Communication method using the entangled state

A first photon in single-photon state is created when one of two photons created by parametric down conversion of a pump light is detected at a first detector. The first photon is divided into two components by a polarization beam splitter, and the first component is sent to a sender while the second component is sent to a receiver, with information that one of the two photons is detected. The sender selects whether he measures the first component or not according to the signal that he wants to transmit to the receiver. The second component of the first photon and a probe light enter into the second nonlinear optical medium. The receiver detects the phase modulation of the probe light caused by the interaction with the second component using homodyne detection during a first span after he receives the information from the first detector.

FIELD

The embodiments discussed herein are related to a communication method using the entangled state, and a communication method using optical Kerr effect.

BACKGROUND OF THE INVENTION

For current communication technology, telecommunication or optical fiber communication has been widely used. In the communication method that uses electricity or light, the signal transmission speed is limited below speed of light.

On the other hand, the quantum communication technology or quantum cryptography based on the principle of quantum mechanics is being actively researched.

Moreover, the quantum teleportation, reproducing a quantum state in another system, is also being researched using the entangled state. In the quantum code or the quantum teleportation, the collapse of the wave packet (decoherence) is used. The collapse of the wave packet occurs instantly when measurement is done, and a strong correlation appears in each measurement result of each part in the entangled state.

However, it is said that it is not possible to use the entangled state to send information because an individual measurement result of the entangled state is quite random and we cannot arbitrarily choose the measurement result. Therefore, even in the quantum code or the quantum teleportation, the communication process at the speed below speed of light is needed to actually send information. So the signal transmission speed becomes below speed of light.

U.S. Pat. No. 8,774,641 shows a communication method using the entangled state created from a single-photon state and the cross phase modulation (optical Kerr effect) in the nonlinear optical medium. But it is often the case that a single-photon state is created probably with relatively small probability. So, the sender and the receiver cannot know when the entangled state is created. And it is not easy to keep enough accuracy of communication because a lot of noise can be mixed in the signal.

Related references are as follows:

Quantum States of Light, SpringerBriefs in Mathematical Physics,

BRIEF SUMMARY OF′THE INVENTION

According to an aspect of the first embodiment, a communication method comprising: the step that two photons are created by parametric down conversion of a pump light in a first nonlinear optical medium, and a first photon in a single-photon state is created by the detection of one of the two photons at a first detector; the step that the first photon is divided into two components by a polarization beam splitter, and the first component is sent to a sender while the second component is sent to a receiver, with an information that one of the two photons is detected at the first detector; the step that the sender measures the first component of the first photon when he sends “1”; the step that the sender doesn't measure the first component of the first photon when he sends “0”; the step that the second component of the first photon and a probe light enter into a second nonlinear optical medium; the step that the second component of the first photon interacts with the probe light in the second nonlinear optical medium; the step that the receiver measures the phase modulation of the probe light caused by the interaction with the second component of the first photon, during first span after the receiver received the information that one of the two photons is detected at the first detector; the step that the receiver distinguishes the signal sent from the sender by utilizing the result of the measurement of the phase modulation.

DETAILED DESCRIPTION OF THE INVENTION

Communication Method of the First Embodiment

A method for communication according to the present first embodiment will be described with reference toFIGS. 1to3.FIGS. 1 to 3are schematic views of the instruments according to the first embodiment. The related reference is U.S. Pat. No. 8,774,641. InFIG. 1, a dotted line41means instruments of a sender and a dotted line42means instruments of a receiver. Almost at the center between the sender and the receiver, a first nonlinear optical medium20and a first detector17and a polarization beam splitter2are arranged.

A pump light1A enters into the first nonlinear optical medium20. And, by parametric down conversion of the pump light1A in the first nonlinear optical medium20, a first photon1and a second photon1B are created with a certain probability. The second photon1B enters into the first detector17. When the second photon1B is detected at the first detector17, we can know that the first photon1in the single-photon state is also created. Above method to obtain a single-photon state is explained in detail in non-patent documents, Quantum States of Light, SpringerBriefs in Mathematical Physics, DOI 10.1007/978-4-431-55960-3. And it is also explained that each photon of the two photons created by parametric down conversion can have orthogonal polarizations. When the first detector17detects the second photon1B, the first detector17sends an information that the second photon1B is detected to the receiver and the sender. InFIG. 1, the path of the information from the detector17to the receiver or the sender is shown as the line30or the line31. The line30or the line31means ordinary telegraphy.

InFIG. 1, the first photon1in the single-photon state enters into the polarization beam splitter2. It is assumed that the first photon1is in the state of 45 degrees polarization. In the polarization beam splitter2, the first photon1is divided into a first component12with the vertical polarization and a second component13with the horizontal polarization. Here, the first component12and the second component13are in the entangled state. U.S. Pat. No. 8,774,641 uses a half beam splitter to divide a photon in the single-photon state. But a half beam splitter can make the vacuum fluctuation interfere with the entangled state of photon as explained in non-patent documents, Prog. Quant. Electr. 1995, Vol. 19, pp.89-130. Above method using a polarization beam splitter can divide the first photon1without interference caused by the vacuum fluctuation. So, above method can achieve the higher accuracy in creation of the entangled state than the method of U.S. Pat. No. 8,774,641.

