1. Introduction

Since Einstein-Podolsky-Rosen [1] proposed their argument against the phenomena currently known as Quantum Entanglement in 1935, it has grasped the interests of all the scientific communities. After almost a century of discussion people have come to the conclusion that, though entanglement can cause particles to collapse at a particular state instantaneously, we cannot use that to transfer classical information faster than the speed of light. In this paper, a novel communication scheme based on interaction-free measurements is proposed, where the above conclusion is disproved for communications over a large distance, as follows. The scheme talks about the technique to manipulate the wave function collapse (which is probabilistic) of an entangled pair of particles, and extract meaningful data out of it. Here we will discuss the scheme using photons just for understanding, but we should keep in mind that it could be demonstrated using electrons and other quantum particles too.

2. Background theory

To understand this particular case of single-photon based communication scheme, first let’s look into the schematic depicted in Fig. 1. The Hong-Ou-Mandel (HOM) experimental setup shown in Fig. 1(a) is well described in [2], that the wave-functions of two indistinguishable photons coming at the two input ports of the Beam Splitter (BS) interfere in such a way that the detectors at port A and B never click simultaneously. This can be understood as follows. After passing through the BS they can end up in four possible configurations as shown in Fig. 1(c). $I$) Both the photons can end up at port A, $I$) Both the photons can end up at port B, $III$) The first photon can end up at port A and second one in port B, and $IV$) The first photon can end up at port B and second one in port A. When the photons are completely indistinguishable (say, both are having Vertical or ’V’ polarization) and reach the BS at the same time, two-photon interference is observed; corresponding output state can be written as follows.

 

Fig. 1. a) Hong-Ou-Mandel experiment with vertically polarized photon streams. b) Hong-Ou-Mandel experiment with vertically polarized photon streams in one input and diagonally polarized light in the other. c) After passing through the beam splitter the photons can end up in four possible configurations. $I$) Both the photons can end up at port A, $II$) Both the photons can end up at port B, $III$) The first photon can end up at port A and second one in port B, and $IV$) The first photon can end up at port B and second one in port A.

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This means, either both the photons go to port A, or both of them go to port B. Hence, the photo-detectors do not click simultaneously, and their coincidence count should be zero for ideal situation.

When the photons are distinguishable, say, one of them is diagonally polarized and the other is vertically polarized as shown in Fig. 1(b), the input state can be written as follows.

3. Proposed experimental setup

The experimental setup required for this new communication scheme is depicted in Fig. 2. Though the setup is explained using photons, analogous experimental setups can be easily prepared for electrons and other quantum particles, where the beam splitters may be replaced by other particle interferometers. Data communication takes place between Alice (transmitter) and Bob (receiver) while single-photon pulses are generated from a third station, say, Joyi. A pair of entangled single-photon pulses is sent to Alice and Bob, each receiving one of them simultaneously.

 

Fig. 2. Proposed Experimental setup for Interaction-Free Measurements based Communication Scheme. Here communication takes place between Alice and Bob, while the entangled pairs of single-photon pulses are supplied to both the transmitter (Alice) and receiver (Bob) from a third station, Joyi.

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At Joyi’s station pump laser is fed into an Entangled Photon Pair Source (EPPS). EPPS generates a pair of polarization entangled photons, one to be sent to Alice as a pulse, another to Bob. The pump laser can be a pulsed laser that itself controls the output pulse-pair transmission frequency. EPPS can be demonstrated using quantum dots [3], trapped ions [4], nonlinear photonic materials [5] etc.

Alice and Bob each receives a single-photon pulse simultaneously from Joyi, and sends it to their respective setups. While Bob’s photon passes through the delay line, Alice passes it through a Polarization Beam Splitter (PBS), which separates the incoming photons into two paths based on their polarizations. Now, quantum state of the photon pair sent from Joyi’s station can be described as

If Alice sets the bomb’s state to $|{live}\rangle$, there can be two possible outcomes. a) Case-1 (50$\%$ probability): The bomb explodes. Hence, the wave function of the photon collapses at the lower arm of the PBS output, i.e., in ’H’ polarization. b) Case-2 (50$\%$ probability): The bomb does not explode. Hence, the wave function of the photon collapses at the upper arm of the PBS output, i.e., in ’V’ polarization.

