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NONLOCAL COMMUNICATIONS BY ENTANGLED STATES

Below is a description of a paper that we wrote exploring a model system for communication through entanglement, followed by a discussion of the feasibility for nonlocal communication. If you have some background and or funding in this area and are interested in a collaboration, please contact me. Thanks.

BREAKTHROUGH PAPER PUBLISHED November, 2004

Y. Aharonov, J. Anandan, J. Maclay, J Suzuki, "Model for entangled states with spin-spin interaction," Physical Review A 70, 052114 (2004). also published in Virtual Journal of Quantum Information.

This paper was done in collaboration with Prof. Yakir Aharonov, one of the premier quantum theorists in the world today. He is one of the greats who laid the foundations of measurement theory and has clarified the relationship between relativity and quantum theory. He is always looking for new and interesting phenomena in quantum theory! The Aharonov-Bohm effect is named after him and his thesis advisor. Another collaborator was the late Prof. Jeeva Anandan, on the faculty at Univ. of South Carolina. He worked with Prof. Aharonov for over a decade, and was a very thoughtful, very skilled quantum physicist, with deep insight and, most admirable, a mind open to new possibilities and new people. He was a caring, gentle, and wonderful human being, whom I miss very much.

This paper describes a very simple system of two uncharged spin ½ particles that interact through their magnetic dipoles. It turns out that this interaction creates an entangled state and several unentangled states. We consider a situation when the two particles are far apart, and a magnetic field is applied in the region occupied by one particle only. The correlated change in the spin of the other particle can be determined using what is called a protective measurement, in which the wavefunction does not collapse. Instead, the classical pointer has an adiabatic and reversible interaction with the system that does not change the state of the system. Using a single protective measurement, it is possible to determine the spin of the particle that was not exposed to the magnetic field, and thereby to determine the magnitude of the field applied to the other particle. After the protective measurement, the magnitude of the magnetic field could be changed, and the new value determined by a new protective measurement. Thus a nonlocal communication link has been established. The only problem is that the range is limited by the strength of the dipole potential to micrometers. We plan to explore other potentials and systems in an effort to extend the range.

There are several important points about this paper vis a vis proofs that it is impossible to communicate nonlocally. All these proofs assume that there is no interaction between the particles, which is not only a major assumption about locality, but also means the Hamiltonian is unphysical for two reasons: 1. there is nothing to guarantee the system has the right statistics, 2. any communication would automatically violate the second law of thermodynamics since a change in information or entropy would necessitate a change in the free energy of the particles, but if there is no interaction Hamiltonian, this is impossible. Our system had a real Hamiltonian and that, I think, is why it worked, at least for a short distance. The question is, is it possible to pick a physical system with a real Hamiltonian so that we have a link when the force between the particles gets very, very small.

Feasibility of Non-Local Communications using Entangled Pairs

Jordan Maclay, Quantum Fields LLC

Overview

For all space missions, it is imperative to have reliable communication links to transmit data, computer codes, or other information. The current electromagnetic communications technologies (including laser, RF, X band, S band) do not scale well as the mission distance increases. With current methods, the power, weight, cost and complexity increase rapidly with distance, while the transmission reliability decreases. For shorter distances, secure and reliable communications that cannot be jammed are very desirable. We propose to explore the possibility of a revolutionary approach to communications based on recent theoretical and experimental developments in quantum physics, in particular based on quantum correlations between entangled atoms or ions (EPR pairs). Recent experiments have verified the existence of quantum correlations between entangled photons, in which the polarization measurement of one photon is always correlated with the measured polarization of another, distant photon. Similar correlations have been observed in entangled ions. Theory indicates it is not possible to use standard quantum mechanical measurements of entangled systems, such as polarization correlations of photons, for communications. Standard measurements collapse the wavefunction and end the entanglement before any information has been transmitted. However, if adiabatic perturbations, which are reversible and do not induce transitions in the atoms, are used to modulate the spin of an entangled pair, and if some of the newly proposed methods of securing information from quantum systems, such as "protective measurements" are employed, it appears there is a possibility that communications may not be altogether prohibited.