InFIG. 1, the first component12of the first photon1is sent to the sender and measured at a second detector15. An optical switch16is arranged just in front of the second detector15, and the optical switch16is in the state “ON” that the light can pass. The sender controls the state of the optical switch using a controller51. InFIG. 1, the sender selects the state “ON” of the optical switch16according to the signal “1” that the sender wants to transmit to the receiver, when the information from the first detector17arrives at the controller51. The line32shows the path through which the command from the controller51to the optical switch16is transmitted. And the first component12of the first photon1arrives at the optical switch16after the state of the optical switch16is fixed to the state “ON” that the sender selects.

On the other hand, the second component13of the first photon1enters into the polarization beam splitter24after the first component12of the first photon1is measured at the second detector15. The second component13of the first photon1passes a polarization beam splitter24, a second nonlinear optical medium21and a polarization beam splitter25.

Moreover, a probe light26enters into the polarization beam splitter24. The probe light26has the vertical polarization, and is reflected in the polarization beam splitter24. The probe light26passes the second nonlinear optical medium21and interacts with the second component13of the first photon1by the optical Kerr effect. Then the probe light26is reflected in the polarization beam splitter25. And the probe light26is measured by instruments for homodyne detection52.

The phase of the probe light26is changed in the second nonlinear optical medium21. The amount of the phase modulation of the probe light26is proportional to the intensity of the second component13of the first photon1. This phenomenon is due to the optical Kerr effect of the second nonlinear optical medium21, and is called cross phase modulation (XPM). The amount of the phase modulation of the probe light26is detected by homodyne detection of the probe light26. The detection of the amount of the phase modulation using homodyne detection is explained in detail in non-patent documents, PRL 93, 250502(2004).

InFIG. 1, instruments for the homodyne detection52is expressed as a box. The line30is connected to the instruments for the homodyne detection52, and the instruments for the homodyne detection52can receive the information from the first detector17. When the instruments for the homodyne detection52receive the information from the first detector17, the second component13of the first photon1arrives at the second nonlinear optical medium21. So, during the first span after the information from the first detector17arrives at the instruments for the homodyne detection52, the probe light26which has the phase modulation caused by XPM enters into the instruments for the homodyne detection52. The result of the homodyne detection during the first span after the information from the first detector17arrives at the instruments for the homodyne detection52is used for communication as follows.

The wave function of the second component13of the first photon1and the probe light26, before the measurement at the second detector15is done inFIG. 1, is expressed in the following Equation 1.

ϕ⁢⁢0=H〉+V〉2⁢α〉Equation⁢⁢1
Initial state Φ0of the entire wave function is shown by the product of the state of the probe light26|α> and the state of .the first photon1(|H>+|V>) /√{square root over (2)}. Here |V> shows the first component12of the first photon1, and |H> shows the second component13of the first photon1. Therefore, |V> and |H> are in the entangled state. Moreover, |α> is the initial state of the probe light26which has the vertical polarization.

In the case that the first component12of the first photon1is not detected in the second detector15inFIG. 1, the state becomes as follows.
ϕ1=||αEquation 2From Equation 1 to Equation 2, the state of the first photon1changes from (|H>+|V>) /√{square root over (2)} to |H>, because it is fixed that |V> doesn't exist by the measurement at the second detector15. Next, the second component13of the first photon1enters into the second nonlinear optical medium21. The probe light26receives the phase modulation by XPM caused by the intensity of the second component13of the first photon1in the second nonlinear optical medium21. The probe light26which gets out from the second nonlinear optical medium21is in the state Φ2expressed by following Equation 3, where the amount of the phase modulation is assumed to be θ.
ϕ2=|H|αeiθEquation 3

Moreover, when the first component12of the first photon1is detected at the second detector15as shown inFIG. 2, the state of the first photon1is fixed to |V>, and the state becomes ϕ3shown by following Equation 4 .
ϕ3=|V|αEquation 4
In this case, because the second component13of the first photon1doesn't enter into the second nonlinear optical medium21, the probe light26which gets out from the second nonlinear optical medium21remains in the state of Φ3. And in this case ofFIG. 2, the amount of the phase modulation is0. The change of the state Φ0into the state of Φ1or Φ3is called the collapse of the wave packet which occurs almost instantly at very short time by the measurement at the second detector15.

Next, the case ofFIG. 3is explained. Optical switch16just in front of the second detector15is set to avert light up inFIG. 3unlike the case ofFIG. 1or FIG.2. Therefore, the measurement of the first component12of the first photon1is not done and the collapse of the wave packet doesn't occur. InFIG. 3, the sender selects the state “OFF” of the optical switch16according to the signal “0” that the sender wants to transmit to the receiver, when the information from the first detector17arrives at the controller51.

