On a proposal for Quantum Signalling

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1 On a proposal for Quantum Signalling Padmanabhan Murali Pune, India pmurali1000@gmail.com Ver1 : 21st Nov 2015 Abstract Present understanding of non-possibility of Quantum communication rests on analysis of possibility of signalling within a Quantum system. Is it possible to achieve signalling by a setup where the system is changed from one to another where the act of change serves as the signal and the change in the measurement probabilities would be detected and deciphered at the receiver end? A proposal is made where a variant of Delayed Choice Quantum Eraser experiment setup of Kim et al is used to achieve the same. The setup is also designed such that the speed of communication can be faster than light. NonLocality and Quantum communication Nonlocality is a feature of Quantum Mechanics that has been firmly established through experiments [Aspect et al, 1981] and well accepted now. Entangled particles separated by a distance still are part of one entity and when that entity changes state by a measurement in one part of it the change happens instantaneously across the domain the entity pervades. Is it possible to use this instantaneous state change to transmit information across at high speeds, faster than light (FTL)? This issue has been dealt with from the time the Einstein raised the EPR paradox [Einstein et al,1935] and has been claimed to be impossible and shown to be so by Peres, [Peres and Tenko, 2004] through the no-communication theorem which shows that any amount of signalling by Alice through measurements done at one end of the quantum system would not be sufficient for Bob to detect and decipher at the other end of the system. However the discussions in literature (as above) always deal with information transfer within a stable quantum system by making measurements at one end and analysing the possibility of detecting it at the other end. Peres and Tenko analyse a Quantum System S of mixed-state where Alice and Bob make measurements at their ends of the system. The authors derive the probability that Bob s outcome is ν as which does not contain any dependency term of Alice s outcomes ( and are Alice s and Bob s outcomes). They conclude that it is impossible for Alice to send a signal if there is no way Bob would be able to detect it in his measurements being as they are, independent of anything that Alice does. Nicolas Gisin uses a similar scenario of Alice and Bob conducting measurements on an imaginary QM setup by pushing joysticks and looking for outcomes (which are 1 or 0) at their end [Gisin, 2014, pg 22]. Whatever be the position of Alice s joystick (and outcomes) the outcomes at Bobs end (0 and 1) would occur equally frequently. Here again the Quantum system remains the same and only measurements within it are attempted to convey signals. What would be the scenario if the system is changed in the middle of the experiment and the change in the state and the measurement probability that results is used to convey a signal? Let System A (which-path known) be changed to System B (which-path not known) and let the act of change constitute the signal to be conveyed which is detected by the change in measurement probabilities (or patterns) at the receiver end. Considering that quantum correlation exists from the moment a system is defined irrespective of whether measurements on entangled particles are separated by space and time (irrespective of event ordering non-causality) is it possible to utilise this phenomena to design a setup and achieve signal transmission FTL though not instantaneous. Cramer dealt with a similar scenario and concluded that such signalling is not possible using the setup described below due to the complementarity principle of one-particle and two-particle systems [Cramer et al, 2014]. Movement of the Beam Splitter A by Alice does not cause any change in the detection pattern at Bob s end. The non-coincident probabilities at Db1 and Db2 are not affected by the BS change at Alice s end, though joint detection probabilities do change. 1

2 Figure 1 Setup used by Cramer et al [2014]. Alice tries to signal Bob by removing BS A The joint probabilities at B1 with BS A in place is, And for BS A removed. Their sum which makes up the non-coincident probabilities is the same for both the cases. Proposal What if one of the coincident detection count is measured and information sent to the receiver? He would subtract this from the total count whereby the remaining counts would carry information that will change depending on whether the BS is there or not. Thus signal transmission of yes or no, of BS Change or not is conveyed to Bob in an unconventional way. For example in the above case if Alice sends the A0 count information to Bob, then using that he can identify coincident A0B1 counts from the overall B1 count and identify what would be the A1B1 pattern. It would be the following for the case where BS is removed (which-path known no interference), = And the following for BS in place (which-path not known interference present), = This information of interference presence or not would form the signal transmitted. Now is it possible to arrange the setup in such a way that this partial information (of detection count of one of the photons) takes almost the same time as the detection of the coupled photons and with the location of the event of BS change physically separated by a large distance from this photon detection but temporally close can we achieve a case a rapid information transfer? This is what this proposal attempts to achieve. Experimental Setup The proposed setup attempts to achieve a similar kind of a result though different in some aspects. It is actually a variant of Delayed Choice Quantum Eraser (DQCE) experimental setup used by Kim et al [Kim et al, 2000], where a physical operation of 2

