63 Sentences With "indistinguishability" | Random Sentence Generator

In the era of indistinguishability, difficult choices will need to be made in order to protect our minds.

The indistinguishability of the two subjects from one another posits the human breath as a pervasive, if modest and invisible, component of the planet's atmosphere.

The sci-fi western, based on its namesake 1973 film, explores a lawless, pre-programmed world in which humans live among and interact with "hosts," robots built to look, speak, and act like us to the point of indistinguishability—a painstaking process seen in its eerie yet breathtaking opening credits.

Ciphertext indistinguishability is a property of many encryption schemes. Intuitively, if a cryptosystem possesses the property of indistinguishability, then an adversary will be unable to distinguish pairs of ciphertexts based on the message they encrypt. The property of indistinguishability under chosen plaintext attack is considered a basic requirement for most provably secure public key cryptosystems, though some schemes also provide indistinguishability under chosen ciphertext attack and adaptive chosen ciphertext attack. Indistinguishability under chosen plaintext attack is equivalent to the property of semantic security, and many cryptographic proofs use these definitions interchangeably.

Foundations of cryptography. Cambridge, UK: Cambridge University Press. If the polynomial-time algorithm can generate samples in polynomial time, or has access to a random oracle that generates samples for it, then indistinguishability by polynomial-time sampling is equivalent to computational indistinguishability.

In complexity-theoretic cryptography, security against adaptive chosen-ciphertext attacks is commonly modeled using ciphertext indistinguishability (IND-CCA2).

Security in terms of indistinguishability has many definitions, depending on assumptions made about the capabilities of the attacker. It is normally presented as a game, where the cryptosystem is considered secure if no adversary can win the game with significantly greater probability than an adversary who must guess randomly. The most common definitions used in cryptography are indistinguishability under chosen plaintext attack (abbreviated IND-CPA), indistinguishability under (non-adaptive) chosen ciphertext attack (IND-CCA1), and indistinguishability under adaptive chosen ciphertext attack (IND-CCA2). Security under either of the latter definition implies security under the previous ones: a scheme which is IND-CCA1 secure is also IND-CPA secure, and a scheme which is IND-CCA2 secure is both IND-CCA1 and IND-CPA secure.

Topological indistinguishability is better behaved in these spaces and easier to understand. Note that this class of spaces includes all regular and completely regular spaces.

As a result, identical particles exhibit markedly different statistical behaviour from distinguishable particles. For example, the indistinguishability of particles has been proposed as a solution to Gibbs' mixing paradox.

For many cryptographic primitives, the only known constructions are based on lattices or closely related objects. These primitives include fully homomorphic encryption, indistinguishability obfuscation, cryptographic multilinear maps, and functional encryption.

Unlinkability and indistinguishability are also well-known solutions to search engine privacy, although they have proven somewhat ineffective in actually providing users with anonymity from their search queries. Both unlinkability and indistinguishability solutions try to anonymize search queries from the user who made them, therefore making it impossible for the search engine to definitively link a specific query with a specific user and create a useful profile on them. This can be done in a couple of different ways.

The indistinguishability of particles has a profound effect on their statistical properties. To illustrate this, consider a system of N distinguishable, non-interacting particles. Once again, let nj denote the state (i.e. quantum numbers) of particle j.

In 2005, Waters first proposed the concepts of attribute- based encryption and functional encryption with Amit Sahai. In 2013, Waters, along with Amit Sahai, Sanjam Garg, Craig Gentry, Shai Halevi, and Mariana Raykova, published a proof of concept of the indistinguishability obfuscation primitive.

If clear plots can be obtained in the above steps, allowing for easy neutron-photon separation, the detection can be termed effective and the rates manageable. On the other hand, smudging and indistinguishability of data points will not allow for easy separation of events.

"Anonymous Traitor Tracing: How to Embed Arbitrary Information in a Key". p. 1. Dan Boneh; Mark Zhandry. "Multiparty Key Exchange, Efficient Traitor Tracing, and More from Indistinguishability Obfuscation". 2013\. p. 5. Michel Abdalla; Alexander W. Dent; John Malone-Lee; Gregory Neven; Duong Hieu Phan; and Nigel P. Smart.

