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Real-time imaging of photonic quantum teleportation

Ebrahim Karimi, Harjaspreet Mand, Hammam Qassim, Robert W. Boyd, Manuel Erhard

Published Feb 25, 2015• 0 citations
Publisher

Abstract

The science fiction depiction of teleportation refers to the transfer of matter between two spatially separated spaces without the transfer of information. This largely differs from the concept of quantum teleportation, one of the most exciting concepts in modern quantum theory, though often misunderstood.1 The key difference between the sci-fi portrayal and quantum teleportation is that information is transferred between two spatially separated parties, rather than a direct transfer of matter. Applications may include quantum key distribution and quantum cryptography. At the heart of such teleportation is the phenomenon of quantum entanglement, in which the quantum state corresponding to non-local particles cannot be described independently. Sender (Alice) and receiver (Bob) share a pair of particles that are entangled. Alice performs a set of measurements (known as the Bell states analysis) on the state of her particle and that of a third particle (Charlie)—the particle whose state should be teleported to Bob. Based on the outcome of her measurements, Alice sends a signal to Bob. Bob applies a set of unitary transformations, without knowing the state, to the state of his particle. After these transformations, the state of Bob’s particle is identical to Charlie’s. Note that, during this process, Alice and Bob have no information about the state of Charlie’s particle. This process is probabilistic when implemented with entangled photons and linear optics,2 and means that sometimes Alice’s measurement outcome—that of two particles’ Bell states analysis—is not determined. Thus, Bob does not receive any classical signal, and the teleportation fails. Nevertheless, when Bob receives the signal from Alice, the state is the correct one, and teleportation has succeeded with a 100% fidelity. We can use a single particle possessing two different quantum properties to present a non-separable state, where Figure 1. (a) The setup for remote-hybrid-teleportation of photons from the spin to the orbital-angular-momentum degree of freedom (OAM DOF). A UV laser pumps a barium borate (BBO) crystal to generate photon pairs that are entangled in their OAM DOF. A polarizing Sagnac interferometer containing a dove prism (PSI-DP), shown in the inset, in combination with the half-wave plate (H), spatial light modulator (SLM), bandpass interference filter (IF) and single mode optical fiber (SMF) perform the single photon spin-OAM non-separable Bell state measurement.4 The photons couple via a fiber coupler (FC) into the SMF for detection by an avalanche photodiode (APD). The APD triggers the intensified charge-coupled camera (ICCD) to record the spatial distribution of photon B. During the preparation and measurement of photon A, photon B propagates in the delay line (D), compensating for electronic delay. (b) First and second columns show the polarization (SAM) state of C and the OAM state of the teleported photon to B. jLi, jH i, and jV i: left, horizontal, and vertical polarization, respectively. M: Mirror. PBS: Polarizing beam splitter. TEM: Transverse electromagnetic mode—this refers to the fundamental transverse mode (beam with a Gaussian profile). Q: Quarter-wave plate.