Now, corresponding to the above case entanglement between Alice and Bob’s photon breaks, and Bob’s photon comes out of the delay line with 50-50 chance of having vertical or horizontal polarization. As we have discussed in the previous section, the probability of coincidence detection ($P_{coin}$) for this case is $\frac {1}{4}$, at Bob’s station. Thus, a $|{live}\rangle$ bomb at Alice’s station is detected by Bob when he calculates $P_{coin}$ as $\frac {1}{4}$. Hence, Alice can use the $|{live}\rangle$ state of the bomb to represent a classical binary bit "1", and transmit the same to Bob. Indeed, the functionality of the "bomb" can be realized using a tunable attenuator or power splitter device.

If Alice sets the bomb’s state to $|{dud}\rangle$, it is equivalent to putting no detector at the PBS outputs. Hence, the initial Bell state of the photons (as described by equation (6)) is undisturbed.

Corresponding to the above case, Bob’s photon comes out of the delay line maintaining the entanglement with Alice’s photon. Similarly like equation (3) in the previous section, the input state entering Bob’s Beam Splitter (BS) can be written as follows.

We can clearly see that Bob extracts the classical binary bit sent by Alice, by repeatedly counting the photon coincidence events at PD1 and PD2. For different values of information ("0" or "1") he gets a significant difference between the coincidence count values ($P_{coin}$ value around $\frac {1}{2}$ or $\frac {1}{4}$), thus identifying one from another. For practical applications Bob can set his algorithm as follows.

Detected bit is interpreted as a "1" if $P_{coin} < \frac {3}{8}$.

Detected bit is interpreted as a "0" if $P_{coin} > \frac {3}{8}$. The most important observation of this scheme lies in the fact that, Bob must not let the Bell state of an incoming photon collapse into one of its basis states, before detecting at PD1 or PD2. This is required to ensure that the photon in Bell state does not involve in two-photon interference, and maintain the $P_{coin}$ value around $\frac {1}{2}$. A high-efficiency polarization insensitive photodetector seems to be a good choice, but that does not ensure that the photodetector atoms absorb the photon before destroying or collapsing its Bell state. Recent investigations on quantum states mapping seem to be promising in this case [7], where we can transfer the photonic state of entanglement into a particular $^{40}Ca^+$ ion. Hence, a photodetector made of $^{40}Ca^+$ atoms may be used to transfer the photon-photon entanglement into photon(Alice)-atom(Bob) entanglement.

4. Information extraction by error correction

From the previous section we have come to know that, when Alice sets the bomb’s state to $|{live}\rangle$ or $|{dud}\rangle$, Bob needs to perform multiple pulse detections to claculate $P_{coin}$, and detect bit "1" or "0" correctly. Consequently, bit error gets reduced as we increase the number of single-photon pulses corresponding to one binary bit. To eliminate this bit error we may use a simple error correction scheme as depicted in Fig. 3.

 

Fig. 3. Error correction scheme: Corresponding to one binary bit, consecutive N number of similar pulses are sent to both Alice and Bob to reduce BER. Here, timestamps having no pulse are intentionally inserted to distinguish one binary bit from another.

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Consecutive N pulses are used to manifest one binary bit. Bob recognizes a binary bit as "1" if $P_{coin} < \frac {3}{8}$, and the bit is interpreted as a "0" if $P_{coin} > \frac {3}{8}$. Now, if we use 100 consecutive single-photon pulses to encode a binary bit, theoretical Bit Error Rate (BER) will go below $0.1 \%$, which can easily be eliminated by well established channel coding schemes.

To eliminate a clock synchronization issue of Alice and Bob with Joyi’s station, after each set of N consecutive pulses, one pulse is removed from the next timestamp (see Fig. 3). Both Alice and Bob can easily detect this timestamp, as there will neither be any click at the photodetectors at Bob’s station, nor any bomb explosion at Alice’s. Hence, they can start transmitting or receiving data in synchronization accordingly.

5. Conclusion

The novelty of this communication scheme lies in the fact that, Bob retrieves real information out of this scheme with a receive-after-transmit delay independent of Alice-Bob separation distance. If both of them receive pulses only at a rate of 1 KHz, still 100 pulses (representing a binary bit) demand just 100 ms delay for Bob to register an information (binary bit). Now, Alice may sit on Earth and send an information to Bob sitting on Mars, around 250 million Km away from the Earth. Entangled pairs of single photon pulses can be continuously supplied to both of them in advance from Joyi, so that they can start utilizing the pulses whenever they want to communicate. Now, after Alice starts transmitting a binary information, Bob receives it with 100 ms receive-after-transmit delay (independent of their distance of separation). So, the equivalent speed of information transfer between Alice and Bob, is