The hidden cost of quantum teleportation and remote state preparation
R. Srikanth
备注：
We introduce remote state preparation as equivalent to the ontic aspect of quantum teleportation, as regards the hidden cost. This frees our discussion from the epistemological difficulty of characterizing the unknown quantum state; 3 new references; 4 pages, no figures, REVTeX
The amount of information transferred during standard quantum teleportation or remote state preparation is equal to the preparation information of the transmitted state, rather than the classical communication required by respective protocol. This is shown by noting that the information required to specify the operation that verifies the transmitted state is identical to the preparation information, at the given level of precision m (in bits). Depending on the resolution of the projective Hilbert space, the preparation information can be made arbitrarily precise and hence indefinitely larger than the classical communication cost. Therefore, the classical communication is insufficient to account for the transfer of preparation information, which is then attributed to the Einstein-Podolsky-Rosen channel. Some fundamental repercussions for relativistic quantum information processing are briefly discussed.
Continuous variable remote state preparation and teleportation are analyzed using Wigner functions in phase space. We suggest a remote squeezed state preparation scheme between two parties sharing an entangled twin beam, where homodyne detection on one beam is used as a conditional source of squeezing for the other beam. The scheme works also with noisy measurements, and provide squeezing if the homodyne quantum efficiency is larger than 50%. Phase space approach is shown to provide a convenient framework to describe teleportation as a generalized conditional measurement, and to evaluate relev…
We demonstrate an experimental realization of remote state preparation via the quantum teleportation algorithm, using an entangled photon pair in the polarization degree of freedom as the quantum resource. The input state is encoded on the path of one of the photons from the pair. The improved experimental scheme allows us to control the preparation and teleportation of a state over the entire Bloch sphere with a resolution of the degree of mixture given by the coherence length of the photon pair. Both the preparation of the input state and the implementation of the quantum gates are performed…
One of the most important applications of quantum physics is quantum teleportation, the possibility to transfer quantum states over arbitrary distances. In this paper, we address the idea of remote sensing in a teleportation scenario with topological qubits more robust against noise. We also investigate the enhancement of quantum teleportation through non-local characteristics of the topological qubits. In particular, we show that how this nonlocal property, helps us to achieve near-perfect quantum teleportation even with mixed quantum states. Considering the limitations imposed by decoherence…
The hitherto unexplored nonlocality of quantum correlations in the information transfer protocol of remote state preparation (RSP) is investigated in terms of a unified nonlocality argument formulated for teleportation as well as for two distinct RSP schemes. The argument differs only in the respective types of local measurements used in each scenario. One of the RSP schemes uses single particle projective measurements, while the other uses joint Bell-basis measurements. Interestingly, the quantum mechanical violations of the Bell-CHSH type inequalities formulated for each of the RSP setups, w…
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…
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…
Quantum discord and quantum entanglement are resources in some quantum information processing (QIP) models. However, in recent years, the evidence that separable states or classically correlated states can also accomplish QIP is demonstrated. It provides a useful tool since such states are easier to prepare. Quantum coherence is a measure of non-classical correlation, containing entanglement and discord as a subset. Nowadays, it is of interest whether quantum coherence can act as a resource in QIP independently or not, without the help from quantum discord or entanglement. In this paper, we sh…
We demonstrate teleportation of quantum bits between two single atoms in distant laboratories. Using a time-resolved photonic Bell-state measurement, we achieve a teleportation fidelity of (88.0+/-1.5)%, largely determined by our entanglement fidelity. The low photon collection efficiency in free space is overcome by trapping each atom in an optical cavity. The resulting success probability of 0.1% is almost 5 orders of magnitude larger than in previous experiments with remote material qubits. It is mainly limited by photon propagation and detection losses and can be enhanced with a cavity-bas…
Quantum teleportation enables the deterministic exchange of qubits via lossy channels. While it is commonly believed that unconditional teleportation requires a preshared entangled qubit pair, here we demonstrate a protocol that is in principle unconditional and requires only a single photon as an ex-ante prepared resource. The photon successively interacts, first, with the receiver and then with the sender qubit memory. Its detection, followed by classical communication, heralds a successful teleportation. We teleport six mutually unbiased qubit states with average fidelity $\overline{\text{F…