If experiment verified that the proposed approach for communications using EPR pairs was viable, it should be possible to develop an almost ideal communication system because the communication link is non-local. By non-local, we mean that there is no known mechanism by which a signal is transmitted from one particle to another, instead the members of the EPR pair seem to be linked as if they were interacting with no distance between them. Einstein referred to this as a " ghost like interaction". There is no know mechanism by which the signal is " broadcast"; no signal has to pass through the atmosphere or space. Because of this non-locality of the EPR interaction, no broadcast power supply or antenna is required on earth or in space, no environmental noise or interference is present, and the signal does not fall off as the inverse square of the distance. For example, the performance of the communications link should not be affected by the presence of matter, such as a star, planet, or atmosphere in the line of sight from a space probe to the Earth. Further since the link is due to entanglement between the two members of an EPR pair, the link should be able to provide secure communications.

The effective speed with which EPR correlations act appears to be orders of magnitude times the speed of light. In a communications system, the data rates would be determined by the characteristic transition frequencies of the elements comprising the EPR pair. For entangled ions, these frequencies are those of atomic motion, and consequently high data rates (a minimum of about 10⁶ bps) would be expected.

There have been great advances in the manipulation of entangled ions primarily driven by the research for quantum computing. The methods developed for manipulating entangled ions suggest that there should be no fundamental difficulty in constructing a compact, and lightweight system for communications should the proposed method of adiabatic modulation be validated by experiment. As always, technical challenges are to be expected.

Figure 2. Schematic of EPR link between two distant modules, each with an atom of an entangled pair in identical environmental chambers. One atom is adiabatically perturbed by impressing a small RF signal using the attached coils. The response is monitored by the corresponding coils in the chamber with the other entangled particle. No standard quantum mechanical measurements are used.

A schematic of the proposed communication link is shown in Figure 2. Two entangled atoms would be separated and maintained in separate environmental enclosures. The enclosures would prevent any environmental interaction, which could cause decoherence and end the entanglement. Today researchers have maintained single electrons and single atoms in such enclosures for over 6 months. The enclosures could be separated as desired. Each enclosure would have an identical means for generating and measuring a time varying electromagnetic field, probably a SQUID device. The electromagnetic field would be modulated in the sending enclosure, causing an adiabatic precession of the spin of the atom at a certain frequency. The receiving module would detect the modulation of the spin using identical circuitry at this characteristic frequency. This would be sending a "one". If the modulation was at another frequency, this would be sending a "zero". Ideally, one wants to make the communication as symmetric as possible, so one can hardly tell the sender from the receiver. Ideally, one would have time reversal invariance and conservation of energy. This perfect arrangement is probably not possible, but the “cut” or classical end in reversibility is as late as possible in the interaction. The modulation and detection would be done as an adiabatic interaction, without any permanent change in the state of the entangled atoms. In practice, probably multiple entangled ions would be used in each send/receive module to enhance reliability and performance.

Background

In order to have a communication link, it is essential to maintain the entanglement, and avoid collapsing the wavefunction. One approach to this is to employ protective measurements, which are based on the standard quantum formalism, but have very different features from the usual von Neumann quantum mechanical measurements in which the wavefunction collapses during the measurement. In effect, the protective measurement employs an adiabatic interaction of a “pointer” with the system to be measured, which avoids any permanent change in the wavefunction (Y. Aharanov, J. Anandan, L Vaidman, “The meaning of Protective Measurements,” Found. Of Physics 26, 117 (1996)).

Using quantum mechanical models of interacting particles, we have explored the effect of applying perturbations and making protective measurements in a simple system. Our model has two separated, entangled spin ½ particles that interact with the spin-spin potential. (Aharanov, Anandan, Maclay and Suzuki, “Model for entangled states with spin-spin interaction,” PRA 70, 052114(2004)). The conclusion of the paper states: “Although the external field is applied only in one part of the system, the other part will be affected by it due to the entanglement of the system. This manifests the nonlocality of the entanglement in quantum mechanics. It appears that protective measurements can be used to determine the density matrix without ending the entanglement. One limitation in the signaling between the two regions of space in the model lies in the requirement that we must have an adiabatic perturbation or transitions will occur between states. When the magnetic field is turned on, it must be done slowly enough so that no transitions are induced between the initial state and other states. Although the specific restrictions depend on the manner in which the perturbations are applied, they require that the dipole interaction does not vanish. ”

