Quantum operations provide a general description of the state changes allowed by quantum mechanics. Simple necessary and sufficient conditions for an ideal quantum operation to be reversible by a unitary operation are derived in this paper. These results generalize recent work on reversible measurements by Mabuchi and Zoller [Phys. Rev. Lett. {\bf 76}, 3108 (1996)]. Quantum teleportation can be understood as a special case of the problem of reversing quantum operations. We characterize completely teleportation schemes of the type proposed by Bennett {\it et al.} [Phys. Rev. Lett. {\bf 70}, 1895 (1993)].
We propose a protocol, based on entanglement procedures recently suggested by [D. Jaksch et al., Phys. Rev. Lett. 82, 1975 (1999)], which allows the teleportation of an unknown state of a neutral atom in an optical lattice to another atom in another site of the lattice, without any irreversible detection.
This paper describes a scheme, through which the quantum information as well as the structural information of a time-reversal invariant system can be teleported over a distance. I show that my teleportation scheme can be viewed as a form of reversible purification process by repeated interactions with an auxiliary quantum system.
We study the Braunstein-Kimble setup for teleportation of quantum state of a single mode of optical field. We assume that the sender and receiver share a two-mode Gaussian state and we identify optimum local Gaussian operations that maximize the teleportation fidelity. We consider fidelity of teleportation of pure Gaussian states and we also introduce fidelity of the teleportation transformation. We show on an explicit example that in some cases the optimum local operation is not a simple unitary symplectic transformation but some more general completely positive map.
We present a feasible scheme to implement the non-deterministic quantum logic operation of Knill, Laflamme and Milburn (Nature, 409, 46-52(2001)) by using a teleportation protocol, which requires only single-photon sources, linear optical elements and photon detectors.
In the standard protocol for quantum teleportation, one assumes that Bob is able to perform ideal operations on his qubit. Here, we analyze the case in which some of these operations are more reliable than others. Moreover, we consider the channel shared by Alice and Bob as non-maximally entangled. In this context, the average fidelity of teleportation can be maximized by properly choosing the basis in which Alice performs her two-qubit measurement.
In our work, we compare three teleportation protocols: the original protocol, the photon subtraction protocol, and the protocol with a cubic phase gate. We evaluate the fidelity of each protocol using the example of teleportation of the squeezed state and the Schrodinger's cat state. We show that, under equal conditions, the teleportation scheme with a cubic phase gate achieves significantly higher fidelity than the other protocols considered.
The standard benchmark for teleportation is the average fidelity of teleportation and according to this benchmark not all states are useful for teleportation. It was recently shown however that all entangled states lead to non-classical teleportation, with there being no classical scheme able to reproduce the states teleported to Bob. Here we study the operational significance of this result. On the one hand we demonstrate that every entangled state is useful for teleportation if a generalization of the average fidelity of teleportation is considered which concerns teleporting quantum correlat…
The progress in quantum operations of continuous-variable (CV) schemes can be reduced to that in CV quantum teleportation. The fidelity of quantum teleportation of an optical setup is limited by the finite degree of quantum correlation which can be prepared with a pair of finitely squeezed states. Reports of improvement of squeezing level have appeared recently, and we adopted the improved methods in our experimental system of quantum teleportation. As a result, we teleported a coherent state with a fidelity $F=0.83\pm 0.01$, which is better than any other figures reported to date. In this pap…
We consider the implementation of an arbitrary unitary operation U upon a distant quantum system. This teleportation of U can be viewed as a quantum remote control. We investigate protocols which achieve this using local operations, classical communication and shared entanglement (LOCCSE). Lower bounds on the necessary entanglement and classical communication are determined using causality and the linearity of quantum mechanics. We examine in particular detail the resources required if the remote control is to be implemented as a classical black box. Under these circumstances, we prove that th…
We study a continuous-variable (CV) teleportation protocol based on a shared entangled state produced by the quantum-nondemolition (QND) interaction of two vacuum states. The scheme utilizes the QND interaction or an unbalanced beam splitter in the Bell measurement. It is shown that in the non-unity gain regime the signal transfer coefficient can be enhanced while the conditional variance product remains preserved by applying appropriate local squeezing operation on sender's part of the shared entangled state. In the unity gain regime it is demonstrated that the fidelity of teleportation can b…
We give a transfer theorem for teleportation based on twisting the entanglement measurement. This allows one to say what local unitary operation must be performed to complete the teleportation in any situation, generalizing the scheme to include overcomplete measurements, non-abelian groups of local unitary operations (e.g., angular momentum teleportation), and the effect of non-maximally entangled resources.
