Computational Nanosciences

QUANTUM TELEPORTATION

In recent years, there has been increased interest in exploiting the unique capabilities that quantum mechanics offers for the processing of information. In that context, quantum teleportation (QT) is a particularly attractive paradigm. It involves the transfer of an unknown quantum state over an arbitrary spatial distance by exploiting the prearranged entanglement (correlation) of "carrier" quantum systems in conjunction with the transmission of a minimal amount of classical information. The potentially enormous economic and national security implications of a successful realization of a loopholes-free QT system has led to an intense competition among the few laboratories that have the experimental capabilities to adequately address this challenge.

Objective

The primary goal of this task is to study the signaling potential of quantum information processing systems based on quantum entanglement. Our initial effort will focus on the development of an ultra-bright EPR source. The emphasis will be on multi-channel quantum teleportation. The nonlocality of the correlations of two particles in quantum entanglement has no classical analog. It allows coherent effects to occur instantaneously in spatially separate locations. Thus, the question naturally arises as to whether a more general formulation of QT could be derived to provide a basis for superluminal communications. The underlying theoretical challenges will be studied.

Background

The concept of Quantum Teleportation (QT) was first discussed by Aharonov and Albert (AA) using the method of nonlocal measurements [1]. Over a decade later, Bennett, Brassard, Crepeau, Jozsa, Peres, and Wooters (BBCJPW) proposed a detailed alternate protocol for teleportation [2]. It consists of three stages. First, an Einstein-Podolsky-Rosen (EPR) [3] source of entangled particles is prepared. Sender and receiver share each a particle from a pair emitted by that source. Second, a Bell-operator measurement is performed at the sender on his EPR particle and the teleportation-target particle, whose quantum state is unknown. Third, the outcome of the Bell measurement is transmitted to the receiver via a classical channel. This is followed by an appropriate unitary operation on the receiver's EPR particle. To justify the name "teleportation", BBCJPW note that the unknown state of the transfer-target particle is destroyed at the sender site and instantaneously appears at the receiver site. Actually, the state of the EPR particle at the receiver site becomes its exact replica. The teleported state is never located between the two sites during the transfer.

A number of exciting theoretical developments have appeared since the publication of the AA and BBCJPW protocols. For instance, Vaidman has shown [4] how nonlocal measurements can be used for the teleportation of the unknown quantum states of systems with continuous variables. In AA, nonlocal refers to measurements that cannot be reduced to a set of local measurements; for example, the measurement of a sum of two variables related to two separated spatial locations. He was also the first to suggest a method for two-way teleportation. Braunstein and Kimble extended Vaidman's analysis to incorporate finite degrees of correlation among the relevant particles and to include inefficiencies in the measurement process [5]. In their proposed implementation of QT of continuous quantum variables, the entangled state shared by sender and receiver is a highly squeezed two-mode state of the electromagnetic field, with the quadrature modes of the field playing the roles of position and momentum. Stenholm and Bardroff have generalized the BBCJPW protocol to systems of arbitrary dimensionality [6]. Zubairy has considered the teleportation of a field state (a coherent superposition of 2n Fock states) from one high-Q cavity to another [7]. In the previously cited studies, QT dealt with "intraspecies" teleportation e.g., photon-to-photon. Maierle, Lidar, and Harris were recently the first to introduce an "interspecies" teleportation scheme [8]. Specifically, in their proposal, the information contained in a superposition of molecular chiral amplitudes is to be teleported to a photon. Finally, Brassard, Braunstein, and Cleve have argued [9] that QT is an essential ingredient for quantum computing, and have presented a simple circuit that implements QT in terms of primitive operations in quantum computing.

Let us turn to experimental realizations of QT. The first laboratory implementation of QT was carried out in 1997 at the University of Innsbruck by a team led by Anton Zeilinger [10]. It involved the successful transfer of a polarization state from one photon to another. A type-II degenerate, pulsed parametric down-conversion process was used to generate the polarization-entangled EPR source. The experimental design is relatively easy to implement. The drawback is that only one of the four EPR-Bell states can be distinguished. In 1998, the Zeilinger team demonstrated that freely propagating particles that never physically interacted with one another could also readily be entangled [11]. In this experiment, one photon each from two pairs of polarization-entangled photons were subjected to Bell-state measurement. As a result, the other two photons were projected into an entangled state. This result is remarkable, since it shows that quantum entanglement does not require entangled particles to originate from a common source or to have interacted in the past. The second QT experiment reported in the open literature in February 1998 was carried out at the University of Rome by a team lead by Boschi and Popescu [12]. It involved a quantum optical implementation. The polarization degree of freedom of one of the photons in the EPR pair was employed for preparing the unknown state. The idea is to exploit the fact that the two degrees of freedom of a single photon can be k-vector entangled. This method cannot, however, be used to teleport an external, unknown quantum state. The conservation of energy and time photon entanglement over distances exceeding 10 km has been demonstrated experimentally [13] using a telecommunications fiber network. In a similar vein, the distribution of cryptographic quantum keys over open space optical paths of approximately 1km was also reported [14].