Remote spatial indistinguishability of identical subsystems as a direct controllable quantum resource at distant sites has not been yet experimentally proven. We design a setup capable to tune the spatial indistinguishability of two photons by independently adjusting their spatial distribution in two distant regions, which leads to polarization entanglement starting from uncorrelated photons. The amount of entanglement uniquely depends on the degree of remote spatial indistinguishability, quantified by an entropic measure $\mathcal{I}$, which enables teleportation with fidelities above the cla…
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…
Most protocols for Quantum Information Processing consist of a series of quantum gates, which are applied sequentially. In contrast, interactions, for example between matter and fields, as well as measurements such as homodyne detection of light, are typically continuous in time. We show how the ability to perform quantum operations continuously and deterministically can be leveraged for inducing non-local dynamics between two separate parties. We introduce a scheme for the engineering of an interaction between two remote systems and present a protocol which induces a dynamics in one of the pa…
In this work we consider a quantum network consisting of nodes and entangled states connecting the nodes. In evrey node there is a single player. The players at the intermediate nodes carry out measurements to produce an entangled state between the initial and final node. Here we address the problem that how much classical as well as quantum information can be sent from initial node to final node. In this context, we present strong theorems along with proosf, which state that how the teleportation capability of this remotely prepared state is linked up with the fidelities of teleportation of t…
In quantum teleportation, neither Alice nor Bob acquires any classical knowledge on teleported states. The teleportation protocol is said to be oblivious to both parties. In remote state preparation (RSP) it is assumed that Alice is given complete classical knowledge on the state that is to be prepared by Bob. Recently, Leung and Shor showed that the same amount of classical information as that in teleportation needs to be transmitted in any exact and deterministic RSP protocol that is oblivious to Bob. We study similar RSP protocols, but not necessarily oblivious to Bob. First it is shown tha…
We quantify and analyze the controller's power in controlled remote state preparation schemes. Our analysis provides a lower bound on the control power required for controlled remote preparation of arbitrary D-dimensional states. We evaluate several existing controlled remote state preparation protocols and show that some proposed non-maximally entangled channels are not suitable for perfect controlled remote preparation of arbitrary quantum states from the con- troller's point of view. We find that for remotely preparing D-dimensional states, the entropy of each controller should be no less t…
We present a scheme of remote preparation of the two-particle state by using two Einstein-Podolsky-Rosen pairs or two partial entangled two-particle states as the quantum channel. The probability of the successful remote state preparation is obtained.
We experimentally demonstrate the first remote state preparation of arbitrary single-qubit states, encoded in the polarization of photons generated by spontaneous parametric downconversion. Utilizing degenerate and nondegenerate wavelength entangled sources, we remotely prepare arbitrary states at two wavelengths. Further, we derive theoretical bounds on the states that may be remotely prepared for given two-qubit resources.
Future quantum internet applications will derive their power from the ability to share quantum information across the network. Quantum teleportation allows for the reliable transfer of quantum information between distant nodes, even in the presence of highly lossy network connections. While many experimental demonstrations have been performed on different quantum network platforms, moving beyond directly connected nodes has so far been hindered by the demanding requirements on the pre-shared remote entanglement, joint qubit readout and coherence times. Here we realize quantum teleportation bet…
We use photon pairs hyperentangled in polarization and orbital angular momentum to implement a novel entanglement-enhanced quantum state communication technique, known as SuperDense Teleportation, to communicate a specific class of single-photon ququart states between two remote parties, with an average fidelity of 87.0(1)%, almost twice the classical limit of 44%. We compare this technique with quantum teleportation and remote state preparation and show that SuperDense teleportation requires less classical information and fewer experimental resources. We discuss the information content of thi…
We discuss the exact remote state preparation protocol of special ensembles of qubits at multiple locations. We also present generalization of this protocol for higher dimensional Hilbert space systems for multiparties. Using the `dark states', the analogue of singlet EPR pair for multiparties in higher dimension as quantum channel, we show several instances of remote state preparation protocol using multiparticle measurement and classical communication.
We consider the problem of remote state preparation recently studied in several papers. We study the communication complexity of this problem, in the presence of entanglement and in the scenario of single use of the channel.
