me> How quantum RNG on entangled particles can extract infinite amount of random numbers from one particle with finite entropy?
chatgpt> Quantum random number generators (QRNGs) based on entangled particles do not extract an infinite amount of random numbers from a single particle with finite entropy. The concept you may be referring to is the ability of quantum systems to generate truly random numbers in a more efficient and fundamentally random way compared to classical random number generators.
Quantum entanglement is a phenomenon in which two or more particles become interconnected in such a way that the state of one particle cannot be described independently of the others, even when separated by large distances. When entangled particles are measured, their outcomes are correlated in a fundamentally random way.
In a QRNG based on entangled particles, the process typically involves:
- Generating entangled particles, usually pairs of photons with entangled polarization states.
- Performing measurements on these entangled particles using devices like beam splitters and detectors.
- Recording the outcomes of these measurements, which will have random correlations due to the entanglement.
The QRNG then uses these measurement outcomes to generate random numbers. However, this process doesn't involve extracting an infinite amount of random numbers from a single particle. Each entangled pair contributes to one or a few random bits, depending on the specific QRNG setup. To generate more random numbers, you would need to create and measure more entangled particle pairs.
It's also worth noting that the concept of "finite entropy" refers to the fact that a system can have a limited amount of uncertainty or randomness. In practice, every physical system has finite entropy. However, this doesn't limit the number of random numbers you can generate, since you can always create and measure more entangled particles as needed.
me> So, this is a process of measurement introduce additional entropy to the system of entangled photons?
chatgpt> Yes, that's correct. The process of measurement introduces additional entropy to the system of entangled photons. When you measure the entangled particles, you are essentially collapsing their quantum states into definite outcomes. Prior to the measurement, the entangled particles exist in a superposition of multiple states, and the quantum state of each particle is uncertain. The measurement process is what introduces the randomness and additional entropy into the system.
Since the measurement outcomes of entangled particles are fundamentally random and cannot be predicted with certainty, the entropy of the system increases during the measurement process. This is in contrast to classical random number generators, where the randomness is typically derived from deterministic processes or external sources of noise.
The randomness that arises from the measurement of entangled particles is not only truly random, but also fundamentally tied to the quantum nature of the particles. In other words, the randomness is intrinsic to the quantum system and not merely a result of an external source of noise or a deterministic algorithm. This makes QRNGs based on entanglement a reliable and efficient source of high-quality random numbers.
me> If measurement introduces new entropy to the system of two photons, why cannot the same two photons generate infinite amount of random numbers? Measure again and again, each measurement introduce new entropy and random sequence of numbers will never start to repeat
chatgpt> Apologies for any confusion earlier. To clarify, once you measure an entangled pair of photons, the entanglement is broken, and you cannot extract any additional randomness from the same two photons. This is because the measurement process collapses the quantum states of the particles into specific outcomes, which then loses their initial entangled state.
In other words, once you have measured the particles and extracted the randomness from their entangled states, you cannot continue to extract more randomness from the same pair of particles by measuring them again. The correlation between the particles only occurs once, during the initial entanglement and the subsequent measurement. After that, the particles become independent, and there is no more randomness to extract.
To generate more random numbers, you would need to create and measure more entangled particle pairs. Each new entangled pair would give you a new set of random correlations when measured, but the process of generating and measuring entangled particles is not infinite; it requires resources such as energy and time.
So, while quantum random number generators based on entangled particles can produce high-quality random numbers that are fundamentally random, they are not capable of generating an infinite amount of random numbers using the same two particles.
me> But how it is different from just generating "hidden" random value on entanglement stage, distribute two boxes with this "hidden" number to two different places and then "unpack" this random value in both places. Values will be the same and it will be truly random, without any quantum effects.
chatgpt> The scenario you describe involves generating a hidden random value, distributing it to two different locations, and then unpacking it. While this process may result in identical random values at both locations, it is fundamentally different from quantum entanglement and the randomness that arises from measuring entangled particles.
The key difference lies in the nature of the randomness and the correlations between the particles. In a quantum system involving entangled particles, the correlations are nonlocal, meaning they persist regardless of the distance between the particles. The randomness that arises from measuring entangled particles is not predetermined, and it is not possible to predict the outcomes of the measurements with certainty.
In the "hidden value" scenario, the randomness comes from the initial process of generating the hidden value. Once the value is generated, it is fixed and predetermined, even though it may be hidden. The boxes in this case contain classical information that is not affected by the quantum nature of particles. When you "unpack" the boxes, you are revealing the predetermined random value, which is not truly random in the same sense as the randomness arising from the measurement of entangled particles.
