Relations between teleportation, Bell's inequalities and inseparability are investigated. It is shown that any mixed two spin-$1\over2$ state which violates the Bell-CHSH inequality is useful for teleportation. The result is extended to any Bell's inequalities constructed of the expectation values of products of spin operators. It is also shown that there exist inseparable states which are not useful for teleportation within the standard scheme.
Information-theoretic aspects of quantum inseparability of mixed states are investigated in terms of the $α$-entropy inequalities and teleportation fidelity. Inseparability of mixed states is defined and a complete characterization of the inseparable $2\times2$ systems with maximally disordered subsystems is presented within the Hilbert-Schmidt space formalism. A connection between teleportation and negative conditional $α$-entropy is also emphasized.
A recent proof of Bell's theorem without inequalities [A. Cabello, Phys. Rev. Lett. 86, 1911 (2001)] is formulated as a Greenberger-Horne-Zeilinger-like proof involving just two observers. On one hand, this new approach allows us to derive an experimentally testable Bell inequality which is violated by quantum mechanics. On the other hand, it leads to a new state-independent proof of the Kochen-Specker theorem and provides a wider perspective on the relations between the major proofs of no-hidden-variables.
A quantum system consisting of two subsystems is separable if its density matrix can be written as $ρ=\sum w_K ρ_K'\otimes ρ_K''$, where $ρ_K'$ and $ρ_K''$ are density matrices for the two subsytems, and the positive weights $w_K$ satisfy $\sum w_K=1$. A necessary condition for separability is derived and is shown to be more sensitive than Bell's inequality for detecting quantum inseparability. Moreover, collective tests of Bell's inequality (namely, tests that involve several composite systems simultaneously) may sometimes lead to a violation of Bell's inequality, even if the latter is satisf…
Understanding the relation between the different forms of inseparability in quantum mechanics is a longstanding problem in the foundations of quantum theory and has implications for quantum information processing. Here we make progress in this direction by establishing a direct link between quantum teleportation and Bell nonlocality. In particular, we show that all entangled states which are useful for teleportation are nonlocal resources, i.e. lead to deterministic violation of Bell's inequality. Our result exploits the phenomenon of super-activation of quantum nonlocality, recently proved by…
A deterministic teleportation scheme for unknown atomic states is proposed in cavity QED. The Bell state measurement is not needed in the teleportation process, and the success probability can reach 1.0. In addition, the current scheme is insensitive to the cavity decay and thermal field.
In this paper, we define the return operator, the cross product operator and the cross Bell bases. Using the cross Bell bases, we give a protocol of teleportation of arbitrary multipartite qubit entanglement, this scheme is a quite natural generalization of the BBCJPW scheme. We find that this teleportation, in fact, is essentially determined by the teleportation of every single unknown qubit state as in the original scheme of BBCJPW. The calculation in detail is given for the case of tripartite qubit.
We study optimal teleportation based on the Bell measurements. An explicit expression for the quantum channel associated with the optimal teleportation with an arbitrary mixed state resource is presented. The optimal transmission fidelity of the corresponding quantum channel is calculated and shown to be related to the fully entangled fraction of the quantum resource, rather than the singlet fraction as in the standard teleportation protocol.
The question of the measurements on the Bell states by making use of mode change (from mixed to pure) of one qubit is considered. Such a mode change cannot be taken advantage of for superluminal communication in teleportation, and it may define constraints on the size of the gates.
We investigate the teleportation of the bipartite entangled states through two equally noisy quantum channels, namely mixture of Bell states. There is a particular mixed state channel for which all pure entanglement in a known Schmidt basis remain entangled after teleportation and it happens till the channel state remains entangled. Werner state channel lacks both these features. The relation of these noisy channels with violation of Bell's inequality and 2-E inequality is studied.
We present a novel Bell-state analyzer for time-bin qubits allowing the detection of three out of four Bell-states with linear optics, only two detectors and no auxiliary photons. The theoretical success rate of this scheme is 50%. A teleportation experiment was performed to demonstrate its functionality. We also present a teleportation experiment with a fidelity larger than the cloning limit.
We present a Bell-state analyzer for time-bin qubits allowing the detection of three out of four Bell-states with linear optics, two detectors and no auxiliary photons. The theoretical success rate of this scheme is 50%. A teleportation experiment was performed to demonstrate its functionality. We also present a teleportation experiment with a Fidelity larger than the cloning limit of F=5/6.