DOI
10.1117/2.1201502.005800

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FINDING: Quantum teleportation relies on shared entanglement and classical communication, not instantaneous matter transfer; mathematical core is Bell state measurement and unitary transformation. | MATH: Bell state basis: \(|\Phi^\pm\rangle = \frac{1}{\sqrt{2}}(|00\rangle \pm |11\rangle)\), \(|\Psi^\pm\rangle = \frac{1}{\sqrt{2}}(|01\rangle \pm |10\rangle)\). Teleportation protocol: Alice performs Bell measurement on her qubit and entangled pair, sends 2 classical bits to Bob, who applies Pauli correction \(I, X, Z, XZ\) based on outcome. Fidelity = \(|\langle \psi | \rho_{\text{out}} | \psi \rangle|^2\). No faster-than-light signaling: classical bits limit speed to ≤ c. | CONNECTION: No direct geometric ratios (0.382, 0.618, 0.786, 1.618, 2.618) appear. However, Bell states are maximally entangled, corresponding to the four vertices of a regular tetrahedron in the Bloch sphere representation (SO(3) symmetry). The Pauli matrices \(X, Y, Z\) generate the Clifford group, which is the sy Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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The science fiction depiction of teleportation refers to the transfer of matter between two spatially separated spaces without the transfer of information. This largely differs from the concept of quantum teleportation, one of the most exciting concepts in modern quantum theory, though often misunderstood.1 The key difference between the sci-fi portrayal and quantum teleportation is that information is transferred between two spatially separated parties, rather than a direct transfer of matter. Applications may include quantum key distribution and quantum cryptography. At the heart of such teleportation is the phenomenon of quantum entanglement, in which the quantum state corresponding to non-local particles cannot be described independently. Sender (Alice) and receiver (Bob) share a pair of particles that are entangled. Alice performs a set of measurements (known as the Bell states analysis) on the state of her particle and that of a third particle (Charlie)—the particle whose state should be teleported to Bob. Based on the outcome of her measurements, Alice sends a signal to Bob. Bob applies a set of unitary transformations, without knowing the state, to the state of his particle. After these transformations, the state of Bob’s particle is identical to Charlie’s. Note that, during this process, Alice and Bob have no information about the state of Charlie’s particle. This process is probabilistic when implemented with entangled photons and linear optics,2 and means that sometimes Alice’s measurement outcome—that of two particles’ Bell states analysis—is not determined. Thus, Bob does not receive any classical signal, and the teleportation fails. Nevertheless, when Bob receives the signal from Alice, the state is the correct one, and teleportation has succeeded with a 100% fidelity. We can use a single particle possessing two different quantum properties to present a non-separable state, where Figure 1. (a) The setup for remote-hybrid-teleportation of photons from the spin to the orbital-angular-momentum degree of freedom (OAM DOF). A UV laser pumps a barium borate (BBO) crystal to generate photon pairs that are entangled in their OAM DOF. A polarizing Sagnac interferometer containing a dove prism (PSI-DP), shown in the inset, in combination with the half-wave plate (H), spatial light modulator (SLM), bandpass interference filter (IF) and single mode optical fiber (SMF) perform the single photon spin-OAM non-separable Bell state measurement.4 The photons couple via a fiber coupler (FC) into the SMF for detection by an avalanche photodiode (APD). The APD triggers the intensified charge-coupled camera (ICCD) to record the spatial distribution of photon B. During the preparation and measurement of photon A, photon B propagates in the delay line (D), compensating for electronic delay. (b) First and second columns show the polarization (SAM) state of C and the OAM state of the teleported photon to B. jLi, jH i, and jV i: left, horizontal, and vertical polarization, respectively. M: Mirror. PBS: Polarizing beam splitter. TEM: Transverse electromagnetic mode—this refers to the fundamental transverse mode (beam with a Gaussian profile). Q: Quarter-wave plate.
There exists two prominent methods to transfer information between two spatially separated parties, namely Alice (A) and Bob (B): quantum teleportation and remote state preparation. However, the difference between these methods is, in the teleportation scheme, the state to be transferred is completely unknown, whereas in state preparation it should be known to the sender. In addition, photonic state teleportation is probabilistic due to the impossibility of performing a two-particle complete Bell-state analysis with linear optics, while remote state preparation can be performed deterministically. Here we report the first realization of photonic hybrid remote state preparation from spin to orbital angular momentum degrees of freedom. In our scheme, the polarization state of photon A is transferred to orbital angular momentum of photon B. The prepared states are visualized in real time by means of an intensified CCD camera. The quality of the prepared states is verified by performing quantum state tomography, which confirms an average fidelity higher than 99.4%. We believe that this experiment paves the way towards a novel means of quantum communication in which encryption and decryption are carried out in naturally different Hilbert spaces, and therefore may provide a means for enhancing security.