Currently, there is an intense competition among the few laboratories that have the experimental capabilities to successfully realize a loopholes-free QT system. A particularly "hot" topic is to demonstrate which scheme is more "complete" [15] or more "unconditional" [16]. However, Vaidman has proved that reliable QT can not be achieved using the methods implemented in the experiments reported to date [17]. Specifically, it is impossible to perform complete Bell operator measurements without using interaction between the quantum states of the particles.

The issue of whether a more general formulation of QT could provide a basis for superluminal communications has recently been the subject of considerable debate in the open literature [18]. There are basically two schools of thought: one, which precludes this possibility (based, for example, on conflicts with the theory of special relativity), and one which allows it under special provisions. Arguing against superluminal communication, Furuya et al analyze a paradigm proposed by Garuccio. There, one of the photons of a polarization-entangled EPR pair is incident upon a Michelson interferometer in which a phase-conjugation mirror (PCM) replaces one of the mirrors [19]. Garuccio postulates that the sender (located at the source site) can superluminally communicate with a receiver (located at the detector site) based on the presence or absence of interferences at the detector. The scheme uses the PCM property that a reflected photon has the same polarization as the incident photon (contrary to reflection by an ordinary mirror), allowing to distinguish between circular and linear polarization. Furuya et al prove that Garuccio's scheme would fail if non coherent light is used, because then the interferometer could not distinguish between unpolarized photons prepared by mixing linear polarization states or by mixing circular polarization states. They admit, however, that their counterproof would not apply to a "generalized" Garuccio approach, which would use coherent light states. In a more encompassing framework, Peres recently formulated [20] criteria that would prevent superluminal signaling. These criteria must be obeyed by various operators involved in classical interventions on quantum systems localized in mutually spacelike regions.

What are the arguments in favor of superluminal information transfer? Gisin shows [21] that Weinberg's general framework [22] for introducing nonlinear corrections into quantum mechanics allows for arbitrarily fast communications. It is interesting to note that, in a recent book [23], Weinberg himself states: "I could not find a way to extend the nonlinear version of quantum mechanics to theories based on Einstein's special theory of relativity (Ö) both N. Gisin in Geneva and my colleague Joseph Polchinsky at the University of Texas independently pointed out that (Ö) the nonlinearities of the generalized theory could be used to send signals instantaneously over large distances". In a similar vein, Mittelstaedt has reviewed [24] the arguments that had been put forward in recent years in order to show that non-local effects in quantum systems with EPR-like correlations can not be used for superluminal communications. He demonstrated that most of these arguments are based on circular proofs. For instance, a "locality principle" can not be used to exclude superluminal quantum signals and to justify quantum causality, since the locality principle itself is justified by either quantum causality or an equivalent "covariance postulate" [24]. Moreover, if the existence of superluminal signals is assumed ab initio [18], and consequently a new space-time metric (different from the Minkowskian metric) is adopted, all the paradoxes and difficulties discussed above would immediately disappear [25].

Approach

The simplest quantum states for QT involve two-level systems, including spin states of a spin particle, the polarization states of a photon, the ground and excited state of an atom or ion, or the Fock states of a microwave cavity. In the following discussion, without loss of generality, we will use polarization states. Before a polarization-entangled photon can be used for QT (including applications such as quantum cryptography or quantum remote sensing), it is essential to characterize the EPR source in detail.

The preparation of polarization-entangled photons uses the process of optical parametric down-conversion (OPDC) [26]. This process employs a nonlinear medium, which allows pump photons to decay into pairs of photons under the restrictions of energy and momentum conservation. Since the two "decay" photons are created at the same time, the detection of one photon indicates with almost certainty the existence of the other. The conservation of energy and momentum also allows the determination of one photon's wavelength and direction provided the other one's are known. Three phase-matching methods are currently available for generation of correlated photons. They are referred to as type-I, type-II and cascaded type-I.

