Continuous Variable Teleportation Research Articles

Limited quantum advantage for stellar interferometry via continuous-variable teleportation

Limited quantum advantage for stellar interferometry via continuous-variable teleportation

Analysis of continuous-variable quantum teleportation enhanced by measurement-based noiseless quantum amplification.

Continuous-variable quantum teleportation enables deterministic teleportation of quantum states of optical modes. However, the state transfer is imperfect and limited by the amount of squeezing in the shared two-mode entangled state. Recently, it has been proposed and experimentally demonstrated that the performance of continuous-variable teleportation can be conditionally improved using a measurement-based noiseless quantum amplification [J. Zhao et al., Nat. Commun.14, 4745 (2023)10.1038/s41467-023-40438-z]. An inverse Gaussian filter with sufficiently high cut-off is applied to outcomes of the continuous-variable Bell measurement, which can increase the fidelity of state teleportation and the cost of making the protocol probabilistic. Here we provide a detailed theoretical analysis of this protocol and discuss its effects and limitations. We focus on teleportation of classes of Gaussian states with fixed covariance matrix and variable displacement. The measurement-based noiseless amplification conditionally improves the precision of estimation of the coherent displacement of the teleported state from the outcomes of continuous-variable Bell measurement. Therefore, more information about the teleported state is revealed and unity-gain teleportation becomes possible with a lower added thermal noise as compared to deterministic teleportation.

Continuous variable port-based teleportation

Port-based teleportation (PBT) is a generalisation of the standard teleportation protocol which does not require unitary operations by the receiver. This comes at the price of requiring N > 1 entangled pairs, while N = 1 for the standard teleportation protocol. The lack of correction unitaries allows PBT to be used as a fundamental theoretical tool to simulate arbitrary channels with a general resource, with applications to study fundamental limits of quantum communication, cryptography and sensing, and to define general programmable quantum computers. Here we introduce a general formulation of port-based teleportation in continuous variable systems and study in detail the N = 2 case. In particular, we interpret the resulting channel as an energy truncation and analyse the kinds of channels that can be naturally simulated after this restriction.

Optimal input states for quantifying the performance of continuous-variable unidirectional and bidirectional teleportation

Continuous-variable (CV) teleportation is a foundational protocol in quantum information science. A number of experiments have been designed to simulate ideal teleportation under realistic conditions. In this paper, we detail an analytical approach for determining optimal input states for quantifying the performance of CV unidirectional and bidirectional teleportation. The metric that we consider for quantifying performance is the energy-constrained channel fidelity between ideal teleportation and its experimental implementation, and along with this, our focus is on determining optimal input states for distinguishing the ideal process from the experimental one. We prove that, under certain energy constraints, the optimal input state in unidirectional, as well as bidirectional, teleportation is a finite entangled superposition of twin-Fock states saturating the energy constraint. Moreover, we also prove that, under the same constraints, the optimal states are unique; that is, there is no other optimal finite entangled superposition of twin-Fock states.

How to verify identity in the continuous variable quantum system?

Continuous variable quantum cryptography has developed rapidly in recent decades, but how to verify identity in the continuous variable quantum system is still an urgent issue. To solve this problem, we propose a continuous variable quantum identification (CV-QI) protocol based on the correlation of the two-mode squeezed vacuum state and the continuous variable teleportation. The bidirectional identity verification between two participants of the communication can be achieved by the proposed CV-QI protocol. To guarantee the security, we make full use of the decoy state sequences during the whole process of the proposed CV-QI protocol. Besides, we provide the security analyses of the proposed CV-QI protocol, and analyses indicate that the security of the proposed CV-QI protocol is guaranteed.

Constraints on Gaussian Error Channels and Measurements for Quantum Communication.

Joint Gaussian measurements of two quantum systems are important for quantum communication between remote parties and are often used in continuous-variable teleportation or entanglement-swapping protocols. Many of the errors in real-world implementations can be modeled by independent Gaussian error channels acting prior to measurement. In this work we study independent single-mode Gaussian error channels on two modes A and B that take place prior to a joint Gaussian measurement. We determine the set of pairs of such channels that render all Gaussian measurements separable, and therefore unsuitable for entanglement swapping or teleportation of arbitrary input states. For example, if the error channels are loss with parameters followed by added noise with parameters then all Gaussian measurements are separable if and only if .

Continuous variable teleportation with indefinite causal order

Continuous variable teleportation with indefinite causal order

Significance of fidelity deviation in continuous-variable teleportation

Performance of quantum teleportation is typically measured by the average fidelity, an overlap between the input and output states. Along with the first moment, we introduce the second moment of fidelity in continuous-variable (CV) teleportation, i.e., the fidelity deviation as the figure of merit to assess the protocol's efficiency. We show that CV states, both Gaussian and non-Gaussian, can be better characterized by considering both average fidelity and fidelity deviation, which is not possible with only average fidelity. Moreover, we shed light on the performance of the teleportation protocol in two different input scenarios: One is when input states are sampled from constrained uniform distribution while the other one is Gaussian suppression of the input states which again leads to a different classification of CV states according to their performance. The entire analysis is carried out in noiseless and noisy scenarios with noise being incorporated in the measurement and the shared channels. We also report that one type of noise can make the protocol robust against the other one, which leads to a ``constructive effect,'' and identify the noise models which are responsible for decreasing average fidelity and the increment in fidelity deviation.