Therefore, the second component13of the first photon1enters into the second nonlinear optical medium21, while the second component13of the first photon1is in the state of |H>/√{square root over (2)}. The probe light26receives the phase modulation in the second nonlinear optical medium21by XPM caused by the second component13of the first photon1. And the amount of the phase modulation becomes θ/2forFIG. 3. The factor √½ comes from the intensity of the second component13of the first photon1in the state of |H>/√{square root over (2)}, because the first photon1is divided in two components. Therefore, the probe light26which gets out from the second nonlinear optical medium21is in the state Φ4shown by the following Equation 5.

ϕ⁢⁢4=V〉2⁢α〉+H〉2⁢α⁢⁢ei⁢⁢θ/2〉Equation⁢⁢5
In this case, the collapse of the wave packet occurs when the amount of the phase modulation of the probe light26is measured using homodyne detection. Then the phase modulation is0or θ2.

In the case ofFIG. 1, the probe light26which gets out from the second nonlinear optical medium21is in the state) |αeiθ. So, the amount of the phase modulation of the probe light26is θ. In the case ofFIG. 2, the amount of the phase modulation of the probe light26is0. So, when the measurement of the first component12of the first photon1is executed as shown inFIG. 1orFIG. 2, the amount of the phase modulation of the probe light26is0or θ.

In the case of FIG.3, the probe light26which gets out from the second nonlinear optical medium21is in the state of |αor |αei θ/2. So, the amount of the phase modulation of the probe light26is0or θ2. These amount of the phase modulation0or θ or θ/2can be detected using the technique that is called homodyne detection as explained in detail in non-patent documents, PRL 93, 250502(2004). Therefore, the case ofFIG. 1,FIG. 2and the case ofFIG. 3can be distinguished.

Moreover, in the case ofFIG. 1,FIG. 2andFIG. 3, the receiver can know when the second component13of the first photon1enters into the second nonlinear optical medium21by the information that the photon1B is detected at the first detector17. The information also means that the second component13of the first photon1arrives at the second nonlinear optical medium21and interacts with the probe light26. And the receiver uses the result of homodyne detection during the first span after he receives the information to distinguish the signal sent from the sender. This can improve the accuracy of communication because the receiver can reject the result of homodyne detection during a second span that the interaction (XPM) doesn't occur. The result of the homodyne detection during the second span that the interaction (XPM) doesn't occur acts as noise. The communication method of U.S. Pat. No. 8,774,641 doesn't use the information when the interaction (XPM) between the second component13of the first photon1and the probe light26occurs. So, above method of communication has the advantage of higher accuracy compared to the method of U.S. Pat. No. 8,774,641.

In above discussion, the difference between the amount of the phase modulation θ and θ/2comes from the change of the wave function (collapse of the wave packet) by the measurement at the second detector15. The collapse of the wave packet is a basic concept of the Copenhagen interpretation of the quantum mechanics. So this method also shows the method to observe the change of wave function by the collapse of the wave packet.

A method of communication using the above-mentioned composition is explained here. Two photons are created by parametric down conversion of the pump light1A in the first nonlinear optical medium20. And the first photon1in single-photon state is created when one of the two photons, the photon1B, is detected at the first detector17. And, the first photon1is divided into two components by the polarization beam splitter2. The first component12of the first photon1is sent to the sender and the second component13of the first photon1is sent to the receiver, with the information that the photon1B is detected at the first detector17.

The sender selects the state of an optical switch16arranged just in front of the second detector15according to the signal that he wants to transmit to the receiver, when he receives the information that the photon1B is detected. The optical switch16is set in the state “ON” that the light can pass and the sender measures the first component12of the first photon1in the case that the sender transmits “1” at time 1. Moreover, in the case that the sender transmits “0”, the first component12of the first photon1is prevented from advancing to the second detector15by the optical switch16which is set in the state “OFF” that the light is averted, and the sender doesn't measure the first component12of the first photon1.

The second component13of the first photon1enters into the nonlinear optical medium21at the time 2 after the time 1. The probe light26enters into the nonlinear optical medium21at the same time. The second component13of the first photon1interacts with the probe light26in the second nonlinear optical medium21. As a result, the probe light26which gets out from the second nonlinear optical medium21gets the phase modulation proportional to the intensity of the second component13of the first photon1.

The receiver measures the phase modulation of the probe light26during the first span after he receives the information that the photon1B is detected. This means that the receiver can measure the phase modulation of the probe light26only when the interaction between the second component13of the first light1and the probe light26is expected to occur by utilizing the information from the first detector17. And the receiver knows that the signal is “1” in the case that the phase modulation is θ. Moreover, the receiver knows that the signal is “0” in the case that the phase modulation is θ/2. When the detected phase modulation is0, the receiver cannot know the signal. But by repeating above sequence, the receiver can distinguish the signal with enough accuracy because the phase modulation isn't0with ½ probability.

In the above-mentioned method, two selections whether the sender measures the first component12of the first photon1or not are used for communication. Because the measurement result is not used to transmit the information, the randomness of measurement result doesn't matter. The collapse of the wave packet (decoherence) by the measurement is assumed to occur almost instantly at very short time. Therefore, the signal transmission speed beyond speed of light can be achieved in principle.