Non-commuting noises may give rise to entanglement sudden death. By considering the decoherence dynamics during establishment of the channel states and noisy recovery operations, we study further the impact of non-commuting noises on single- and two-qubit teleportation. We show that in the presence of these noises there exists a critical rate of recovery operation below which teleportation will fail.
Using invariance of the $n$-th tensored state w.r.t. the $n$-th symmetric group, we propose a 'variable length' universal entanglement concentration without classical communication. Like variable length data compression, arbitrary unknown states are concentrated into perfect Bell states and not approximate Bell states and the number of Bell states obtained is equal to the optimal rate asymptotically with the probability 1. One of the point of our scheme is that we need no classical communication at all. Using this method, we can construct a universal teleportation and a universal dense coding.
In this article, we exploit the different notions of quantumness measure to understand the properties of the Heisenberg XY model with and without PT-symmetric operation. In the absence of PT-symmetry, we study the significance of different measures, namely entanglement and measurement induced nonlocality (MIN), in the detection of the quantumness of the Heisenberg XY model. It is observed that the quantum correlations and teleportation fidelity monotonically decreases with respect to temperature. Furthermore, the intervention of PT-symmetric operation enhances the strengths of quantum correlat…
The scheme for entanglement teleportation is proposed to incorporate multipartite entanglement of four qubits as a quantum channel. Based on the invariance of entanglement teleportation under arbitrary two-qubit unitary transformation, we derive relations of separabilities for joint measurements at a sending station and for unitary operations at a receiving station. From the relations of separabilities it is found that an inseparable quantum channel always leads to a total teleportation of entanglement with an inseparable joint measurement and/or a nonlocal unitary operation.
We present simplification schemes for probabilistic and controlled teleportation of the unknown quantum states of both one-particle and two-particle and construct efficient quantum logic networks for implementing the new schemes by means of the primitive operations consisting of single-qubit gates, two-qubit controlled-not gates, Von Neumann measurement and classically controlled operations. In these schemes the teleportation are not always successful but with certain probability.
A simplification scheme of probabilistic teleportation of two-particle state of general form is given. By means of the primitive operations consisting of single-qubit gates, two-qubit controlled-not gates, Von Neumann measurement and classically controlled operations, we construct an efficient quantum logical network for implementing the new scheme of probabilistic teleportation of a two-particle state of general form.
We firstly present an all-optical scheme to implement the non-deterministic quantum logic operation of Knill, Laflamme and Milburn (Nature, 409, 46-52(2001)). In our scheme, squeezed vacuum state is acted as auxiliary state instead of single photon resources. Then we demonstrate that same setup can be used to teleport a superposition of vacuum and single photon state of the form $α|0>+β|1>$ and a superposition of vacuum and single polarized photon state of the form $α|0>+β|H>+γ|V>$.