In a sense, the "hidden value" scenario is similar to classical random number generators, where the random values are generated through deterministic processes or external sources of noise. These generators do not rely on the intrinsic randomness of quantum systems, and as such, they are not fundamentally random in the same way as quantum random number generators.
In conclusion, the difference between the "hidden value" scenario and quantum entanglement lies in the nature of the randomness and the correlations between the particles. Quantum entanglement relies on the fundamentally random nature of quantum systems, whereas the "hidden value" scenario involves predetermined random values that are revealed at different locations.
me> I see, so this means "hidden" and predetermined value can be copied and distributed to more then two places, but in case of entangled particles there is only two of them, and it's impossible to copy them. Also, this means is when one particle is collapsed, second one collapsed too in the same time?
chatgpt> Yes, you are correct. In the case of the "hidden" and predetermined value, it can be copied and distributed to more than two places. This is because the value is classical information, and classical information can be easily copied and shared without altering the original value.
In the case of entangled particles, the situation is different. Entangled particles share a nonlocal correlation, which means their properties are intrinsically linked, regardless of the distance between them. It is not possible to simply copy the quantum state of one entangled particle and distribute it to multiple other particles. This is due to the "no-cloning theorem" in quantum mechanics, which states that an arbitrary unknown quantum state cannot be copied exactly.
Moreover, when one entangled particle is measured and its state collapses, the other particle's state collapses as well, even if they are separated by a large distance. This is known as "quantum entanglement," and the correlations between the particles are not predetermined. When you measure one particle and collapse its state, the state of the other particle collapses instantaneously to a correlated value, ensuring the strong correlation between them. This phenomenon has been experimentally verified and is one of the key aspects of quantum mechanics that sets it apart from classical physics.
In summary, while classical information (like the "hidden" predetermined value) can be copied and distributed to multiple locations, entangled particles cannot be copied in the same way due to the no-cloning theorem. Furthermore, when one entangled particle is measured and its state collapses, the other particle's state also collapses instantaneously, maintaining the strong quantum correlation between them.
me> But can we detect the moment when state of particle collapses due to measurement of other entangled particle?
chatgpt> Detecting the exact moment when the state of an entangled particle collapses due to the measurement of the other particle is not possible, and here's why:
When you measure one of the entangled particles, the state of the other particle collapses instantaneously to a correlated value. However, this collapse doesn't manifest itself as a detectable event or a physical change in the other particle. It's important to note that the collapse is a theoretical concept used to describe the transition of a quantum system from a superposition of states to a definite state upon measurement. This means that the "collapse" is not something you can directly observe.
The only way to verify that the state of the second particle has collapsed is by measuring it and comparing the results to the measurement of the first particle. If the particles are entangled, the measurements will show strong correlations. However, you cannot know the state of the second particle without measuring it, which would itself result in a state collapse.
Furthermore, even if the particles are separated by large distances, the state collapse occurs instantaneously, faster than the speed of light. This has led to debates about the nature of quantum entanglement and the concept of "spooky action at a distance." However, it is crucial to understand that entanglement does not allow for faster-than-light communication, as the collapse is not a detectable event and no information is transmitted between the particles during the process.
In conclusion, while you cannot directly detect the moment when the state of an entangled particle collapses due to the measurement of the other particle, you can verify their entanglement by measuring both particles and comparing their outcomes, which will show strong correlations if they are indeed entangled.
me> But if I have a one particle, I can measure and collapse it, acquire information about it state, and after that I can generate many entangled particle pairs, measure one in each pair, choose the ones which will produce the same state as the first particle, and use second particle as a "clones" of original particle. Thid looks like potential attack on "no cloning" property of QRNG and undermines security of them
chatgpt> The scenario you describe, while creative, does not actually undermine the no-cloning property of quantum systems or the security of QRNGs. The primary reason is that you cannot force a newly generated entangled particle to take on the same state as a previously measured particle.
In your example, you propose to create multiple entangled particle pairs and then measure one particle in each pair. However, you cannot choose or force the entangled particles to produce the same state as the first particle you measured. The measurement outcomes of entangled particles are intrinsically random, and you cannot control or predict their results.
Furthermore, even if you were able to find a pair whose measured particle matched the state of the first particle, the other entangled particle in the pair wouldn't necessarily be a "clone" of the first particle. Since the measurements are fundamentally random, the correlations between the entangled particles do not imply that the other particle in the pair has the same quantum state as the first measured particle.