Optimal tests for continuous-variable quantum teleportation and photodetectors

Quantum teleportation is a primitive in several important applications, including quantum communication, quantum computation, error correction, and quantum networks. In this work, we propose an optimal test for the performance of continuous-variable (CV) quantum teleportation in terms of the energy-constrained channel fidelity between ideal CV teleportation and its experimental implementation. Work prior to ours considered suboptimal tests of the performance of CV teleportation, focusing instead on its performance for particular states, such as ensembles of coherent states, squeezed states, cat states, etc. Here we prove that the optimal state for testing CV teleportation is an entangled superposition of twin Fock states. We establish this result by reducing the problem of estimating the energy-constrained channel fidelity between ideal CV teleportation and its experimental approximation to a quadratic program and solving it. As an additional result, we obtain an analytical solution to the energy-constrained diamond distance between a photodetector and its experimental approximation. These results are relevant for experiments that make use of CV teleportation and photodetectors.

Telefilters, telemirrors, and causality

We present new theoretical models for quantum optical mode-selective filters and mirrors using continuous-variable teleportation. We call these devices telefilters and telemirrors respectively. Both devices act as the identity channel on a mode of interest from an input multi-mode field while filtering or reflecting all the orthogonal modes. We utilise these models to analyse a causality problem in relativistic quantum optics, specifically the apparently acausal transmission and propagation of temporally delocalised wavepackets through mode-selective mirrors. Firstly, we show how telemirrors - and thus mode-selective operations generally - enact a fundamental time-delay on such wavepackets, which is necessary in order to prevent violations of causality. In an attempt to circumvent this delay, we next consider teleporting the independent temporal components of the input field separately and continuously, that is, performing operations on-the-run. In this scenario, the telemirror transmits the mode of interest as well as orthogonal modes which carry with them uncorrelated noise. In this scenario, the device may be considered mode-discriminating but not mode-selective.

Dissipation-driven entanglement between two microwave fields in a four-mode hybrid cavity optomechanical system.

The generation and manipulation of highly pure and strongly entangled steady state in a quantum system are vital tasks in the standard continuous-variable teleportation protocol. Especially, the manipulation implemented in integrated devices is even more crucial in practical quantum information applications. Here we propose an effective approach for creating steady-state entanglement between two microwave fields in a four-mode hybrid cavity optomechanical system. The entanglement can be achieved by combining the processes of three beam-splitter interactions and two parametric-amplifier interactions. Due to the dissipation-driven and cavity cooling processes, the entanglement obtained can go far beyond the entanglement limit based on coherent parametric coupling. Moreover, our proposal allows the engineered bath to cool both Bogoliubov modes almost simultaneously. In this way, a highly pure and strongly entangled steady state of two microwave modes is obtained. Our finding may be significant for using the hybrid opto-electro-mechanical system fabricated on chips in various quantum tasks, where the strong and pure entanglement is an important resource.

Role of quadrature squeezing in continuous-variable quantum teleportation

Quantum teleportation (QT) lies at the heart of modern day quantum information science and technology. Despite extensive studies over past two decades, obtaining the necessary and/or sufficient criterion for QT with continuous-variable (CV) resources, besides entanglement, still remains an open concern. In this backdrop, here we analyze the role of a purely quantum optical (QO) attribute, known as quadrature squeezing, in CV teleportation. We first provide an analytic proof that for Gaussian resources quadrature squeezing is necessary for QT. However, for non-Gaussian resources we show a clear distinction between the pure and the mix states. For the pure states, quadrature squeezing appears to be necessary for QT, in the sense that there is no QT without quadrature squeezing. However, in the case of mix states we observe otherwise, i.e., QT could be achieved even without quadrature squeezing. Our results present the exotic character of the QO attributes of the CV resources and necessitate a deeper search for the necessary and/or sufficient criterion for CV QT.

Asymmetric quantum steering in cascaded nonlinear process

Asymmetric quantum steering can achieve one-way control, which is different from multipartite quantum steering and can accomplish some work that quantum entanglement cannot complete. The cascaded nonlinear process of spontaneous parametric down-conversion cascaded with double sum-frequency generations can be realized in one optical superlattice by quasi-phase-matching technique. Here the asymmetric quantum steering is investigated in this cascaded nonlinear process and the asymmetry of quantum steering is confirmed in a wide range of the parameters both below and without the oscillation threshold, respectively. The generation of asymmetric quantum steering in present scheme has potential applications in quantum key distribution and continuous variable teleportation.

Continuous-variable gate teleportation and bosonic-code error correction

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 cluster states, generated by constant-depth linear optical networks, supplemented with a probabilistic supply of GKP states. The upshot of our technique is that state injection for both gate teleportation and error correction can be achieved without active squeezing operations -- an experimental bottleneck for quantum optical implementations.