Quantum operations provide a general description of the state changes allowed by quantum mechanics. The reversal of quantum operations is important for quantum error-correcting codes, teleportation, and reversing quantum measurements. We derive information-theoretic conditions and equivalent algebraic conditions that are necessary and sufficient for a general quantum operation to be reversible. We analyze the thermodynamic cost of error correction and show that error correction can be regarded as a kind of ``Maxwell demon,'' for which there is an entropy cost associated with information obtain…
Quantum discord is a prominent measure of quantum correlations, playing an important role in expanding its horizon beyond entanglement. Here we provide an operational meaning of (geometric) discord, which quantifies the amount of non-classical correlation of an arbitrary quantum system in terms of its minimal distance from the set of classical states, in terms of teleportation fidelity for general two qubit and $d \otimes d$ dimensional isotropic and Werner states. A critical value of the discord is found beyond which the two qubit state must violate the Bell inequality. This is illustrated by…
We show how to construct a universal set of quantum logic gates using control over exchange interactions and single- and two-spin measurements only. Single-spin unitary operations are teleported instead of being executed directly, thus eliminating a major difficulty in the construction of several of the most promising proposals for solid-state quantum computation, such as spin-coupled quantum dots, donor-atom nuclear spins in silicon, and electrons on helium. Contrary to previous proposals dealing with this difficulty, our scheme requires no encoding redundancy. We also discuss an application …
This study proposes a pioneering protocol for teleporting an arbitrary single particle state and simultaneously performing a rotation operation on that particle. There are protocols for either only teleporting particles or only remotely controlling quantum particles. If one has to remotely control a teleported quantum, then he/she has to first do the quantum teleportation and then perform the remote control on the teleported quantum. Both operations were done separately on two sets of entanglements. However, this intuitive solution is inefficient because many resources are wasted. Therefore, t…
In this paper, different from the other existing methods that only the special and limited numbers of qubits transmit between Alice and Bob, a general method is proposed to implement Bidirectional Quantum Controlled/uncontrolled Teleportation (BQCT/BQT) that Alice and Bob can transmit each type of arbitrary n and m-qubits to each other, simultaneously. This protocol is based on Controlled-NOT (CNOT) operation, appropriate single-qubit unitary operations and single-qubit measurement in the Z-basis and X-basis. Also, the quantum channel can be created by using Hadamard and CNOT operations. One o…
Teleportation is a crucial element in fault-tolerant quantum computation and a complete understanding of its capacity is very important for the practical implementation of optimal fault-tolerant architectures. It is known that stabilizer codes support a natural set of gates that can be more easily implemented by teleportation than any other gates. These gates belong to the so called $\mathcal{C}_k$ hierarchy introduced by Gottesman and Chuang (Nature \textbf{402}, 390). Moreover, a subset of $\mathcal{C}_k$ gates, called semi-Clifford operations, can be implemented by an even simpler architect…
Quantum teleportation schemes in which operations are performed before establishing the quantum channel are not constrained by resource limits set in H.K.Lo and Bennett et al. We compare the standard teleportation protocol to the one proposed by Kak on the basis of the classical communication cost. Due to its unique architecture we study the problems in implementing Kak teleportation protocol.
Large-scale quantum computers will require quantum gate operations between widely separated qubits. A method for implementing such operations, known as quantum gate teleportation (QGT), requires only local operations, classical communication, and shared entanglement. We demonstrate QGT in a scalable architecture by deterministically teleporting a controlled-NOT (CNOT) gate between two qubits in spatially separated locations in an ion trap. The entanglement fidelity of our teleported CNOT is in the interval [0.845, 0.872] at the 95% confidence level. The implementation combines ion shuttling wi…
In the present paper, a novel bidirectional quantum teleportation protocol is proposed. By using entanglement swapping technique, two GHZ states are shared as a quantum channel between Alice and Bob as legitimate users. In this scheme, based on control-not operation, single-qubit measurement and appropriate unitary operations, two users can simultaneously transmit a pure EPR state to each other. While, in the previous protocols, the users can just teleport a single-qubit state to each other via more than four-qubit state. Therefore, the proposed scheme is economical compared with previous prot…
We experimentally demonstrate a programmable quantum gate that applies a sign flip operation to data qubit in an arbitrary basis fully specified by the quantum state of a two-qubit program register. Our linear-optical implementation is inspired by teleportation-based schemes for quantum computing and relies on multiphoton interference and coincidence detection. We confirm the programmability of the gate and its high-fidelity performance by carrying out full quantum process tomography of the resulting operation on data qubit for several different programs.
We consider a single copy of a mixed state of two qubits and derive the optimal trace-preserving local operations assisted by classical communication (LOCC) such as to maximize the fidelity of teleportation that can be achieved with this state. These optimal local operations turn out to be implementable by one-way communication, and always yields a teleportation fidelity larger than 2/3 if the original state is entangled. This maximal achievable fidelity is an entanglement measure and turns out to quantify the minimal amount of mixing required to destroy the entanglement in a quantum state.
The development of techniques for manipulation of quantum information has opened the door to a variety of protocols for accomplishing unprecedented tasks. In particular, a new protocol of quantum teleportation was proposed in 2008 to achieve effective energy transportation simply via local operations and classical communication without breaking any known physical laws. This is achieved by extracting zero-point energy of entangled many-body systems by local operations dependent on information obtained by a distant measurement. The concept is reviewed from an introductory viewpoint herein.