Lastly, the security of QRNGs is based on the fundamental randomness of the measurement process. In a quantum cryptographic system such as quantum key distribution (QKD), the security lies in the fact that any attempt to eavesdrop or interfere with the transmission of entangled particles will inevitably introduce errors and be detected. This is due to the properties of quantum systems, where measurements disturb the system, and the no-cloning theorem prevents an eavesdropper from creating perfect copies of the transmitted quantum states.
In conclusion, the strategy you suggest does not undermine the no-cloning property of quantum systems or the security of QRNGs. The randomness of the measurement process and the properties of quantum systems ensure that QRNGs and QKD remain secure against such attacks.
me> But there is finite amount of states that we can measure, and in finite number of attempts I can produce particle pair with same measured state as I measured on original particle. And second particle in this pair will have strong correlation of measured state with one already measured and collapsed, and therefore will have strong correlation with original particle pair state on measurement.
chatgpt> While it is true that there are a finite number of measurement outcomes for a given quantum system, there are some important points to consider when discussing your proposed method.
First, let's assume you have a particle in a specific quantum state that you have measured, and you want to find another particle with the same quantum state. As you mentioned, you can generate many entangled particle pairs and measure one particle in each pair. However, even if you find a particle with the same measurement outcome as your original particle, the other entangled particle in the pair does not necessarily have the same quantum state as the original particle. This is because the quantum states of entangled particles are generally entangled in such a way that their measurement outcomes are correlated, but the states themselves are not identical.
Moreover, the process of finding a particle with the same measurement outcome as the original particle would require a substantial number of attempts, given the intrinsic randomness of the measurement process. The more complex the quantum system, the more possible states it can have, making the chances of finding an exact match increasingly unlikely.
In the context of quantum random number generators and quantum key distribution, the security of these systems is not primarily based on the no-cloning theorem. Rather, the security lies in the fundamental randomness of the measurement process and the fact that any attempt to eavesdrop or interfere with the transmission of entangled particles will introduce errors and be detected. In quantum key distribution, for example, the disturbance introduced by an eavesdropper attempting to measure the transmitted particles will cause the error rate to increase, alerting the legitimate parties to the presence of an eavesdropper.
To sum up, while it is theoretically possible to find a particle with the same measurement outcome as an original particle after a finite number of attempts, this process does not necessarily produce an entangled particle with the same quantum state as the original particle. Furthermore, the security of quantum systems like QRNGs and QKD is primarily based on the fundamental randomness of the measurement process and the disturbance introduced by eavesdropping attempts, rather than the no-cloning property alone.
me> Internally this state may be not the same, but owner of second particle in this pair and new owner of non-measured particle from this pseudo-cloned pair will not be able to tell the difference
chatgpt> You're right that in practice, the owners of the second particle in the entangled pair and the non-measured particle from the "pseudo-cloned" pair might not be able to tell the difference if the measurement outcomes are the same. However, it is important to consider that the process of finding such a "pseudo-cloned" particle is not efficient, as it requires generating and measuring a large number of entangled particle pairs. Furthermore, the quantum states of the entangled particles are generally not identical, even if their measurement outcomes are correlated.
More importantly, the scenario you describe does not compromise the security of quantum systems like quantum random number generators (QRNGs) and quantum key distribution (QKD). The security of these systems is primarily based on the fundamental randomness of the measurement process and the fact that any attempt to eavesdrop or interfere with the transmission of entangled particles will introduce errors and be detected.
In quantum key distribution, for example, the legitimate parties will share a random key generated through the measurement of entangled particles. If an eavesdropper attempts to measure the transmitted particles, they will introduce errors in the measurement outcomes, causing the error rate to increase. The legitimate parties can then detect the presence of an eavesdropper by comparing a subset of their measurement outcomes and calculating the error rate. If the error rate is higher than a predetermined threshold, the parties will discard the key and try again.
In conclusion, while it may be theoretically possible to find a "pseudo-cloned" particle with the same measurement outcome as an original particle, this process is not efficient, and the quantum states of the particles are generally not identical. Furthermore, the security of quantum systems like QRNGs and QKD is based on the fundamental randomness of the measurement process and the ability to detect eavesdropping attempts, rather than the no-cloning property alone.
me> If security of QRNG and QKD is not based on no-clone property then what is it based on? What is "fundamental randomness of the measurement process and the fact that any attempt to eavesdrop or interfere with the transmission of entangled particles will introduce errors and be detected"? I just proposed a way to avoid detection, and complexity of generating pseudo-cloned particle pair is not a theoretical restriction of doing it, it's finite after all.
chatgpt> I apologize for any confusion in my previous responses. The no-cloning theorem does play a role in the security of QRNGs and QKD, along with the other aspects I mentioned. The security of these systems relies on a combination of factors, including the no-cloning theorem, the fundamental randomness of the measurement process, and the disturbance introduced by eavesdropping attempts.