On foundational aspects of optical quantum communication

ABSTRACTUsing a simple model of the quantized photon field in an optical fibre we suggest a model of quantum teleportation of continuous variables which is more realistic than the usual one in the sense that the localization properties of the quantities to be teleported are taken into account.

Quantum non-Gaussianity and secure quantum communication

No-cloning theorem, a profound fundamental principle of quantum mechanics, also provides a crucial practical basis for secure quantum communication. The security of communication can be ultimately guaranteed if the output fidelity via the communication channel is above the no-cloning bound (NCB). In quantum communications using continuous-variable (CV) systems, Gaussian states, more specifically, coherent states have been widely studied as inputs, but less is known for non-Gaussian states. We aim at exploring quantum communication covering CV states comprehensively with distinct sets of unknown states properly defined. Our main results here are (i) to establish the NCB for a broad class of quantum non-Gaussian states, including Fock states, their superpositions, and Schrodinger-cat states and (ii) to examine the relation between NCB and quantum non-Gaussianity (QNG). We find that NCB typically decreases with QNG. Remarkably, this does not mean that QNG states are less demanding for secure communication. By extending our study to mixed-state inputs, we demonstrate that QNG specifically in terms of Wigner negativity requires more resources to achieve output fidelity above NCB in CV teleportation. The more non-Gaussian, the harder to achieve secure communication, which can have crucial implications for CV quantum communications.

Super sensitivity and super resolution with quantum teleportation

We propose a method for quantum enhanced phase estimation based on continuous variable (CV) quantum teleportation. The phase shift probed by a coherent state can be enhanced by repeatedly teleporting the state back to interact with the phase shift again using a supply of two-mode squeezed vacuum states. In this way a sequential protocol exhibiting both super-resolution and super-sensitivity can be obtained due to the coherent addition of the phase shift. The protocol enables Heisenberg-limited sensitivity and super-resolution given sufficiently strong squeezing. The proposed method could be implemented with current or near-term technology of CV teleportation.

Teleportation simulation of bosonic Gaussian channels: strong and uniform convergence

We consider the Braunstein–Kimble protocol for continuous variable teleportation and its application for the simulation of bosonic channels. We discuss the convergence properties of this protocol under various topologies (strong, uniform, and bounded-uniform) clarifying some typical misinterpretations in the literature. We then show that the teleportation simulation of an arbitrary single-mode Gaussian channel is uniformly convergent to the channel if and only if its noise matrix has full rank. The various forms of convergence are then discussed within adaptive protocols, where the simulation error must be propagated to the output of the protocol by means of a “peeling” argument, following techniques from PLOB [S. Pirandola et al., Nat. Comm. 8, 15043 (2017)]. Finally, as an application of the peeling argument and the various topologies of convergence, we provide complete rigorous proofs for recently claimed strong converse bounds for private communication over Gaussian channels.Graphical abstract

Strong and uniform convergence in the teleportation simulation of bosonic Gaussian channels

In the literature on the continuous-variable bosonic teleportation protocol due to [Braunstein and Kimble, Phys. Rev. Lett., 80(4):869, 1998], it is often loosely stated that this protocol converges to a perfect teleportation of an input state in the limit of ideal squeezing and ideal detection, but the exact form of this convergence is typically not clarified. In this paper, I explicitly clarify that the convergence is in the strong sense, and not the uniform sense, and furthermore, that the convergence occurs for any input state to the protocol, including the infinite-energy Basel states defined and discussed here. I also prove, in contrast to the above result, that the teleportation simulations of pure-loss, thermal, pure-amplifier, amplifier, and additive-noise channels converge both strongly and uniformly to the original channels, in the limit of ideal squeezing and detection for the simulations. For these channels, I give explicit uniform bounds on the accuracy of their teleportation simulations. I then extend these uniform convergence results to particular multi-mode bosonic Gaussian channels. These convergence statements have important implications for mathematical proofs that make use of the teleportation simulation of bosonic Gaussian channels, some of which have to do with bounding their non-asymptotic secret-key-agreement capacities. As a byproduct of the discussion given here, I confirm the correctness of the proof of such bounds from my joint work with Berta and Tomamichel from [Wilde, Tomamichel, Berta, IEEE Trans. Inf. Theory 63(3):1792, March 2017]. Furthermore, I show that it is not necessary to invoke the energy-constrained diamond distance in order to confirm the correctness of this proof.

Quantum error correction of continuous-variable states with realistic resources

Gaussian noise induced by loss on Gaussian states may be corrected by distributing EPR entanglement through the loss channel, purifying the entanglement using a noiseless linear amplifier (NLA) and then using it for continuous-variable teleportation of the input state. Linear optical implementations of the NLA unavoidably introduce small amounts of excess noise and detection and source efficiency will be limited in current implementations. In this paper, we analyze the error-correction protocol with non-unit efficiency sources and detectors and show the excess noise may be partially compensated by adjusting the classical gain of the teleportation protocol. We present a strong case for the potential of demonstrable error-correction with current technology.