3 movement of BS (not unlike what is done in Cramers experiment) is used to cause a signal namely a change of pattern detected at D0. The original setup by Kim et al was used to conduct the DQCE Experiment. The setup is shown below. Figure 2 Experimental Setup used by Kim et al for DQCE [Kim et al, 2000] Kim et al s is an improvised double slit experiment where entangled photons, idler-signal pairs, exit from regions A and B with the signal photons moving towards Detector D0 (which is movable along the x direction) while the idler photons move towards the prism and thence towards Detectors D1 to D3 as shown. The idea of this setup is to enable two types of idler photons be detected, those going to D3 (and D4 not shown) will have their which-paths known while the ones reaching D1,D2 will have their which-path unknown (since the Beam splitter and the mirrors ensure that photons reaching D1,D2 could have come either from region A or B). The D0 signal photons corresponding to the idler ones striking D1,D2 would show an interference pattern while the ones corresponding to D3,D4 will show a diffraction pattern. This is since the former have their which-paths unknown while the latter are known. In spite of the delay in the idler photon detection due to a longer path they take, the interference and diffraction patterns (after accounting for the time delay) were observed as shown below. The plots are only of coincident idlersignal photons (after considering the time delay) to ensure that the signal-idler photons belong to a single entangled pair. This demonstrates that Quantum correlation exists between entangled photons even if the path of one of the photons is apparently decided after the other photons detection. Figure 3 D0 pattern corresponding to D3,D4 [Kim et al,2000] Figure 4 D0 pattern corresponding to D1,D2, [Kim et al,2000] 3

$When the BS is removed the which-path would be known for all idler photons and hence both D1,D2 and D3,D4 would show diffraction pattern.$ There should be no reason to doubt this as what applies for D3,D4 should apply for D1,D2 too. When the BS is placed back D1,D2 should show interference again.

There should be no reason to doubt this as what applies for D3,D4 should apply for D1,D2 too. When the BS is placed back D1,D2 should show interference again.

4 This setup is suggested to be used for Quantum signalling where the locations of the detectors are modified and most importantly the Beam splitter BS is made removable. When the BS is removed the which-path would be known for all idler photons and hence both D1,D2 and D3,D4 would show diffraction pattern. There should be no reason to doubt this as what applies for D3,D4 should apply for D1,D2 too. When the BS is placed back D1,D2 should show interference again. Thus a signal of presence or absence of interference is conveyed by the action of removal or placement of the BS. This however would not make for anything significant since the coincidence counters are needed and count data is transferred via conventional media at speeds not more than c. The difference suggested is to send only part of the counts, those of D3,D4 and letting a processor subtract it from the total count to extract the pattern of D1,D2 as mentioned earlier. This still may not appear to achieve anything unless the locations of the detectors are placed such that the D3,D4 count data almost follows the signal photon and does not cause a significant drop in signal transmission. This needs more explanation and is detailed as follows. The proposed setup is laid out as shown with key features as follows 1. Detectors D3,D4 are placed much earlier in the circuit and idler photon detection Event-B there happens first immediately after exiting the prism Event-A. 2. Beam splitter BS and detectors D1 and D2 are placed a distance away d away from D3,D4. 3. Signal detection photon detection Event-D happens last just after the idler photon impinges on BS Event-C the time lag between the two events (Event-C and Event-D) being t. 4. The location of BS (Location-M) and detector D0 (Location-L) are separated by a large distance D. 5. BS is arranged to be removable at a rapid rate. 6. Immediately after D3,D4 detection the event data are sent to a Coincident counter which is located close to D0. It is sent through EM waves to reduce travel time Figure 5 Proposed Setup for Quantum Signalling The intent of the setup is to separate the two events of BS change and Signal photon detection in space but keep them close in time. The detection of D3,D4 is done early and the count information is sent almost along with the signal photon, keeping the time lag minimum. 4