It has been shown [M.-Y. Ye, Y.-S. Zhang, and G.-C. Guo, Phys. Rev. A 69, 022310 (2004)] that it is possible to perform exactly faithful remote state preparation using finite classical communication and any entangled state with maximal Schmidt number. Here we give an explicit procedure for performing this remote state preparation. We show that the classical communication required for this scheme is close to optimal for remote state preparation schemes of this type. In addition we prove that it is necessary that the resource state have maximal Schmidt number.
We prove that it is possible to remotely prepare an ensemble of non-commuting mixed states using communication equal to the Holevo information for this ensemble. This remote preparation scheme may be used to convert between different ensembles of mixed states in an asymptotically lossless way, analogous to concentration and dilution for entanglement.
An upper bound on the low-entanglement remote state preparation (RSP) ebits vs. bits tradeoff curve (Bennett et al.,quant-ph/0006044) is found using techniques of classical information theory. We prove our coding scheme to be optimal amongst an important class of protocols, and conjecture the bound to be tight.
The process of quantum state teleportation is described from the point of view of the properties of projections onto one-dimensional subspaces. It is introduced as a generalization of the remote preparation of a known state by use of an EPR pair. The discrete and continuous cases are treated in a unified way. The conceptual and calculational simplicity is pedagogically advantageous.
When a subset of particles in an entangled state is measured, the state of the subset of unmeasured particles is determined by the outcome of the measurement. This first measurement may be thought of as a state preparation for the remaining particles. In this paper, we examine how the duration of the first measurement effects the state of the unmeasured subsystem. The state of the unmeasured subsytem will be a pure or mixed state depending on the nature of the measurement. In the case of quantum teleportation we show that there is an eigenvalue equation which must be satisfied for accurate tel…
Known quantum pure states of a qudit can be remotely prepared onto a group of particles of qubits exactly or probabilistically with the aid of two-level Einstein-Podolsky-Rosen states. We present a protocol for such kind of remote state preparation. We are mainly focused on the remote preparation of the ensembles of equatorial states and those of states in real Hilbert space. In particular, a kind of states of qudits in real Hilbert space have been shown to be remotely prepared in faith without the limitation of the input space dimension.
An interesting aspect of multipartite entanglement is that for perfect teleportation and superdense coding, not the maximally entangled W states but a special class of non-maximally entangled W-like states are required. Therefore, efficient preparation of such W-like states is of great importance in quantum communications, which has not been studied as much as the preparation of W states. In this letter, we propose a simple optical scheme for efficient preparation of large-scale polarization based entangled W-like states by fusing two W-like states or expanding a W-like state with an ancilla p…
We propose a new generalized remote state preparation protocol for using non-maximally entangled state as a shared resource. Different from the previous schemes, the parameters of measurement basis depend on not only the state of preparation but also the state of quantum channel. The advantage of the present protocols is that, by constructing a set of appropriate mutually orthogonal measurement basis, the success probability is improved. It is worthwhile noticing that the probability of success is determined by Alice's measurement. If Alice's measurement is appropriate, the remote preparation …
We present a practical and general scheme of remote preparation for pure and mixed state, in which an auxiliary qubit and controlled-NOT gate are used. We discuss the remote state preparation (RSP) in two important types of decoherent channel (depolarizing and dephaseing). In our experiment, we realize RSP in the dephaseing channel by using spontaneous parametric down conversion (SPDC), linear optical elements and single photon detector.
It is shown that a realistic, controlled bidirectional remote state preparation is possible using a large class of entangled quantum states having a particular structure. Existing protocols of probabilistic, deterministic and joint remote state preparation are generalized to obtain the corresponding protocols of controlled bidirectional remote state preparation (CBRSP). A general way of incorporating the effects of two well known noise processes, the amplitude-damping and phase-damping noise, on the probabilistic CBRSP process is studied in detail by considering that noise only affects the tra…
We propose a deterministic remote state preparation scheme for photon polarization qubit states, where entanglement, local operations and classical communication are used. By consuming one maximally entangled state and two classical bits, an arbitrary (either pure or mixed) qubit state can be prepared deterministically at a remote location. We experimentally demonstrate the scheme by remotely preparing 12 pure states and 6 mixed states. The fidelities between the desired and achieved states are all higher than 0.99 and have an average of 0.9947.