In a type-I process, the generated photon pair shares the same polarization. With this method, a broad range of momentum and energy entangled photon pairs can be produced, either in a non-degenerate geometry, such that they have different wavelengths, or in a degenerate geometry, where the two photons share the same wavelength. The limitation of type-I OPDC is that the photons are actually created in polarization product-states, and may not violate a true test of Bell's inequalities. In a type-II process [27], the photon pair is created with orthogonal polarizations. Therefore, as opposed to the type-I source, the photons emitted into two distinct modes are usually not entangled, because they can be distinguished on the basis of their polarization. It was found that, when the cut angle of the crystal is larger than that of the degenerate OPDC (or when the crystal is tilted toward that direction), the two emission cones corresponding to different modes would overlap. In the two directions determined by the cones' intersection the polarization distinguishability disappears. Therefore, such a source can produce polarization-entangled photon pairs. Typical emission patterns of type-I and type-II OPDC are shown in Figure 1. Here, the type-I BBO crystal has a cut angle of 29.6† and was tilted 0.2† (internal), while the type-II BBO crystal has a cut angle of 42.9† and was tilted 2.5† (internal). Detailed explanations are provided in the caption.

Figure 1. Simulated emission patterns of extraordinary beams (left), ordinary beams (center) and separations between extraordinary beams ("¥") and ordinary beams ("+") with (a) type-I and (b) type-II phase matched OPDC in a BBO crystal. The pump wavelength is 395 nm. The solid circles correspond to a degenerate case. All patterns are calculated over a 10†×10† solid angle except the top right one, which is calculated over a 4†×4† solid angle.

In Figure 2 we show a possible geometry where the crystal cut angle is larger than that of the degenerate OPDC. Polarization-entangled photon pairs, labeled as A and B, propagate along the two directions where the cones intersect. The horizontal polarization (Æ, ordinary) and the vertical polarization (‚, extraordinary) are orthogonal, and the corresponding polarization-entangled two-photon state is given by

(1)

The relative phase a arises from the crystal birefringence, and an overall phase shift is omitted. With the help of additional half wave or quarter wave plates, one can easily produce any of the four EPR-Bell states,

(2)

(3)

Figure 2. Geometry of a type-II OPDC. Polarization entangled photons are found along the two intersection directions (A and B) of the two emission cones.

We have already demonstrated type-II OPDC with a femtosecond pump source. The pump laser system is a mode-locked Ti: Sapphire laser (Mira 900-F from Coherent) pumped by an Argon laser (INNOVA Sabre from Coherent). The output gives a 76 MHz pulse train at a wavelength of 790 nm, with 120 femtosecond pulse width and 1.2 watt CW power. The UV beam is generated with a 7-mm thick LBO crystal (from CASIX) cut for second harmonic generation (SHG) at 790 nm. The conversion efficiency from IR to UV is about 40%. After passing through a prism pair for dispersion compensation and fundamental removal, the final UV beam has a pulse width of less than 200 fs and 300 mW power. Figure 3 shows the overlapped photon cones, generated by type-II OPDC. An interference filter with a bandwidth of 2 nm (from Avdover) is placed before the single photon counting module (SPCM-AQR-14 from EG&G Canada). The maximum photon counting rate is 7000 (sec-1) (counted by fiber with background subtracted). The polarization correlations can be measured using the setup shown in Figure 2. With q1 set at -45ƒ,

Figure 3. Emitted photon cones scanned with a 100-mm diameter fiber over a 1 cm ¥ 1 cm area, 6.5 cm behind the crystal's output surface. A 3-mm thick BBO with cut angle of 43ƒ is used for type-II OPDC. An interference filter with bandwidth of 2 nm is placed before the SPCM. a) corresponds to a collinear and b) corresponds to a non-collinear case. The angleq is the effective internal angle between the optical axis and the pump UV beam direction.

and q2 rotated from -45ƒ to 315ƒ, the coincidence rate from the two detectors can be recorded. This measurement will determine which of the four Bell states given in Eqs (2,3) is produced [28].

Research Tasks

A new method, that uses the process of OPDC in an innovative geometry involving two type-I crystals, has recently been reported [29]. Two adjacent, relatively thin nonlinear crystals are operated with type-I phase matching. The identically cut crystals are oriented so that their optic axes are aligned in perpendicular planes. Under such conditions, a 45ƒ polarized pump photon will be equally likely to down convert in either crystal. Generally photons generated by different crystals can be distinguished by their polarizations. This problem was solved by inserting quarter-wave plates behind the crystal pairs. Furthermore, these two possible down-conversion processes are coherent with one another. We propose an innovative variant to such an architecture, which should result in an ultra-bright EPR source.