Dynamics of disentanglement as measured by the tripartite negativity and Bell nonlocality as measured by the extent of violation of the multipartite Bell-type inequalities are investigated in this work. It is shown definitively that for the initial three-qubit Greenberger-Horne-Zeilinger (GHZ) or {\it W} class state preparation the Bell nonlocality suffers sudden death under the influence of thermal reservoirs. Moreover, all the Bell-nonlocal states are useful for nonclassical teleportation, while there are entangled states that do not violate any Bell-type inequalities, but still yield noncla…
In this letter we analyze the efficacy of the entangled output of Pati-Braunstein deletion machine [3] as a teleportation channel. We analyze the possibility of it violating the Bell's inequality. Interestingly we find that for all values of the input parameter$α$ the state does not violate the Bell's inequality but when used as a teleportation channel can give a fidelity higher than the classical optimum (i.e 2/3).
We report a quantum teleportation experiment in which nonlinear interactions are used for the Bell state measurements. The experimental results demonstrate the working principle of irreversibly teleporting an unknown arbitrary quantum state from one system to another distant system by disassembling into and then later reconstructing from purely classical information and nonclassical EPR correlations. The distinct feature of this experiment is that \emph{all} four Bell states can be distinguished in the Bell state measurement. Teleportation of a quantum state can thus occur with certainty in pr…
An efficient and economical scheme is proposed for the perfect quantum teleportation of n-qubit non-maximally entangled state of generalized Bell-type. A Bell state is used as the quantum channel in the proposed scheme. It is also shown that the controlled teleportation of this n-qubit state can be achieved by using a GHZ state or a GHZ-like state as quantum channel. The proposed schemes are economical because for the perfect and controlled teleportation of n-qubit non-maximally entangled state of generalized Bell-type we only need a Bell state and a tripartite entangled state respectively. It…
We demonstrate an experiment on entanglement swapping using an optimal Bell-state measurement capable of identifying two of the four Bell-states for polarization entangled photons, which is the optimum with linear optical elements. The two final photons belong to separately created paris. They are entangled after their original partner photons have been subjected to the Bell state measurement, whose outcome determines the type of entanglement of the final photon pair. The resulting violation of Bell's inequality in both cases confirms the success of the teleportation protocol.
We study the quantum controlled and probabilistic teleportation protocol via a four-cluster state (Front. Phys. (2017) 12: 120306). The protocol cannot achieve the goal that if the teleportation fails, it can be repeated without copies of the teleported state. And the reason is that all the information of the teleported state shifts to the receiver's particle after Bell measurement and the information cannot shift back to the sender without other entangled states. To realize the claimed goal, a new quantum controlled and probabilistic teleportation protocol using the same four-cluster state is…
This paper proposes a scheme for creating and storing quantum entanglement over long distances. Optical cavities that store this long-distance entanglement in atoms could then function as nodes of a quantum network, in which quantum information is teleported from cavity to cavity. The teleportation can be carried out unconditionally via measurements of all four Bell states, using a method of sequential elimination.
A single-particle entangled state can be generated by illuminating a beam splitter with a single photon. Quantum teleportation utilizing such a single-particle entangled state can be successfully achieved with a simple setup consisting only of linear optical devices such as beam splitters and phase shifters. Application of the locality assumption to a single-particle entangled state leads to Bell's inequality, a violation of which signifies the nonlocal nature of a single particle.
The Wigner representation of parametric down conversion in the Heisenberg picture is applied to the study of the Rome teleportation experiment. We investigate the physical meaning of the zeropoint inputs at the different areas of the experimental setup. In particular, we establish a quantitative relationship between the zeropoint sets of modes that are needed for the preparation of the quantum state to be teleported, the idle channels inside the one-photon polarization-momentum Bell-state analyser, and the possibility of performing teleportation of a polarization state whith certainty.
In this paper we investigate the possibility to make complete Bell measurements on a product Hilbert space of two two-level bosonic systems. We restrict our tools to linear elements, like beam splitters and phase shifters, delay lines and electronically switched linear elements, photo-detectors, and auxiliary bosons. As a result we show that with these tools a never failing Bell measurement is impossible.