A magnetic field is applied in one region, essentially containing one particle, and the response of the particle in the other region is observed. Based on our preliminary models, it appears current theory restricts but may not deny altogether the possibility of using quantum mechanical correlations of adiabatic perturbations of entangled atoms as a means of communicating information. This is an important conclusion. If an interaction between the particles in the EPR pair is present, for example, dipole-dipole forces, then communication is possible using protective measurements. Some limitations were identified in our model that highlight the requirements for a higher bandwidth system. The use of the 1/r^3 potential limited the range of the communication link to microns. In addition, because of the energy levels of this particular system, meeting the requirement for the adiabatic approximation limited the modulation frequency and therefore the baud rate. These technical limitations can be circumvented by using other systems with longer range interactions, for example a 1/r interaction, and more favorable energy levels which would be available with ions. Hopefully, however, correlations are present for adiabatic perturbations when there is no interaction through a potential between the EPR pair, which eliminates issues with range. (This is the case for photons.) Also, by selection of the proper ions, with widely spaced, non degenerate energy levels, greater bandwidth can be obtained.

In order to explore the possibility of correlations with well separated members of an EPR pair with a magnetic moment, we did a calculation of the spin and trajectory of each of the entangled particles in a Stern Gerlach experiment. The calculation was done using Bohm’s causal interpretation of quantum mechanics, which predicts the same eigenvalues in a measurement as standard quantum mechanics. In standard quantum mechanics, there is a non-unitary collapse of the wavefunction, and the observable assumes an eigenvalue. On the other hand, in the causal interpretation, the wave evolves in time gradually until it finally reaches a state with the same eigenvalue. The causal interpretation allows us to calculate the time dependence of the wavefunction as it evolves into a eigenfunction for the eigenvalue measured.

We used the causal theory to calculate the relative orientation of the spin vectors for two entangled particles as they both pass through a magnetic field. This calculation was first done by Dewdney et al, “Causal account of EPR spin correlations,” J. Phys. A: Math. Gen. 20, 4717-4732 (1987). It is also discussed in P. Holland, The Quantum Theory of Motion, (Cambridge U., Cambridge, England, 1993). Our results (calculated by Paul Alsing) were in agreement, showing that the spin of each particle is rotated as it passes through the magnetic field, and that during this entire process Sz1(t) + Sz2(t) =0. In this equation we have shown the spins as a function of time, and total spin remains zero at all times. The particles are deflected in opposite directions (splitting of the beam). The final state is Sz1 = ½ and Sz2 = -½. Thus the spins remain continuously correlated during the entire process. A plot of the wavefunctions for a time after the two particles have passed through the magnetic field is show in the left side of Figure 2. Here x is about the same for each wavepacket, and y is different due to the separation of the wavepackets by the magnetic field. The left side shows the deviation from perfect spin correlation, and is of the order of 10^-17, the limits of the calculation.

Figure 2. The left side shows the wavepacket for two separated spin +-½ particles after passing through a homogeneous magnetic field. The right side shows the deviation on the total spin from zero. The deviation is at the level of the precision of the calculations, about 10^-17.

We did a second calculation, also in agreement with Holland, in which only one of the entangled particles passed through the magnetic field. Again in this case, the spins remained continuously correlated Sz1(t) + Sz2(t) =0. Only the particle that passed through the magnetic field was displaced, but the spins of both were rotated. These calculations show that the spins of two entangled particles are correlated continuously when only one particle is exposed to a perturbation. If we imagine applying a time dependent electromagnetic field to one member of an EPR pair, the causal theory of quantum mechanics appears to predict that the spin of other member would respond accordingly, maintaining the entanglement, which would support the feasibility of communication if we have suitable way to detect the spins, such as using a protective measurement.

Our current understanding of correlations in EPR pairs, based on experiments and our calculations, is shown in Figure 3, where the distance between the pairs is plotted horizontally, and the strength of the perturbation on each member of the pair is plotted vertically. The only experimentally explored and verified region is for strong interactions which use conventional quantum mechanical measurements, for separations from microns (entangled ions) to km (photons).

Figure 3. EPR correlations in the behavior of the members of an entangled pair as a function of the separation and the strength of the perturbation.

