本文研究了远程态制备任务中纠缠和通信成本的权衡问题，提出了针对混合态的近似匹配上下界，展示了纯纠缠态在通信成本为o(d)时可提取log d ebits纠缠，反之亦然。
摘要：
我们研究了以下任务：Alice被给出一个秩为k的投影算子P在C^d上的经典描述，Alice和Bob希望通过共享的纠缠和经典通信在Bob的一侧制备量子态P/k。该任务的一般形式称为远程态制备（RSP）。我们为RSP的P/k态的纠缠成本和通信成本给出了近似的下界和上界。我们的结果是首次针对混合态RSP的近似匹配上下界，在纯态的特殊情况下，我们的下界优于已知的最佳下界。我们的结果表明，任何能够用o(d)比特通信进行这些态RSP的纯纠缠态，可以提取log d ebits的纠缠；反之，任何能够提取log d ebits纠缠的状态都可以高效地用于这些态的RSP。作为我们的结果的应用，我们重新推导了形式为P/k的态的不可压缩性结果，并给出了一个新的基于纠缠的通信协议，用于等式函数，该协议使用1/2 log n + O(1)个ebits和O(1)的通信。
英文摘要：
We study the following task: Alice is given a classical description of a rank-$k$ projector $P$ on $\mathbb{C}^d$, and Alice and Bob want to prepare the quantum state $P/k$ on Bob's side using shared entanglement and classical communication. The general form of this task is known as remote state preparation (RSP). We give nearly-matching lower and upper bounds for the entanglement cost and communication cost for RSP of the states $P/k$. Ours are the first nearly matching upper and lower bounds for RSP of mixed states, and in the special case of pure states, our lower bound outperforms the best previously known lower bound. Our results show that any pure entangled state that can be used to do RSP of these states with $o(d)$ bits of communication, can distill $\log d$ ebits of entanglement, and conversely, any state that can distill $\log d$ ebits of entanglement can be used to do RSP of these states efficiently. As applications of our results, we rederive a previously-known incompressibility result for states of the form $P/k$, and give a new entanglement-assisted communication protocol for the equality function that uses $\frac{1}{2}\log n + O(1)$ many ebits, and $O(1)$ communication.
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.
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.
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.
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…
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…
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 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 …
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 present a scheme for optimal joint remote state preparation of two-qubit equatorial states. Our protocol improves on a previous scheme (B. S. Choudhury and A. Dhara 2015 Quantum Inf. Process. 14 373) that had a success probability of 25%, which increased to 50% when extra classical information is sent to the receiver. We show that using our modified scheme, the desired state can be prepared deterministically with the same quantum channel. Moreover, we generalize the scheme to prepare N-qubit equatorial states in which the receiver can reconstruct the original state with 100% success probabi…
We introduce a new multipartite communication scheme, with the aim to enable the senders to remotely and obliviously provide the receivers with an arbitrary amount of multipartite entanglement. The scheme is similar to Remote State Preparation (RSP). However, we show that even though the receivers are restricted to local unitary operations, the required resources for remote entanglement preparation are less than for RSP. In order to do so we introduce a novel canonical form of arbitrary multipartite pure states describing an arbitrary number of qubits. Moreover, we show that if the receivers a…
We consider remote state preparation protocols for a set of pure states whose projectors form a basis for operators acting on the input Hilbert space. If a protocol (1) uses only forward communication and entanglement, (2) deterministically prepares an exact copy of the state, and (3) does so obliviously -- without leaking further information about the state to the receiver -- then the protocol can be modified to require from the sender only a single specimen of the state. Furthermore, the original protocol and the modified protocol use the same amount of classical communication. Thus, under t…
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…
We present a two-step exact remote state preparation protocol of an arbitrary qubit with the aid of a three-particle Greenberger-Horne-Zeilinger state. Generalization of this protocol for higher-dimensional Hilbert space systems among three parties is also given. We show that only single-particle von Neumann measurement, local operation and classical communication are necessary. Moreover, since the overall information of the quantum state can be divided into two different parts, which may be at different locations, this protocol may be useful in the quantum information field.
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 t…
We present many ensembles of states that can be remotely prepared by using minimum classical bits from Alice to Bob and their previously shared entangled state and prove that we have found all the ensembles in two-dimensional case. Furthermore we show that any pure quantum state can be remotely and faithfully prepared by using finite classical bits from Alice to Bob and their previously shared nonmaximally entangled state though no faithful quantum teleportation protocols can be achieved by using a nonmaximally entangled state.
