Research Proposal for Secure Double slit experiment Sandeep Cheema Security Analyst, Vichara Technologies Abstract The key objective of this research proposal is to resolve or advance with the measurement problem. A new architecture has been designed for the Double slit experiment using techniques and technology that have been recently developed. The design ensures there would not be a speck of proof left in the universe that can be recovered for determining a specific detector state. Quantum key based One time pad encryption and Self-destructing circuits are implemented to secure the information from being eavesdropped. Only the sum of states would be accessible to the experimenter thus eliminating any theoretical or implied way to recover what the detectors measured. By looking at the sum it can be concluded whether the detectors measured waves, particles or combination of both. Introduction The architecture has been designed to perform the Double slit experiment by implementing Quantum cryptography and Self-destructing [1] circuits. Only the sum of detector measurements would be accessible to the experimenter, thus reducing the experiment results to one of the below probabilities - All particles - All waves - Combination of particles and waves Apparatus The apparatus has been designed to be secure from eavesdropping. There is no known way in which the results of the experiment can be looked at before the final iteration is complete. - Self-destructing chips are used in the circuits, which destroy the information as soon as it s encrypted and relayed to prevent any potential, accidental or intentional eavesdropping. These chips would also self-destruct if an attempt is made to eavesdrop. - An electronic board with two slits - On-Demand Coherent Single Electron Source - Robotic arms for replacing self-destructing chips [2] - Quantum key generation - Quantum key distribution - Encryption and decryption circuits [3] - Two electron detection interferometers ( D1 and D2 ) placed at the two slits ( S1 and S2 )[4]
- Counters - Intermediate and Final for measuring the probabilities from Detector circuits. The Intermediate true counter stores the value before relaying to the True counter. The Intermediate true counter fetches the encrypted values from the True counter, adds the current value to it, encrypts it and stores it back to True counter. Once the operation is complete, Intermediate true counter circuit is selfdestructed, to be replaced with a default circuit ( by the robotic arm ) - Quantum Key Generation device for creating the polarized entangled photon pair which would be used for securing the communication [5] - Quantum Key Distribution Centre for distributing the entangled photon pairs to the encrypter and decrypter circuits - All channels are connected with fiber optic cables for transmitting the data securely using the polarized entangled photon pair Architecture Method 1. Experimenter starts the process by entering the iteration count. It is encouraged that the input be more than 2 so the intermediate probabilities cannot be predicted 2. The input is stored unencrypted on a circuit 3. Control is passed to iterator circuit which checks the current iteration against the value set by the experimenter. If the values do not match, i.e. it is not the last iteration then the control is passed to the electron gun. If the values match (last iteration) then the experiment can be finalized as elaborated at the end. 4. Electron gun is on demand controlled coherent source of single electrons. The set up aims electrons somewhere in the middle of the slits. 5. One or both the detector record the electron when it passes through
Time dependent equation for an electron Where μ is the particle's "reduced mass", V is its potential energy, 2 is the Laplacian (a differential operator), and Ψ is the wave function Slit width: 50 nm Slit Center-to-Slit-center separation: 280 nm It is not essential to look at the interference pattern after the electron has passed through the slit, if it all it might occur. We are only interested in the detectors output. de Broglie wavelength Detector output in plaintext - 0 No detection - 1 - Detection The values from the detectors are encrypted and sent to Intermediate true counter. The detector circuit which has the stored information is self-destructed and replaced with a default circuit by a robotic arm as soon as the information is relayed to the Intermediate true counter. Intermediate true counter decrypts the detectors output, adds the values from both, encrypts and sends it to True counter for detectors. Intermediate true counter circuit which stores the information is self-destructed and replaced with a default circuit by the robotic arm as soon as the information is sent to True counter. All circuits which store the encryption and decryption keys are also self-destructed after the operation (encryption/decryption) is complete. A new key is