We examine continuous-variable gate teleportation using entangled states made from pure product states sent through a beamsplitter. We show that such states are Choi states for a (typically) non-unitary gate, and we derive the associated Kraus operator for teleportation, which can be used to realize non-Gaussian, non-unitary quantum operations on an input state. With this result, we show how gate teleportation is used to perform error correction on bosonic qubits encoded using the Gottesman-Kitaev-Preskill code. This result is presented in the context of deterministically produced macronode cl…
In general, it is important to identify what is the informational resource for quantum tasks. Quantum energy teleportation (QET) is a quantum task, which attains energy transfer in an operational meaning by local operations and classical communication, and is expected to play a role in future development of nano scale smart grids. We consider QET protocols in a three-element Ising spin system with non periodic boundary conditions coupled to a thermal bath. The open chain is the minimal model of QET between two edge spins that allows the measurement and operation steps of the QET protocol to be…
There are a few obstacles, which bring about imperfect quantum teleportation of a continuous variable state, such as unavailability of maximally entangled two-mode squeezed states, inefficient detection and imperfect unitary transformation at the receiving station. We show that all those obstacles can be understood by a combination of an {\it asymmetrically-decohered} quantum channel and perfect apparatuses for other operations. For the asymmetrically-decohered quantum channel, we find some counter-intuitive results; one is that teleportation does not necessarily get better as the channel is i…
We study the remote implementation of a unitary transformation on a qubit. We show the existence of non-trivial protocols (i.e., using less resources than bidirectional state teleportation) which allow the perfect remote implementation of certain continuous sets of quantum operations. We prove that, up to a local change of basis, only two subsets exist that can be implemented remotely with a non-trivial protocol: Arbitrary rotations around a fixed direction $\vec{n}$ and rotations by a fixed angle around an arbitrary direction lying in a plane orthogonal to $\vec{n}$. The overall classical inf…
We analyze in a critical way the mathematical treatment of a quantum teleportation experiment performed with photon particles, showing that a symmetrization operation over both the polarization and spatial degrees of freedom of all the particles involved is necessary in order to reproduce correctly the observed experimental data.
Quantum teleportation with partially entangled joint measurements induced by coherent errors
Korea Institute of Science and Technology (KIST)（韩国科学技术院）；Kyung Hee University（庆熙大学）；Korea University of Science and Technology (UST)（韩国科学技术院）；Korea Institute for Advanced Study（韩国高等研究院）；Pohang University of Science and Technology (POSTECH)（浦项工科大学）
Using the quantum teleportation in continuous variables as a test scheme, we compare two entangled transformations - mixing of signals on a beamsplitter and by the CZ operation. We evaluate these transformations in terms of the errors added to teleported oscillators. We have shown that the CZ operation leads to the lower error of teleportation. This error can be further reduced by choosing appropriate weight coefficients for the CZ transforms. We have compared the errors of the theoretical CZ scheme and its practical implementation in the optical design. Although the CZ optical scheme adds int…
We establish the optimal quantum teleportation protocol for the realistic scenario when both input state and quantum channel are afflicted by noise. In taking these effects into account higher fidelities are achieved. The optimality of the proposed protocol prevails even when restricted to a reduced set of generically available operations.
We describe a reversible quantum interface between an optical and a microwave field using a hybrid device based on their common interaction with a micro-mechanical resonator in a superconducting circuit. We show that, by employing state-of-the-art opto-electro-mechanical devices, one can realise an effective source of (bright) two-mode squeezing with an optical idler (signal) and a microwave signal, which can be used for high-fidelity transfer of quantum states between optical and microwave fields by means of continuous variable teleportation.
The scheme for probabilistic teleportation of an N-particle state of general form is proposed. As the special cases we construct efficient quantum logic networks for implementing probabilistic teleportation of a two-particle state, a three-particle state and a four-particle state of general form, built from single qubit gates, two-qubit controlled-not gates, Von Neumann measurement and classically controlled operations.