Memory effect of non-Markovian dynamics in open quantum systems is often believed to be beneficial for quantum information processing. In this work, we employ an experimentally controllable two-photon open system, with one photon experiencing a dephasing environment and the other being free from noise, to show that non-Markovian effect may also have a negative impact on quantum tasks such as remote state preparation: For a certain period of controlled time interval, stronger non-Markovian effect yields lower fidelity of remote state preparation, as opposed to the common wisdom that more inform…
Quantum teleportation faces increasingly demanding requirements for transmitting large or even entangled systems. However, knowledge of the state to be transmitted eases its reconstruction, resulting in a protocol known as remote state preparation. A number of experimental demonstrations to date have been restricted to single-qubit systems. We report the remote preparation of two-qubit "hybrid" entangled states, including a family of vector-polarization beams. Our single-photon states are encoded in the photon spin and orbital angular momentum. We reconstruct the states by spin-orbit state tom…
Herein, we present a feasible, general protocol for quantum communication within a network via generalized remote preparation of an arbitrary $m$-qubit entangled state designed with genuine tripartite Greenberger--Horne--Zeilinger-type entangled resources. During the implementations, we construct novel collective unitary operations; these operations are tasked with performing the necessary phase transfers during remote state preparations. We have distilled our implementation methods into a five-step procedure, which can be used to faithfully recover the desired state during transfer. Compared …
Remote state preparation (RSP) provides an indirect way of manipulating quantum information based on the nonlocal effect of quantum measurement. Although RSP has been demonstrated in recent years to remotely prepare multi-photon states, quantum measurement on the same number of photons was required, i.e., to prepare N-photon states via RSP, quantum measurement on the other N-photons was required, hence significantly limiting practicality and applicability of RSP. Here we report the first experimental demonstration of remote preparation of three-photon entangled states by measuring only a singl…
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 …
How to uses shared entanglement and forward classical communication to remotely prepare an arbitrary (mixed or pure) state has been fascinating quantum information scientists. A constructive scheme has been given by Berry for remotely preparing a general pure state with a pure entangled state and finite classical communication. Based on this scheme, for high-dimensional systems it is possible to use a coding of the target state to optimize the classical communication cost. Unfortunately, for low-dimensional systems such as a pure qubit the coding method is inapplicable. Because qubit plays a c…
Transferring quantum information between distant nodes of a network is a key capability. This transfer can be realized via remote state preparation where two parties share entanglement and the sender has full knowledge of the state to be communicated. Here we demonstrate such a process between heterogeneous nodes functioning with different information encodings, i.e., particle-like discrete-variable optical qubits and wave-like continuous-variable ones. Using hybrid entanglement of light as a shared resource, we prepare arbitrary coherent-state superpositions controlled by measurements on the …
We have experimentally implemented remote state preparation (RSP) of a qubit from a hydrogen to a carbon nucleus in molecules of carbon-13 labeled chloroform $^{13}$CHCl$_{3}$ over interatomic distances using liquid-state nuclear magnetic resonance (NMR) technique. Full RSP of a special ensemble of qubits, i.e., a qubit chosen from equatorial and polar great circles on a Bloch sphere with Pati's scheme, was achieved with one cbit communication. Such a RSP scheme can be generalized to prepare a large number of qubit states and may be used in other quantum information processing and quantum comp…
We present a strategy for implementing multiparty-controlled remote state preparation (MCRSP) for a family of four-qubit cluster-type states with genuine entanglements while employing, Greenberg-Horne-Zeilinger-class states as quantum channels. In this scenario, the encoded information is transmitted from the sender to a spatially separated receiver via the control of multi-party. Predicated on the collaboration of all participants, the desired state can be entirely restored within the receiver's place with high success probability by application of appropriate local operations and necessary c…
The aim of this paper is to define in theoretical terms and summarise the available experimental evidence that physical and mental "objects", if considered "information units", may present similar classical and quantum models of communication beyond their specific characteristics. Starting with the Remote State Preparation protocol, a variant of the Teleportation protocol, for which formal models and experimental evidence are already available in quantum mechanics, we outline a formal model applied to mental information we defined Remote State Preparation of Mental Information (RSPMI), and we …
Transmission of quantum states is a central task in quantum information science. Remote state preparation (RSP) has the same goal as teleportation, i.e. transferring quantum information without sending physically the information carrier, but in RSP the sender knows the state which is to be transmitted. We present experimental demonstrations of RSP for two and three locations. In our experimental scheme Alice (the preparer) and her three partners share four and six photon polarization entangled singlets. This allows us to perform RSP of two or three copies of a single qubit states, a two qubit …
A necessary and sufficient condition is given for general exact remote state preparation (RSP) protocols to be oblivious, that is, no information about the target state can be retrieved from the classical message. A novel criterion in terms of commutation relations is also derived for the existence of deterministic exact protocols in which Alice's measurement eigenstates are related to each other by fixed linear operators similar to Bob's unitaries. For non-maximally entangled resources, it provides an easy way to search for RSP protocols. As an example, we show how to reduce the case of parti…
Remote state preparation (RSP) provides a useful way of transferring quantum information between two distant nodes based on the previously shared entanglement. In this paper, we study RSP of an arbitrary single-photon state in two degrees of freedom (DoFs). Using hyper-entanglement as a shared resource, our first goal is to remotely prepare the single-photon state in polarization and frequency DoFs and the second one is to reconstruct the single-photon state in polarization and time-bin DoFs. In the RSP process, the sender will rotate the quantum state in each DoF of the photon according to th…