Summary form only given. Quantum teleportation allows to transfer the quantum state of a particle to a remote location without sending the particle itself. This makes it a versatile tool for the distribution of quantum states over long distances or the remote preparation of quantum memories as they are necessary in various scenarios of quantum information processing and quantum communication. In this context atomic systems are often discussed as promising candidates for the storage and manipulation of qubit states whereas photonic qubit states are easy to prepare and to distribute. Hybrid systems of entangled atom-photon pairs can serve as an interface between those different carriers of quantum information. We utilize this property to perform teleportation of the polarization state of an attenuated laser pulse onto a single atom over a distance of 20m.Our experimental sequence consists of two steps. First the spin state of the single atom is entangled with the polarization state of a single photon in a spontaneous emission process [1]. The single photon is then sent to a second laboratory 20m away where an attenuated laser pulse with a well defined polarization state |Ψ) is prepared. In a second step a Bell-state measurement on the joint polarization state of the single photon from the atom and the attenuated laser pulse is performed (Fig. 1a). This is done via interference of the photon and the pulse at a fiber beam-splitter and subsequent coincidence detection of photons at the outputs of the beam-splitter (Fig. 1b). This teleports the input state |Ψ) onto the atom - up to a unitary tranformation depending on the outcome of the Bell-state measurement.need to be indistinguishable in all degrees of freedom except for their polarization. In particular, the temporal shape of the pulse was matched to that of the single photon using an arbitrary waveform generator and an AOM in a closed-loop feedback control. We performed this experiment with input states |Ψ) = |H), |+45°) and |R) and evaluated the fidelity to find the atom in the correspondig output state. For |+45°) and |R) the fraction of coherent pulses containing two or more photons can cause the same signal as expected from a successful Bell-state projection which reduces the overall fidelity to 0.81 and 0.84, respectively. However, for |H) the fidelty is practically only limited by the precision of the atomic state readout and reaches a value of 0.93.
Quantum teleportation provides a "disembodied" way to transfer quantum states from one object to another at a distant location, assisted by priorly shared entangled states and a classical communication channel. In addition to its fundamental interest, teleportation has been recognized as an important element in long-distance quantum communication, distributed quantum networks and measurement-based quantum computation. There have been numerous demonstrations of teleportation in different physical systems such as photons, atoms, ions, electrons, and superconducting circuits. Yet, all the previous experiments were limited to teleportation of one degree of freedom (DoF) only. However, a single quantum particle can naturally possess various DoFs -- internal and external -- and with coherent coupling among them. A fundamental open challenge is to simultaneously teleport multiple DoFs, which is necessary to fully describe a quantum particle, thereby truly teleporting it intactly. Here, we demonstrate the first teleportation of the composite quantum states of a single photon encoded in both the spin and orbital angular momentum. We develop a method to project and discriminate hyper-entangled Bell states exploiting probabilistic quantum non-demolition measurement, which can be extended to more DoFs. We verify the teleportation for both spin-orbit product states and hybrid entangled state, and achieve a teleportation fidelity ranging from 0.57 to 0.68, above the classical limit. Our work moves a step toward teleportation of more complex quantum systems, and demonstrates an enhanced capability for scalable quantum technologies.
Quantum teleportation is a useful quantum information technology to transmit quantum states between different degrees of freedom. Here we report a quantum state transfer experiment in the linear optical system, transferring a single-photon state in the polarization degree of freedom (DoF) to another photon in the orbital angular momentum (OAM) quantum state via a biphoton OAM entangled channel. Our experimental method is based on quantum teleportation technology. The differences between ours and the original teleportation scheme is that the transfer state is known in ours, and our method is for different particles with different DoFs, while the original one is for different particles with the same DoF. In addition, our present experiment is implemented with a high Bell efficiency since each of the four hybrid-entangled Bell states can be discriminated. We use six states of poles of the Bloch sphere to test our experiment, and the fidelity of the quantum state transfer is $91.8\ifmmode\pm\else\textpm\fi{}1.3%$.
Teleporting a quantum state,the sender Alice disassembles the entire informations into two parts: one purely classical information and the another purely non-classical information,then sends them to the receiver Bob via two different channels.Firstly,sending the purely non-classical part,the EPR pair which consists of two fermions with the spin of 1 2 here plays the key role in the teleportation,one EPR particle is given to Alice,while the other is given to Bob.Alice performs a complete measurement of the von Neumann type on the joint system consisting of the original particle and her EPR particle,this measurement performed in the four eigenstates of the Bell operator leads to collapse the wave packet of the joint wavefunction into the four correlated Bell bases.Through applying the appropriate unitary transformation to the state of his EPR particle Bob can reconstruct a replica of the original state destroyed in Alice's hand.Moreover,this Bell measurement produces two bits of classical information which is sent to Bob,a quantum teleportation is therefore completed.The paper studies the interior relation between EPR pairs of particles and the quantum teleportation.
FINDING: Quantum teleportation relies on shared entanglement and classical communication, not instantaneous matter transfer; mathematical core is Bell state measurement and unitary transformation. | MATH: Bell state basis: ∣Φ±⟩=12(∣00⟩±∣11⟩)|\Phi^\pm\rangle = \frac{1}{\sqrt{2}}(|00\rangle \pm |11\rangle)∣Φ±⟩=2​1​(∣00⟩±∣11⟩), ∣Ψ±⟩=12(∣01⟩±∣10⟩)|\Psi^\pm\rangle = \frac{1}{\sqrt{2}}(|01\rangle \pm |10\rangle)∣Ψ±⟩=2​1​(∣01⟩±∣10⟩). Teleportation protocol: Alice performs Bell measurement on her qubit and entangled pair, sends 2 classical bits to Bob, who applies Pauli correction I,X,Z,XZI, X, Z, XZI,X,Z,XZ based on outcome. Fidelity = ∣⟨ψ∣ρout∣ψ⟩∣2|\langle \psi | \rho_{\text{out}} | \psi \rangle|^2∣⟨ψ∣ρout​∣ψ⟩∣2. No faster-than-light signaling: classical bits limit speed to ≤ c. | CONNECTION: No direct geometric ratios (0.382, 0.618, 0.786, 1.618, 2.618) appear. However, Bell states are maximally entangled, corresponding to the four vertices of a regular tetrahedron in the Bloch sphere representation (SO(3) symmetry). The Pauli matrices X,Y,ZX, Y, ZX,Y,Z generate the Clifford group, which is the sy Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com