We should mention, that with an adiabatic perturbation in our protective measurement approach, the wavefunction evolves continuously as an eigenfunction of the instantaneous Hamiltonian. The perturbation can become large, and still reversible, as long as the energy of the system does not cross the energy for another state, which could result in a transition, ending the entanglement.

Experimental Background

The proposed approach to communication via entangled states is enabled by recent advances in the three overlapping areas of research: 1)New experimental methods for generating and manipulating entangled ions; 2)Recent advances in experimental measurements of EPR correlations, especially with photons; 3) New methods for quantum mechanical measurement. The primary objective for these new experimental methods with trapped ions is to advance quantum computing. Entangled states of multiple ⁹Be⁺ ions have been prepared by Dr. David Wineland's group at NIST. The entanglement of the trapped ⁹Be⁺ is accomplished by coupling the center of mass movement to the spin using Raman transitions. Single atoms can be manipulated in cavity QED. Dr. Wineland, with whom we have had discussions regarding this project, suggested using an “ancilla,” an extra ion weakly coupled to the entangled ion, in order to perform the measurements adiabatically. EPR pairs of entangled ¹⁹⁹Hg atoms have been created using Raman stimulated dissociation of a mercury dimer by Prof. Edward Fry at Texas A&M. EPR correlations in polarization have been demonstrated for distances of 10s of km, with effective speed of transmission of over 10⁴ c.

Causality Issues

FTL communication is prohibited by "Impossibility Proofs." John Bell describes impossibility proofs as an indication of lack of creativity. We believe that by

avoiding violation of the assumptions made in standard impossibility proofs, such as the use of standard measurements or using an assymetric Hamiltonian that depends on only the coordinates of one member of an entangled pair, it may be possible to have FTL communication. Another issue with FTL communication is potential violations of causality. By going to different reference frames, it is possible to change the order of the time difference between two events, thus switching cause and effect. Much has been written on this issue, with the suggestion that nature has a way of protecting what is important, and of preventing inconsistencies, but not necessarily making a blanket prohibition on all FTL communication. A principal of self-consistency states that “a local solution to the equations of physics can occur in the real Universe only if it can be extended to be part of a global solution, one which is well defined throughout space time. “ (Friedman et al, “Cauchy problems in spacetimes with closed timelike curves,” Phys. Rev. D 42, 1915 (1990)).

G. Jordan Maclay, PI - NIAC Phase I contract, May 1, 2000

ABSTRACT: FEASIBILITY OF COMMUNICATIONS USING QUANTUM CORRELATIONS

For all space missions, it is imperative to have reliable communication links to transmit data, computer codes, or other information. The current electromagnetic communications technologies (including laser, RF, X band, S band) do not scale well as the mission distance increases. With current methods, the power, weight, cost and complexity increase rapidly with distance, while the transmission reliability decreases. We propose to explore the possibility of a revolutionary approach to communications based on recent theoretical and experimental developments in quantum physics, in particular based on quantum correlations between entangled atoms or ions (EPR pairs). Recent experiments have verified the existence of quantum correlations between entangled photons, in which the polarization measurement of one photon is always correlated with the measured polarization of another, distant photon. Theory indicates it is not possible to use standard quantum mechanical measurements on entangled systems, such as polarization correlations of photons, for communications. Current theory restricts but may not deny the possibility of using quantum mechanical correlations in small movements or adiabatic perturbations of entangled atoms as a communication means. Further, if non-linear modifications to quantum mechanics suggested by Nobel Laureate S. Weinberg are present, then EPR communication is clearly allowed. If experiment verified that the use of EPR pairs was viable, it should be possible to develop an almost ideal communication system, a compact, low weight, communication architecture in which no broadcast power or antenna is required, no environmental noise is present, the signal does not fall off as the inverse square of the distance, and high data rates with complete security are possible. The purpose of this effort is to investigate the possibility of using quantum correlations in the adiabatic movements of atoms as a means of communication, to perform an initial theoretical feasibility analysis, identifying the key issues with such an approach, and to propose an experiment to resolve some of the fundamental questions.

NIAC Phase I Slide Presentation

NIAC (NASA Institute for Advanced Concepts)

http://www.niac.usra.edu/studies/studies.jsp see under Jordan Maclay

NIAC Final Report Phase I (pdf file)