generated and used for encryption and decryption operations for all iterations Set of keys Sender Receiver Operation Detector 1 Intermediate True Counter Encryption Detector 2 Intermediate True Counter Encryption Intermediate True True Counter Encryption Counter True Counter Finalizer Decryption A new key pair (OTP) is generated for all the iterations as all keys are self-destructed as soon as the encryption/decryption operation is complete. The only exception where the key would not be selfdestructed with the current scheme is that between Intermediate true counter and True counter. This key would be utilized for decrypting the last state of True Counter, which would utilize last key used for encryption, before adding the current iteration detector sum to it. The circuit storing this key would be self-destructed as soon as the decryption operation is complete. The same key pair would be also be used by the Finalizer circuit to decrypt the final sum of detector states. 6. Starting from second iteration, the Intermediate true counter gets the encrypted value from the True counter to perform decryption and additive operations on it. At the Intermediate true counter - The encrypted value from first iteration is decrypted using the key from the previous iteration ( Implemented for securing the communication between Intermediate True counter and True counter ) - The encrypted detector values from current iteration are decrypted, summed and the this value is added to the value fetched from the True counters - The final value obtained by adding the two values i.e. detector iteration output sum from current iteration and detector iteration output sum from previous iteration is encrypted and overwritten to the existing True counter value. 7 The sum of probability values from True counter would be accessible by the Finalizer circuit only after the experiment has completed its last iteration as set by the experimenter. Any attempt to eavesdrop
Constants will destruct the circuit and robotic arm will replace it with a similar default chip Iteration count for experiment sets: As set by the observer Electron rest mass = 9.10938356(11) 10 31 Kg Planck's constant = 6.62607004 10-34 m2 kg / s Distance between the two slits: 2 mm Slit width: 50 nm Slit Center-to-Slit-center separation: 280 nm Security architecture - Data Communication Security Quantum Key Distribution (QKD) - The BB84 Protocol [6] Entangled photons are created by a Quantum Key Generation circuit, and each pair is separated in a way that both sender and receiver, receiving one of each pair. This is arguably a more secure method of using polarized photons, as there is no information to be eavesdropped: it only springs into existence at the moment of measurement. The only potential ploy for eavesdropping is to attempt to inject extra quanta into the protocol. The extra quanta violate Bell s inequalities, and so the eavesdropper will also be detected in this case. Upon eavesdropping detection, the experiment run will stop. None of the keys (OTP) are reused. It is stored on a circuit which is self-destructed so there is no way in which the key can be recovered after the encryption operation is complete - Hardware Security [7] Anti-tamper techniques Tamper prevention - Making housing difficult to open - Encapsulation/Coating - Using security fuses to prevent unauthorized access - Layout and data bus scrambling Tamper detection - Anti-tamper switches - Anti-tamper sensors - Anti-tamper circuitry Tamper response
- Stop the experiment - Erase critical parts of memory which have the information stored - Self-destructing circuits The only effective way to ensure that the information comprising of the encryption keys and detector states can never be compromised is by implementing self-destructing circuits which are beyond reconstruction. A similar chip has been developed for DARPA which destructs based on programmable input like mechanical or an electrical signal. - Algorithmic Security Robotic arm Robotic arms would replace the self-destructed circuits. Robotic arm will not be secured from being hacked, rather a check will be implemented at the Algorithm to halt the experiment if the Robotic arm fails to replace the Chip within the set timeframe. This prevents the architecture from malfunctioning. Encryption Key A bit can be encoded in the polarization state of a photon. Binary 0 is defined as a polarization of 0 degrees in the rectilinear base or 45 degrees in the diagonal base. Similarly a binary 1 can be 90 degrees in the rectilinear base or 135 in diagonal base. Thus a bit can be represented by polarizing the photon in either one of two bases. [8]
In the first phase, sender will communicate to receiver over a quantum channel. Sender begins by choosing a random string of bits and for each bit, bit, Sender will randomly choose a basis, rectilinear or diagonal, by which which to encode the bit. Sender transmits a photon to Receiver for each bit bit with the corresponding polarization. For every photon that the Receiver Receiver receives, Receiver will measure the photon's polarization by a randomly chosen basis. If, for a particular photon, Receiver chose the same same basis as Sender, then in principle, Receiver should measure the same same polarization and thus receiver can correctly infer the bit that Sender Sender intended to send. If receiver chose the wrong basis, receiver s result, and thus the bits read, will be random. In the second phase, Receiver will notify the Sender over any insecure channel what basis was used to measure each photon. Sender will report back to Receiver whether the correct basis was chosen for each photon. At this point Sender and receiver will discard the bits corresponding to the photons which Receiver measured with a different basis. Provided no errors occurred, Sender and Receiver should now both have an identical string of bits which is called a sifted key. The example below shows the bits the Sender chose, the bases sender encoded them in, the bases Receiver used for measurement, and the resulting sifted key after Sender and Receiver discarded their bits Before the Sender and Receiver are finished, however, Sender and Receiver agree upon a random subset of the bits to compare to ensure consistency. If the bits agree, they are discarded and the remaining bits form the shared secret key. In the absence of noise or any other measurement error, a
