knowledge on the states. The optimal success probability by means of local operations and classical communication is shown to be less than the maximum attainable by the global measuring scheme.
Simulating high-weight Hamiltonians can convert local noise on the original Hamiltonian into undesirable nonlocal noise on the simulated Hamiltonian. Here we show how starting from two-local Hamiltonian in the presence of non-Markovian noise, a desired computation can be simulated as well as protected using fast pulses, while maintaining an energy gap against the errors created in the process.
We provide a first operational method for checking indistinguishability of orthogonal states by local operations and classical communication (LOCC). This method originates from the one introduced by Ghosh et al. (Phys. Rev. Lett. 87, 5807 (2001) (quant-ph/0106148)), though we deal with pure states. We apply our method to show that an arbitrary complete multipartite orthogonal basis is indistinguishable by LOCC, if it contains at least one entangled state. We also show that probabilistic local distinguishing is possible for full basis if and only if all vectors are product. We employ our method…
We experimentally demonstrate the nonlocal reversal of a partial-collapse quantum measurement on two-photon entangled state. Both the partial measurement and the reversal operation are implemented in linear optics with two displaced Sagnac interferometers, which are characterized by single qubit quantum process tomography. The recovered state is measured by quantum state tomography and its nonlocality is characterized by testing the Bell inequality. Our result will be helpful in quantum communication and quantum error correction.
Non-local observables play an important role in quantum theory, from Bell inequalities and various post-selection paradoxes to quantum error correction codes. Instantaneous measurement of these observables is known to be a difficult problem, especially when the measurements are projective. The standard von Neumann Hamiltonian used to model projective measurements cannot be implemented directly in a non-local scenario and can, in some cases, violate causality. We present a scheme for effectively generating the von Neumann Hamiltonian for non-local observables without the need to communicate and…
Entanglement of two parts of a quantum system is a non-local property unaffected by local manipulations of these parts. It is described by quantities invariant under local unitary transformations. Here we present, for a system of two qubits, a set of invariants which provides a complete description of non-local properties. The set contains 18 real polynomials of the entries of the density matrix. We prove that one of two mixed states can be transformed into the other by single-bit operations if and only if these states have equal values of all 18 invariants. Corresponding local operations can …
We consider the recently proposed "no-go" theorem of Lamata et al [Phys. Rev. Lett. 101, 180506 (2008)] on the impossibility of sequential implementation of global unitary operations with the aid of an itinerant ancillary system and view the claim within the language of Kraus representation. By virtue of an extremely useful tool for analyzing entanglement properties of quantum operations, namely, operator-Schmidt decomposition, we provide alternative proof to the "no-go" theorem and also study the role of initial correlations between the qubits and ancilla in sequential preparation of unitary …
Spatial separation restricts the set of locally implementable quantum operations on distributed multipartite quantum systems. We propose that indefinite causal structure arising due to quantum superposition of different space-time geometries can be used as an independent universal resource for local implementation of any quantum operation on spatially distributed quantum systems. Consequently, all such quantum tasks that are not accomplishable by local operations and classical communication (LOCC) only also become locally accomplishable. We show that exploiting indefinite causal structure as t…
Bell nonlocality describes a manifestation of quantum mechanics that cannot be explained by any local hidden variable model. Its origin lies in the nature of quantum entanglement, although understanding the precise relationship between nonlocality and entanglement has been a notorious open problem. In this paper, we resolve this problem by developing a dynamical framework in which quantum Bell nonlocality emerges as special form of entanglement, and both are unified as resources under local operations and classical communication (LOCC). Our framework is built on the notion of quantum processes…
A dynamic scheme basing on equation for T-matrix momentum transfer spectral density and integral representation for Jost function is proposed for local Dirac Hamiltonians in arbitrary N- dimension spaces and for Schrodinger one with singular or nonlocal generalized Yukawa-type potentials. A generalization of the off-shell-Jost function method for that Hamiltonians and universal renormalization procedure of Jost function calculation for singular and nonlocal potentials is proposed.