5 At the coincidence counter the D3,D4 count data would be used to extract the D1,D2 pattern, from now onwards called the message from the D0 counts. The setup has been arranged such that if the spatial distance D is much larger than the time t which represents the lag from the message sending event which starts with the BS change and the receipt event D0 detection (ignoring the processing time which we will come to later) then information transfer speed would be fast. The more this ratio D/t the faster would be communication speed. This exercise needs the D3,D4 count data to be sent to the D0 observer. Let us assume that the time delay between when D3,D4 count data receipt at the coincidence counter (+processing time) and the D0 measurement is δ. Speed of message transmission = D / (t + δ) This speed can be increased if D is increased and if t+ δ is reduced. Most importantly these are independent variables and can be separately changed. For example t defines the time lag between the BSchange event and D0 event and is independent of how far apart the events are physically located. If the D3,D4 event is done very close to the light source and data immediately sent to D0 observer at the speed of light (through EM waves) δ can be kept minimum. D can be increased to the extent needed to ensure that the speed is higher than the target, say the speed of light. It would also help to keep the signal pulse duration much smaller than light time. The delay δ ensures that the speed cannot be instantaneous as long we stick to the condition that BS change happens before D0 detection (which is just a starting point of this proposal though ideally it can be done away with considering that Quantum correlations are atemporal [ Suarez, 2001]). Processing at the coincidence counter Now, let the starting condition be BS ON. Let the signal photon measurements happen. Now signal photon counts would consist of the sum of D1,D2 and D3,D4 counts. Since the D3,D4 counts are already known, it would be possible to filter out these from the overall pattern and extract what would be the D1,D2 coincident pattern. This is with the assumption that all the signal and idler photon detection events are recordable. And further that 100% count tallying exists, i.e, idler photon counts of D1,D2,D3,D4 together tally with the Signal photon measurements allowing for the time difference due to the difference in path lengths of the photons. A representational image is shown below where the detection events as they happen over time in each of the detectors are shown. D0 is split to many detectors along the detection plane to cover all photons falling on the plane. Since this method involves elimination of a set of counts to get the signal it is necessary that all photons falling in D0 plane be captured. D0 as shown in (a) would consist of the overall counts which would be the sum of those of D1,D2 (c) and D3,D4 (b). Figure 6 Sample Detection pattern in Detectors (a) D0 (b) D3,D4 (c) D1,D2 and (d) Pattern (message) extracted from D0 after removing counts mapped to D3,D4. Dotted lines indicate mapping of D0 counts to other detector counts. Since D3 happens before D0 the events are shown to happen earlier. To every event in D0 it should be possible to map an event in either D3,D4 or D1,D2 which is shown by the dotted lines. Now, since D3,D4 are already known the event corresponding to them can be found out in the D0 event set by accounting for time delay. These counts can be removed from the overall count and the remaining ones would form the pattern that would constitute the signal being transmitted which is shown in (d). 5

6 Messaging time can be further reduced if the photon generation rate is high with the result that patterns are formed in no time, though this would mean the processor which detects coincidences also has to be fast. One can imagine a scenario where there is a continuous stream of photons forming a pattern over D0 which changes whenever BS is moved instantaneously, but the message in the change is revealed by the Coincidence Processor a small instant later after it subtracts the data it gets of D3,D4. If the distance of separation of the events is large enough, say the BS is located in Jupiter and D0 in Uranus and D3,D4 in the earth the message transfer time would be fast. Nicolas Gisin (Gisin, 2014, pg 79) mentions the issue of detection loophole seen during experiments with entangled photons where some photons disappear and are not part of the count. Obviously this would cause noise in the above experiment since it relies on count tallying. Still, if the message is binary presence or absence of a clear pattern, should it not be possible to detect the pattern in spite of the noise? Summary a) A mechanism is proposed for quantum signalling by making a change in a Quantum system and using that change as a signal which is detected by an observer who monitors the change in measurement probabilities at his end. b) A variation of the Delayed Choice Quantum Eraser experimental setup of Kim et al is proposed where the location and events are arranged in such a way that a message which is initiated by a setup change is received and detected as a change in photon detection pattern at a velocity possibly faster than light. Questions 1. Is the above proposal for quantum signalling faster than light possible? 2. If not what could be the mechanism that would prevent it? Will the one-particle-two-particle complementarity principle [Jaeger et al, 1993] prevent this? 3. If possible what are its implications? 4. If the above is possible, considering that quantum correlation exists irrespective of the time ordering of the events [Suarez, 2001] the above action of BS change can be delayed till after D0 is measured and still convey the intended message, instantaneously if adjusted appropriately, or even into the past. If so, in the latter case, what if the message is returned through another similar setup and is programmed to prevent the BS change? Would there be a Godelian case of self-reference then? What would stop this? Acknowledgement The author is an amateur and the above is more of an exploratory question than a proposal. The author would like to thank the reader for taking the time to read this and welcomes criticism or acknowledgement (if the reader thinks this makes sense). References 1. A. Aspect, P. Grangier, and G. Roger, Phys. Rev. Lett. 47, 460 (1981). 2. Einstein, A., Podolsky, B. & Rosen, N. Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777_780 (1935). 3. Peres, A. and Terno, D. (2004). "Quantum Information and Relativity Theory". Rev. Mod. Phys. 76: Nicolas Gisin, Quantum Chance (English Ed.,2014) 5. John G. Cramer and Nick Herbert (2014), "An Inquiry into the Possibility of Nonlocal Quantum communication", 6. Antoine Suarez (2001), Is there a real time ordering behind the nonlocal correlations?, 7. Kim, Y-H., Yu, R., Kulik, S., Shih, Y. & Scully, M. O. Delayed `choice' quantum eraser. Phys. Rev. Lett. 84, 1_4 (2000). 8. G. Jaeger, M. A. Horne, and A. Shimony, Complementarity of one-particle two-particle interference, Physical Review A48, (1993). 6

On a proposal for Quantum Signalling

On a proposal for Quantum Signalling Padmanabhan Murali Pune, India pmurali1000@gmail.com Ver1 : 21st Nov 2015 Abstract Present understanding of non-possibility of Quantum communication rests on analysis