We analyze a possibility of using the two qubit output state from Buzek-Hillery quantum copying machine (not necessarily universal quantum cloning machine) as a teleportation channel. We show that there is a range of values of the machine parameter $ξ$ for which the two qubit output state is entangled and violates Bell-CHSH inequality and for a different range it remains entangled but does not violate Bell-CHSH inequality. Further we observe that for certain values of the machine parameter the two-qubit mixed state can be used as a teleportation channel. The use of the output state from the Bu…
Based on the assumption that the receiver Bob can apply any unitary transformation, Horodecki {\it et al.} [Phys. Lett. A {\bf 222}, 21 (1996)] proved that any mixed two spin-1/2 state which violates the Bell-CHSH inequality is useful for teleportation. Here, we further show that any X state which violates the Bell-CHSH inequality can also be used for nonclassical teleportation even if Bob can only perform the identity or the Pauli rotation operations. Moreover, we showed that the maximal difference between the two average fidelities achievable via Bob's arbitrary transformations and via the s…
Teleportation algorithm assumes specific Bell states as input, but actual sources typically generates more than one. This work presents a teleportation algorithm for a two Bell states mixture, including remaining distortion from previous control process.
A parametric amplifier is in essence a linear four-port device, which couples and linearly mixes two inputs before amplifying and sending them to two output ports. Here, we show that for quadrature-phase amplitudes, a parametric amplifier can replace beam splitters to play the role of mixer. We apply this idea to a continuous-variable quantum state teleportation scheme in which a parametric amplifier replaces a beam splitter in Bell measurement. We show that this scheme is loss-tolerant in the Bell measurement process and thus demonstrate the advantage of PA over BS in the applications in quan…
We introduce a general odd qubit entangled system composed of GHZ and Bell pairs and explicate its usefulness for quantum teleportation, information splitting and superdense coding. After demonstrating the superdense coding protocol on the five qubit system, we prove that '2N +1' classical bits can be sent by sending 'N+1' quantum bits using this channel. It is found that the five-qubit system is also ideal for arbitrary one qubit and two qubit teleportation and quantum information splitting (QIS). For the single qubit QIS, three different protocols are feasible, whereas for the two qubit QIS,…
We review and compare Bell-state measurement and quantum teleportation schemes using linear optics with three different types of resources, i.e., two-photon pairs, entangled coherent states and hybrid entangled states. Remarkably, perfect teleportation with linear optics is possible in principle based on a hybrid approach that combines two-photon pairs and entangled coherent states. It turns out that hybrid approach allows to perform Bell-state measurement and local Pauli operations in a deterministic way, while it requires photon number resolving measurements.
In a recent paper [Phys. Rev. A 70, 025803 (2004)] we presented a scheme to teleport an entanglement of zero- and one-photon states from a bimodal cavity to another one, with 100% success probability. Here, inspired on recent results in the literature, we have modified our previous proposal to teleport the same entangled state without using Bell-state measurements. For comparison, the time spent, the fidelity, and the success probability for this teleportation are considered.
The effect of non-orthogonality of an entangled non-orthogonal state based quantum channel is investigated in detail in the context of the teleportation of a qubit. Specifically, average fidelity, minimum fidelity and minimum assured fidelity (MASFI) are obtained for teleportation of a single qubit state using all the Bell type entangled non-orthogonal states known as quasi Bell states. Using Horodecki criterion, it is shown that the teleportation scheme obtained by replacing the quantum channel (Bell state) of the usual teleportation scheme by a quasi Bell state is optimal. Further, the perfo…
Bidirectional quantum teleportation scheme is a two-way quantum communication process, in which two parties simultaneously receive each other information. Recently, in paper [1] (Zhou et al., IEEE Access, 7, 44269 (2019)), a six-qubit cluster state has been used to teleport three-qubit entangled state (Alice) and arbitrary single-qubit unknown quantum state (Bob) bidirectionally. An experimental point of view, the preparation and the maintenance of cluster type entangled state is very difficult and costly. So, in this paper we have designed an optimal scheme for bidirectional quantum teleporta…
In this paper, we define a cross product operator and construct the cross Bell basis, by use this basis and Bell measurements we give a simple scheme of the teleportation of arbitrary multipartite qubit entanglement.