We propose two controlled remote state preparation protocols via partially entangled channels. One prepares a single-qubit state and the other prepares a two-qubit state. Different from other controlled remote state preparation schemes which also utilize partially entangled channels, neither auxiliary qubits nor two-qubit unitary transformations are required in our schemes and the success probabilities are independent of the coefficients of the quantum channel. The success probabilities are 50% and 25% for arbitrary single-qubit states and two-qubit states, respectively. We also show that the …
We propose and experimentally verify a novel method for the remote preparation of entangled bits (ebits) made of a single-photon coherently delocalized in two well-separated temporal modes. The proposed scheme represents a remotely tunable source for tailoring arbitrary ebits, whether maximally or non-maximally entangled, which is highly desirable for applications in quantum information technology. The remotely prepared ebit is studied by performing homodyne tomography with an ultra-fast balanced homodyne detection scheme recently developed in our laboratory.
Using the negativity as an entanglement measure, we investigate the possible amount of remotely prepared entanglement. For two identical isotropic states on two-qudit systems 12 and 34, we calculate the average amount of entanglement remotely distributed on the system 13 by joint measurement on the system 24, and show that the remote preparation of entanglement by the generalized Bell-measurement is optimal among rank-one measurements if the isotropic states have a certain fidelity with a maximally entangled state in higher dimensional quantum systems, or if the fidelity of the isotropic state…
Quantum teleportation provides a way to transmit unknown quantum states from one location to another. In the quantum world, multilevel systems which enable high-dimensional systems are more prevalent. Therefore, to completely rebuild the quantum states of a single particle remotely, one needs to teleport multilevel (high-dimensional) states. Here, we demonstrate the teleportation of high-dimensional states in a three-dimensional six-photon system. We exploit the spatial mode of a single photon as the high-dimensional system, use two auxiliary entangled photons to realize a deterministic three-…
Storage and distribution of quantum information are key elements of quantum information processing and quantum communication. Here, using atom-photon entanglement as the main physical resource, we experimentally demonstrate the preparation of a distant atomic quantum memory. Applying a quantum teleportation protocol on a locally prepared state of a photonic qubit, we realized this so-called remote state preparation on a single, optically trapped 87Rb atom. We evaluated the performance of this scheme by the full tomography of the prepared atomic state, reaching an average fidelity of 82%.
We investigate all possible noise environments for controlled remote state preparation. We find that the optimal efficiency is not only dependent on the isolate decay rate but also dependent on the coupling term of environments. Such a coupling provides a clue to control the noisy quantum system for realistic quantum communication. We show that, furthermore, the noise channel can be used as an important resource for quantum information tasks. Especially, an approach is proposed to realize a perfect controlled remote state preparation under the noisy effects environments by choosing the noisy e…
We discuss the structure of teleportation. By associating matrices to the preparation and measurement states, we show that for a unitary transformation M there is a full teleportation procedure for obtaining M|S> from a given state |S>. The key to this construction is a diagrammatic intepretation of matrix multiplication that applies equally well to a topological composition of a maximum and a minimum that underlies the structure of the teleportation. This paper is a preliminary report on joint work with H. Carteret and S. Lomonaco.
Photon pairs produced in spontaneous parametric down-conversion are naturally entangled in their transverse spatial degrees of freedom including the orbital angular momentum. Pumping a non-linear crystal with a zero order Gaussian mode produces quantum correlated signal and idler photons with equal orbital angular momentum and opposite signs. Measurements performed on one of the photons prepares the state of the other remotely. We study the remote state preparation in this system from the perspective of its potential application to Quantum Thermodynamics.
A qubit chosen from equatorial or polar great circles on a Bloch sphere can be remotely prepared with an Einstain-Podolsky-Rosen (EPR) state shared and a cbit communication. We generalize this protocal into an arbitrary longitudinal qubit on the Bloch sphere in which the azimuthal angle phi can be an arbitrary value instead of only being zero. The generalized scheme was experimentally realized using liquid-state nuclear magnetic resonance (NMR) techniques. Also, we have experimentally demonstrated remote state measurement (RSM) on an arbitary qubit proposed by Pati.