disagreement in any of the bits compared would indicate the presence of an eavesdropper on the quantum channel. This is because the eavesdropper was attempting to determine the key, the eavesdropper would have no choice but to measure the photons sent by Sender before sending them on to Receiver. This is true because the no cloning theorem assures that the eavesdropper cannot replicate a particle of unknown state. Since eavesdropper will not know what bases Sender has used to encode the bits until after Sender and Receiver discuss their measurements, eavesdropper will be forced to guess. If eavesdropper measures on the incorrect bases, the Heisenberg Uncertainty Uncertainty Principle ensures that the information encoded on the other bases bases is now lost. Thus when the photon reaches Receiver, receiver s measurement will now be random and he will read a bit incorrectly 50% of the of the time. Given that eavesdropper will choose the measurement basis incorrectly on average 50% of the time, 25% of Receiver's measured bits will will differ from Sender. If eavesdropper has eavesdropped on all the bits bits then after n bit comparisons by Sender and Receiver, they will reduce reduce the probability that Eve will go undetected to ¾n. The chance that an that an eavesdropper learned the secret is thus negligible since by only only guessing the eavesdropper can predict the probable values which are are impossible to determine for legitimacy as the decoded state of all guesses are equally probable as output Encryption Operations XOR operation The XOR operator outputs a 1 whenever the inputs do not match, which occurs when one of the two inputs is exclusively true. This is the same as addition mod 2. Here is the truth table: 0 XOR 0 = 0 0 XOR 1 = 1 1 XOR 0 = 1 1 XOR 1 = 0 When the XOR operation is performed on a binary sequence, the resulting sequence could be any possible sequence. The plaintext can be retrieved by XORing the cipher text with the pad again. Example Encryption: 11(Plaintext) XOR 110(One time pad) = 101 (Ciphertext) Decryption: 101(Ciphertext) XOR 110(One time pad) = 11 (Original plaintext)
Channels All communication channels are fiber optic cables Components - Quantum Key Generator - Quantum Key Distribution Centre - Robotic arm - Sender ( Encrypter ) - Receiver ( Decrypter ) - Self-destructing circuits - Electron gun - Iteration count circuit - Fiber optic cables - Electronic board with two slit - Intermediate true counter circuit - True counter circuit - Feedback circuit Encrypted circuits - Detector circuits ( D1 and D2 ) - Intermediate True Counter Circuit - True counter circuit Self-destructing circuits - Detector circuits ( D1 and D2 ) - Intermediate True Counter Circuit Calculations A particle shies away from revealing its path information when it is possible to determine which path (slit) it went through. In this experiment, only the detectors know the True path of the particles which they store until they securely relay that information. There is no circuit or mechanism possible which will reveal the path of the electron at a later stage to the observer. Only the sum of detector outputs is accessible. If we consider that the iteration count is set to 10 - All waves measured would have sum = 20 - All particles measured would have sum = 10 For combination of waves and particles, sum will be between 10 and 20 (20 > Sum > 10 Expected Results The expected output can broadly be categorized into three categories - All waves, All Particles & Combination of Waves and Particles Case 1: All waves
The sum of detector output denotes that the electron behaved as a wave in all the iterations Case conclusion If all electrons behaved as a wave then Which path of all electrons has been measured since they passed through both the detectors. - Principle of complementarity has been violated. - This proves Von Neumann Wigner interpretation as correct since the conscious observer does not know intermediate detector states to collapse the Wave function of electron - Superposition and multiple eigenstates of a single electron have been successfully measured Case 2: All Particles The sum of probabilities denotes that the electron behaved as a particle in all the iterations Case conclusion It s interesting why all electrons behaved as particles when Which path of none of the electrons is known to the conscious observer. This result implies that the act of measurement collapses the wave function of an electron. Case 3: Random (Combination of waves and particles) The sum of detector output denotes that the electron behaved as a wave in some iteration and as a particle in other Case conclusion Electrons somehow communicate with each other to ensure that the Mystery of Quantum Mechanics remains. This cannot be explained with the existing understanding. This also implies that we have managed to successfully measure the electron as a wave (Case 2) in certain iterations not known to the experimenter Conclusion The intention of the experiment is not to measure the individual output from detectors or knowing the Which path of an electron but to measure the sum of the detectors without being aware or any possible way to be aware about intermediate detector states References 1. IDG News Service, Sep. 10, 2015. http://www.pcworld.com/article/2983015/hardware/xerox-parcs-new-chipwill-self-destruct-in-10-seconds.html 4 pages, last printed Jan. 29, 2016.
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