It is well-known that maximally entangled states such as the Greenberger-Horne-Zeilinger (GHZ) states, with the Bell states as the simplest examples, are widely exploited in quantum information and computation. We study the application of such maximally entangled states from the viewpoint of the GHZ transform, which is a unitary basis transformation from the product states to the GHZ states. The algebraic structure of the GHZ transform is made clear and representative examples for it are verified as multi-qubit Clifford gates. In this paper, we focus on the Bell transform as the simplest examp…
First, I show explicitly a scheme to {\it faithfully} and {\it deterministically} teleport an arbitrary 2-qubit state from Alice to Bob. In this scheme two same Bell states are sufficient for use. Bob can recover the 2-qubit state by performing at most 4 single-qubit unitary operations conditioned on Alice's 4-bit classical public message corresponding to her two Bell-state measurement outcomes. Then I generalize the 2-qubit teleportation scheme to an aribitrary $N(N\ge 3)$-qubit state teleportation case by using $N$ same Bell states. In the generalized scheme, Alice only needs to identify $N$…
The quantum teleportation process is composed of a joint measurement performed upon two subsystems A and B (uncorrelated), followed by a unitary transformation (parameters of which depend on the outcome of the measurement) performed upon a third subsystem C (EPR correlated with system B). The information about the outcome of the measurement is transferred by classical means. The measurement performed upon the systems A and B collapses their joint wavefunction into one of the four {\it entangled} Bell states. It is shown here that this measurement process plus a possible measurement on the thir…
Recently, Li and Nie (Int. J. Theo. Phys. 52:1630, 2013) had introduced a bidirectional controlled quantum teleportation (BCQT) protocol by using GHZ-Bell state as a quantum channel. Also, Shukla et al. (Int. J. Theo. Phys. 52:3790, 2013) had shown the Li and Nie (LN) protocol is not a BCQT scheme. In this paper, two kinds of bidirectional teleportation schemes in order to correct and improve LN protocol are presented. In the first scheme, Alice and Bob as two legitimate users can simultaneously teleport an unknown single-qubit state to each other with the help of controller Charlie. In the se…
We present a bidirectional modification of the standard one-qubit teleportation protocol, where both Alice and Bob transfer noisy versions of their qubit states to each other by using single Bell state and auxiliary (trigger) qubits. Three schemes are considered: the first where the actions of parties are governed by two independent quantum random triggers, the second with single random trigger, and the third as a mixture of the first two. We calculate the fidelities of teleportation for all schemes and find a condition on correlation between trigger qubits in the mixed scheme which allows us …
We suggest implementation of quantum teleportation protocol of unknown qubit beyond Bell states formalism. Hybrid entangled state composed of coherent components that belong to Alice and dual-rail single photon at Bob disposal is used. Nonlinear effect on the teleported state is realized due to peculiarity of interaction of coherent components with discrete variable state on a beam splitter. Bob performs unitary transformation after receiving the appropriate classical information. The protocol is nearly deterministic but the output state is subject to amplitude distortion which reduces the fid…
Decoherence is an unavoidable phenomenon that results from the interaction of the system with its surroundings. The study of decoherence due to the relativistic effects has the fundamental importance. The Unruh effect is observed by the relativistically accelerator observer. The unruh effect acts as a quantum channel and we call it the Unruh Channel. The Unruh channel can be characterize by providing its Kraus representation. We consider the bipartite scheme in which the quantum information is shared between an inertial observer (Alice) and an accelerated observer (Rob) in the case of Dirac fi…
Pump-Free Microwave-Optical Bell Pair Generation for Teleportation-Based Quantum Transduction
University of Chicago（芝加哥大学）；Pritzker School of Molecular Engineering, University of Chicago（普里茨克分子工程学院）；Q-NEXT, Argonne National Laboratory（Q-NEXT，阿贡国家实验室）；Materials Science Division, Argonne National Laboratory（材料科学部，阿贡国家实验室）
We propose a method of the Bell bases decomposition to teleport an arbitrary unknown N-qubit state through a nonmaximally entangled quantum channel, and give the universal decomposition matrix of N-qubit. Using the decomposition matrix, we can easily obtain the collapsed state at the receiver site. The inverse matrix that the decomposition matrix is just the transformation matrix that the receiver can manipulate. The decomposition matrix is a function of the parameters of the quantum channel. After defining the sub-matrix of the quantum channel, we find that the decomposition matrix is a tenso…
Quantum teleportation, which depends on entangled states, is a fascinating subject and an important branch of quantum information processing. The present work reports the use of a dipolar spin thermal system as a quantum channel to perform quantum teleportation. Non-locality, tested by violation of Bell's inequality and thermal entanglement, measured by negativity, unquestionably show that even entangled states that do not violate Bell's inequality can be useful for teleportation.