In this paper we discuss a quantum multi-tasking protocol for preparation of known one-qubit and two-qubit states respectively in two different locations. The ideal remote state preparation protocol is discussed in the first place in which a five-qubit entangled state is utilized. The design for the preparation of such entanglement is also presented and run on IBM quantum composer platform. The effects of three types of noises on the protocol are discussed and in all these cases the reduced fidelities of the process are calculated. The variations of these fidelities with respect to different p…
Optical beams with periodic lattice structures have broadened the study of structured waves. In the present work, we generate spin-orbit entangled photon states with a lattice structure and use them in a remote state preparation protocol. We sequentially measure spatially-dependent correlation rates with an electron-multiplying intensified CCD camera and verify the successful remote preparation of spin-orbit states by performing pixel-wise quantum state tomography. Control of these novel structured waves in the quantum regime provides a method for quantum sensing and manipulation of periodic s…
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 propose various protocols for joint remotely prepare a four-dimensional quantum state by using two- and three-particle four-dimensional entangled state as the quantum channel. The single- and two-particle generalized projective measurement and the appropriate unitary operation are needed in our protocols. It is shown that the receiver can reconstruct the unknown original state only if two senders collaborate with each other.
We prove a powerful theorem for tripartite remote entanglement distribution protocols that establishes an upper bound on the amount of entanglement of formation that can be created between two single-qubit nodes of a quantum network. Our theorem also provides an operational interpretation of concurrence as a type of entanglement capacity.
We present a scheme in which any pure qubit $|ϕ=\cosθ|0+\sinθe^{i\varp hi}|1$ could be remotely prepared by using minimum classical bits and the previously shared non-maximally entangled states, on condition that the receiver holds the knowledge of $θ$. Several methods are available to check the trade-off between the necessary entanglement resource and the achievable fidelity.
We extend exact deterministic remote state preparation (RSP) with minimal classical communication to quantum systems of continuous variables. We show that, in principle, it is possible to remotely prepare states of an ensemble that is parameterized by infinitely many real numbers, i.e., by a real function, while the classical communication cost is one real number only. We demonstrate continuous variable RSP in three examples using (i) quadrature measurement and phase space displacement operations, (ii) measurement of the optical phase and unitaries shifting the same, and (iii) photon counting …
Quantum information theory has revolutionized the way in which information is processed using quantum resources such as entangled states, local operations and classical communications. Two important protocols in quantum communications are quantum teleportation and remote state preparation. In quantum teleportation neither the sender nor the receiver know the identity of a state. In remote state preparation the sender knows the state which is to be remotely prepared without ever physically sending the object or the complete classical description of it. Using one unit of entanglement and one cla…
The role played by quantum discord in mixed-state computation is widely debated since, in spite of evidence of its importance in creating quantum advantages, even in the absence of entanglement, there are not direct proofs of its necessity in these computational tasks. Recently the presence of discord was shown to be necessary and sufficient for remote state preparation for a broad class of quantum channels [B. Dakić et al., Nat. Phys. 8, 666 (2012)]. Here, we show that this property is not universal. There are states whose discord cannot be considered as a quantum resource, since it has been …
An electromagnetic field quadrature measurement, performed on one of the modes of the nonlocal single-photon state $a|1,0>-b|0,1>$, collapses it into a superposition of the single-photon and vacuum states in the other mode. We use this effect to implement remote preparation of arbitrary single-mode photonic qubits conditioned on observation of a preselected quadrature value. The quantum efficiency of the prepared qubit can be higher than that of the initial single photon.
This paper proves that the remote state preparation (RSP) scheme in real Hilbert space can only be implemented when the dimension of the space is 2,4 or 8. This fact is shown to be related to the parallelazablity of the $n$-1 dimensional sphere $S^{n-1}$. When the dimension is 4 and 8 the generalized scheme is explicitly presented. It is also shown that for a given state with components having the same norm, RSP can be generalized to arbitrary dimension case.
Remote state preparation (RSP) enables a sender to remotely prepare the quantum state of a receiver without sending the state itself. Recently, it has been recognized that quantum discord is a necessary resource for RSP. Here, we theoretically and experimentally investigate whether RSP can outperform dynamic classical remote state preparation processes. We show that such classical processes can describe certain RSPs powered by quantum discord. Rather, we argue that a new kind of Einstein-Podolsky-Rosen steering for dynamical processes, called quantum process steering, is the resource required …