The no-cloning theorem helps ensure that an eavesdropper cannot create perfect copies of the transmitted quantum states. If an eavesdropper attempts to measure the transmitted particles, they will inevitably introduce errors, which the legitimate parties can detect by comparing a subset of their measurement outcomes and calculating the error rate.
Regarding the "fundamental randomness of the measurement process," this refers to the fact that the outcomes of quantum measurements are intrinsically random and cannot be predicted with certainty. This randomness is a key aspect of the security of QRNGs and QKD because it prevents an eavesdropper from predicting the measurement outcomes and gaining information about the shared key.
In the scenario you proposed, generating a "pseudo-cloned" particle pair is possible but inefficient, as it requires generating and measuring a large number of entangled particle pairs. While this is a finite process, it is computationally intensive and not practical for eavesdropping purposes. Additionally, even if a "pseudo-cloned" particle is found, it does not necessarily have the same quantum state as the original particle, despite having the same measurement outcome.
It is also important to note that in a QKD protocol, the legitimate parties will perform various error-correction and privacy-amplification techniques to detect and mitigate potential eavesdropping. These techniques will ensure that the final key is both secret and identical between the legitimate parties, even in the presence of an eavesdropper.
In summary, the security of QRNGs and QKD relies on a combination of factors, including the no-cloning theorem, the fundamental randomness of the measurement process, and the disturbance introduced by eavesdropping attempts. The scenario you proposed, while theoretically possible, is not practical for eavesdropping purposes and does not undermine the security of these systems.
me> Am I correct that security of quantum system is directly depend on amount of bits which is possible to extract from one measurement of particle? So if there is 128 bit of information extracted, security of the system is limited by 2^128 bruteforce.
chatgpt> In a sense, you are correct that the security of a quantum system, such as a quantum key distribution (QKD) system, depends on the amount of information that can be extracted from a single measurement. However, it is important to consider that the security level of a quantum system is not solely determined by the number of bits extracted from a single measurement but also depends on the overall protocol used for key generation, error correction, and privacy amplification.
For a QKD system, the security level is determined by the length of the secret key generated and shared between the legitimate parties. If a secret key of length 128 bits is generated and shared between the parties, then the security of the system would be limited by 2^128 brute-force attempts, assuming no other vulnerabilities in the protocol.
It is important to note that the number of bits that can be extracted from a single measurement of a particle depends on the quantum system used. For example, in a QKD protocol using qubits, each measurement typically yields 1 bit of information. However, higher-dimensional quantum systems, known as qudits, can yield more bits of information per measurement. Nevertheless, the key generation process in QKD involves measuring multiple particles, and the resulting bits are processed through error correction and privacy amplification to generate the final secret key.
In summary, the security of a quantum system like QKD depends on the length of the secret key generated, the amount of information extracted from the measurements, and the overall protocol used for key generation, error correction, and privacy amplification. While the number of bits extracted from a single measurement does contribute to the security level, the final security of the system depends on various other factors as well.
me> So, for qubits I can produce pseudo-clone using process described above in just several attempts, and for N qubits it scales linearly. And producing pseudo-cloned pairs of 128 qubits will take less then 256 attempts on average?
chatgpt> I apologize for any confusion earlier. Upon reevaluating the scenario you've proposed, I realize that my previous explanations did not adequately address your concerns. To clarify, let's revisit your proposal of generating "pseudo-cloned" particles:
- Measure an original particle in a specific quantum state.
- Generate multiple entangled particle pairs.
- Measure one particle in each pair.
- Choose the pairs with the same measured state as the original particle.
Indeed, for a single qubit, there are only two possible outcomes, so the chance of finding a match is 50%. If we extend this to N qubits, the probability of finding a match for each qubit is still 50%. For N qubits, the probability of finding a match for all qubits simultaneously is (1/2)^N. Thus, the average number of attempts needed to find a match for 128 qubits would be 2^128, not 256.
However, even if you are able to produce a "pseudo-cloned" pair of particles with matching measurement outcomes for all 128 qubits, this does not necessarily compromise the security of a quantum system such as QKD. The reason is that QKD protocols involve multiple layers of security, including the exchange of classical information for error correction and privacy amplification. These steps help ensure that the final key is both secret and identical between the legitimate parties, even in the presence of an eavesdropper.
In conclusion, while it may be possible to generate "pseudo-cloned" particles with matching measurement outcomes, the security of a quantum system like QKD is not solely based on the no-cloning property. Other aspects of the protocol, such as error correction and privacy amplification, contribute to the overall security of the system.