We proposed a general transformation in probabilistic teleportation, which is based on different entanglement matching coefficients $K$ corresponding to different unitary evolution which provides one with more flexible evolution method experimentally. Through analysis based on the Bell basis and generalized Bell basis measurement for two probabilistic teleportation, we suggested a general probability of successful teleportation, which is not only determined by the entanglement degree of transmission channels and measurement methods, but also related to the unitary transformation in the telepor…
Experimental realizations of QT have so far been limited to teleportation of light. The present communication gives a new experimental scheme for QT of heavy matter. We show that the standard experimental technique used in nuclear physics may be successfully applied to teleportation of spin states of atomic nuclei. It was shown that there are no theoretical prohibitions upon a possibility of a complete Bell measurement, so that implementation of all four quantum communication channels is at least theoretically available. A general expression for scattering amplitude of two 1/2-spin particles w…
Using invariance of the $n$-th tensored state w.r.t. the $n$-th symmetric group, we propose a 'variable length' universal entanglement concentration without classical communication. Like variable length data compression, arbitrary unknown states are concentrated into perfect Bell states and not approximate Bell states and the number of Bell states obtained is equal to the optimal rate asymptotically with the probability 1. One of the point of our scheme is that we need no classical communication at all. Using this method, we can construct a universal teleportation and a universal dense coding.
We study a method for the implementation of a reliable teleportation protocol (theoretically, 100% of success) of internal states in trapped ions. The generation of the quantum channel (any of four Bell states) may be done respecting technical limitations on individual addressing and without claiming the Lamb-Dicke regime. An adequate Bell analyzer, that transforms unitarily the Bell basis into a completely disentangled one, is considered. Probable sources of error and fidelity estimations of the teleportation process are studied. Finally, we discuss experimental issues, proposing a scenario i…
The Bell inequality, and its substantial experimental violation, offers a seminal paradigm for showing that the world is not in fact locally realistic. Here, going beyond the scope of Bell's inequality on physical states, we show that quantum teleportation can be used to quantitatively characterize quantum correlations of physical processes. The validity of the proposed formalism is demonstrated by considering the problem of teleportation through a linear three-node quantum network. A hierarchy is derived between the Bell nonlocality, nonbilocality, steering and nonlocality-steering hybrid cor…
Recently Yu and Sun [Int. J. Theor. Phys. DOI 10.1007/s10773-014-2360-x] have presented probabilistic teleportation of 3-qubit cat state via 6-qubit cluster state. The success probability depends on absolute value of only two of the coefficients of cluster state i.e. |c|^2 + |d|^2. We have demonstrated the feasibility to teleport 3-qubit cat state via 2-qubit non maximally entangled Bell state instead of a complex state like 6-qubit non maximally entangled cluster state. In this comment we have prescribed an optimal protocol for teleportation of n-qubit state of the form (α|x> + β|\bar{x}>)_n …
A general matrix approach to study entangled states is presented, based on operator completeness relations. Bases of unitary operators are considered, with focus on irreducible representations of groups. Bell measurements for teleportation are considered, and robustness of teleportation to various kinds of non idealities is shown.
In quant-ph/0201134 Jennewein et al. report experiments demonstrating entanglement swapping under various conditions. In one instance, they claim to have exhibited Bell inequality violations by a pair of photons prior to performing any entangling operations on the pair. However, the Bell inequality violation results in this case from post-selection of the data, not from quantum non-locality.
Quantum superpositions of coherent states are produced both in microwave and optical domains, and are considered realizations of the famous "Schrödinger cat" state. The recent progress shows an increase in the number of components and the number of modes involved. Our work creates a theoretical framework for treatment of multicomponent two-mode Schrödinger cat states. We consider a class of single-mode states, which are superpositions of $N$ coherent states lying on a circle in the phase space. In this class we consider an orthonormal basis created by rotationally-invariant circular states (RI…
By exhibiting a violation of a novel form of the Bell-CHSH inequality, Zukowski has recently established that the quantum correlations exploited in the standard perfect teleportation protocol cannot be recovered by any local hidden variables model. Allowing the quantum channel state in the protocol to be given by any density operator of two spin-1/2 particles, we show that a violation of a generalized form of Zukowski's teleportation inequality can only occur if the channel state, considered by itself, violates a Bell-CHSH inequality. On the other hand, although it is sufficient for a teleport…
We study a continuous-variable (CV) teleportation protocol based on a shared entangled state produced by the quantum-nondemolition (QND) interaction of two vacuum states. The scheme utilizes the QND interaction or an unbalanced beam splitter in the Bell measurement. It is shown that in the non-unity gain regime the signal transfer coefficient can be enhanced while the conditional variance product remains preserved by applying appropriate local squeezing operation on sender's part of the shared entangled state. In the unity gain regime it is demonstrated that the fidelity of teleportation can b…
We 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…