Teleportation protocol is conventionally treated as a method for quantum state transfer between two spatially separated physical carriers. Recent experimental progress in manipulation with high-dimensional quantum systems opens a new framework for implementation of teleportation protocols. We show that the one-qubit teleportation can be considered as a state transfer between subspaces of the whole Hilbert space of an indivisible eight-dimensional system. We explicitly show all corresponding operations and discuss an alternative way of implementation of similar tasks.
We show that the phenomenon of superadditivity of distillable entanglement observed in multipartite quantum systems results from the consideration of states created during the execution of the standard end-to-end quantum teleportation protocol (and a few additional local operations and classical communication (LOCC) steps) on a linear chain of singlets. Some of these intermediate states are tensor products of bound-entangled (BE) states, and hence, by construction possess distillable entanglement, which can be unlocked by simply completing the rest of the LOCC operations required by the underl…
We report on the experimental quantum teleportation of strongly nonclassical wave packets of light. To perform this full quantum operation while preserving and retrieving the fragile non-classicality of the input state, we have developed a broadband, zero-dispersion teleportation apparatus that works in conjunction with time-resolved state preparation equipment. Our approach brings within experimental reach a whole new set of hybrid protocols involving discrete- and continuous-variable techniques in quantum information processing for optical sciences.
We investigate a game where a sender (Alice) teleports coherent states to two receivers (Bob and Charlie) through a tripartite Gaussian state. The aim of the receivers is to optimize their teleportation fidelities by means of local operations and classical communications. We show that a non-cooperative strategy, corresponding to the standard telecloning protocol, can be outperformed by a cooperative strategy, which gives rise to a novel (cooperative) telecloning protocol.
We analyse quantum teleportation (QT) and entanglement swapping (ES) for spin systems. If the permitted operations are restricted to the Ising interaction, plus local rotations and spin measurements, high-fidelity teleportation is achievable for quantum states that are close to the maximally weighted spin state. ES is achieved, and is maximized for a combination of entangled states and Bell measurements that is different from the QT case. If more general local unitary transformations are considered, then it is possible to achieve perfect teleportation and ES.
Quantum entanglement, like othre resources, is now coonsidered to be a resource which can be produced, concentrated if required, transported and consumed. After its inception [1] in 1933, various schemes of quantum state teleportation have been proposed using different types of channels. Not restricting to qubit based systems, qutrit states and channels have also been of considerable interest. In the present paper we investigate the teleportation of an unknown single qutrit state as well as two qutrit state through a three qutrit quantum channel along with the required operations to recover th…
EPR steering is an important quantum resource in quantum information and computation. In this paper, its applications in quantum teleportation are investigated. First of all, the upper bound of the average teleportation fidelity based on the EPR steering is derived. When the receiver can only perform the identity or the Pauli rotation operations, the X-type states which violate the three-setting linear steering inequality could be used for teleportation. In the end, the steering observables and the average teleportation fidelities of the two-qubit reduced states for three-qubit pure states mai…
We investigate the resources needed for secure teleportation of coherent states. We extend continuous variable teleportation to include quantum tele-amplification protocols, that allow non-unity classical gains and a pre-amplification or post-attenuation of the coherent state. We show that, for arbitrary Gaussian protocols and a significant class of Gaussian resources, two-way steering is required to achieve a teleportation fidelity beyond the no-cloning threshold. This provides an operational connection between Gaussian steerability and secure teleportation. We present practical recipes sugge…
In quant-ph/0201134 Jennewein et al. report experiments demonstrating entanglement swapping under various conditions. In one instance, they claim to have exhibited Bell inequality violations by a pair of photons prior to performing any entangling operations on the pair. However, the Bell inequality violation results in this case from post-selection of the data, not from quantum non-locality.
We show that a universal set of gates for quantum computation with optics can be quantum teleported through the use of EPR entangled states, homodyne detection, and linear optics and squeezing operations conditioned on measurement outcomes. This scheme may be used for fault-tolerant quantum computation in any optical scheme (qubit or continuous variable). The teleportation of nondeterministic nonlinear gates employed in linear optics quantum computation is discussed.
We present a method to create a variety of interesting gates by teleporting quantum bits through special entangled states. This allows, for instance, the construction of a quantum computer based on just single qubit operations, Bell measurements, and GHZ states. We also present straightforward constructions of a wide variety of fault-tolerant quantum gates.