Cascaded Type-II Optical Parametric Down-conversion. Our EPR source will be based on optical parametric down-conversion, but with a novel, cascaded type-II OPDC configuration. It is expected to combine the main advantages of, and outperform previously reported entangled photon generators. It will consist of two adjacent thin nonlinear crystals with identically cut angles, which correspond to degenerated type-II phase matching. The two crystals will be oriented with their optic axes aligned in opposite direction. A pump photon may then be equally down-converted in either crystal, and these two possible downconversion processes will generate two pairs of correlated photons. The advantages of our proposed architecture are obvious. First, the limitation in overlap of idler and signal photons will be greatly relaxed compared with the case in cascaded type-I OPDC. Our architecture will thus be able to provide much brighter polarization-entangled photons in either degenerate or non-degenerate cases. Second, the outputs will be naturally polarization-entangled. Third, in the directions corresponding to the intersections of the two cones, the two pairs of polarization-entangled photons will coincide exactly. By selected alignment, such a source may work as a four-photon entanglement source.

(4)

Two-photon interferometry for analyzing entanglement. If one overlaps two photons at a beamsplitter, interference effects determine the probabilities to find the two photons incident one each from A and B either both in one of the two outputs or to find one in each output. Only if two photons are in the state will they leave the beam splitter in different output arms. If one puts detectors there, a click in each of them, i.e. a coincidence, means the projection of the two photons onto the state |y->. For the other three Bell states both photons will exit together through one of the two output arms. To register two photons in one output arm, additional detectors or a certain detuning of the setup is necessary since these detectors do not distinguish between one or more photons. This architecture will be used to study multi-photon entanglement.

Figure 4. Experimental setup for measure- ment of entanglement and interference

Superluminal signaling. Formidable theoretical challenges must be overcome if an application of QT technology to communications is to become possible. The ultimate feasibility question is, in our minds, still open. We will focus our attention on two recent gedankenexperiments for superluminal communications. Greenberger has shown [30] that if one can construct a macroscopic Schrodinger cat state (i.e., a state that maintains quantum coherence), then such a state can be used for sending superluminal signals. His scheme assumes that the following two requirements can be realized. First, it should be possible to entangle the signal-transmitting device with the signal itself, thereby constructing a GHZ state. Second, non-unitary evolution can be established and controlled in a subset of the complete Hilbert space. This latter property has already been demonstrated successfully in several downconversion experiments. Greenberger uses an optical phase shifter as model for his signaling device. We believe that as of this date better alternatives are available. The second gedankenexperiment we intend to examine was introduced by Srikanth [31]. His proposed method uses a momentum-entangled EPR source. Assuming a pure ensemble of entangled pairs, either position or momentum is measured at the sender. This leaves the counterpart in the EPR pair as either a localized particle or a plane wave. In Srikanth's scheme, the receiver distinguishes between these outcomes by means of interferometry. Since the collapse of the wavefunction is assumed to be instantaneous, superluminal signal transmission would be established. We intend to explore both the theoretical implications and the possible experimental realizations of the above paradigms.

Deliverables and Milestones

Proposed major milestones for the basic research tasks described in this section are given below. All work will be performed on a best-effort basis.

FY 01: A cascaded type-II EPR source will be demonstrated (03/01). Its brightness will be at least one order of magnitude higher than previously reported polarization-entangled EPR sources. This brightness will allow increased coherence and reduced measurement time. A QT experiment using the new, ultra-bright source in an innovative architecture will be performed (09/01).

FY 02: A theoretical framework for possible superluminal communication will explored (02/02). A four-photon entanglement source using our cascaded type-II EPR architecture will be demonstrated. A multi-channel QT experiment using our new four-photon entanglement source will be conducted (05/02). Opto-electronic implementations of the Greenberger and Srikanth gedankenexperiments will be completed (09/02).

FY 03: An experimental demonstration of superluminal communications will be attempted (06/03). Potential applications of QT to remote sensing will be formulated (09/03).

Furthermore, we will deliver to DOE/BES one copy of each publication submitted to the open literature, and one copy of each invention disclosure submitted for patent. Major technical highlights will also be provided to DOE/BES on a timely basis.

References

CESAR - Center for Engineering Science Advanced Research Oak Ridge National Laboratory

Disclaimers    -