A cryptosystem is considered secure in terms of indistinguishability if no adversary, given an encryption of a message randomly chosen from a two-element message space determined by the adversary, can identify the message choice with probability significantly better than that of random guessing (). If any adversary can succeed in distinguishing the chosen ciphertext with a probability significantly greater than , then this adversary is considered to have an "advantage" in distinguishing the ciphertext, and the scheme is not considered secure in terms of indistinguishability. This definition encompasses the notion that in a secure scheme, the adversary should learn no information from seeing a ciphertext. Therefore, the adversary should be able to do no better than if it guessed randomly.

With the increasing prevalence of virtual reality, augmented reality, and photorealistic computer animation, the "valley" has been cited in reaction to the verisimilitude of the creation as it approaches indistinguishability from reality. The uncanny valley hypothesis predicts that an entity appearing almost human will risk eliciting cold, eerie feelings in viewers.

Indistinguishability obfuscation (IO) is a cryptographic primitive that provides a formal notion of program obfuscation. Informally, obfuscation hides the implementation of a program while still allowing users to run it. A candidate construction of IO with provable security under concrete hardness assumptions relating to multilinear maps was published in 2013.

Indeed, the equivalence relation determined by ≤ is precisely that of topological indistinguishability: :x ≡ y if and only if x ≤ y and y ≤ x. A topological space is said to be symmetric (or R0) if the specialization preorder is symmetric (i.e. x ≤ y implies y ≤ x). In this case, the relations ≤ and ≡ are identical.

In combinatorial game theory, and particularly in the theory of impartial games in misère play, an indistinguishability quotient is a commutative monoid that generalizes and localizes the Sprague–Grundy theorem for a specific game's rule set. In the specific case of misere-play impartial games, such commutative monoids have become known as misere quotients.

The notion of semantic security was first put forward by Goldwasser and Micali in 1982. However, the definition they initially proposed offered no straightforward means to prove the security of practical cryptosystems. Goldwasser/Micali subsequently demonstrated that semantic security is equivalent to another definition of security called ciphertext indistinguishability under chosen- plaintext attack.S. Goldwasser and S. Micali, Probabilistic encryption.

In mathematics, a tolerance relation is a relation that is reflexive and symmetric, but not necessarily transitive; a set X that possesses a tolerance relation can be described as a tolerance space. Tolerance relations provide a convenient general tool for studying indiscernibility/indistinguishability phenomena. The importance of those for mathematics had been first recognized by Poincaré.

Where Taiji is a differentiating principle that results in the emergence of something new, Dao is still and silent, operating to reduce all things to equality and indistinguishability. He argued that there is a central harmony that is not static or empty but was dynamic, and that the Supreme Ultimate is itself in constant creative activity.

Topological indistinguishability of points is an equivalence relation. No matter what topological space X might be to begin with, the quotient space under this equivalence relation is always T0. This quotient space is called the Kolmogorov quotient of X, which we will denote KQ(X). Of course, if X was T0 to begin with, then KQ(X) and X are naturally homeomorphic.

Schrödinger logics are logical systems in which the principle of identity is not true in general. The intuitive motivation for these logics is both Erwin Schrödinger's thesis (which has been advanced by other authors) that identity lacks sense for elementary particles of modern physics, and the way which physicists deal with this concept; normally, they understand identity as meaning indistinguishability (agreement with respect to attributes).

It applies to cases of total symmetry. This logic is used to develop particle physics (see indistinguishability) and explain quantum phenomena. At the time of his death, Parker-Rhodes was completing his last book, The Inevitable Universe, which combines elements of metaphysics with mathematics, resulting in actual physics. It claims that one can infer various facts of modern physics solely by using logic and mathematics with very few assumptions.

This open set can then be used to distinguish between the two points. A T0 space is a topological space in which every pair of distinct points is topologically distinguishable. This is the weakest of the separation axioms. Topological indistinguishability defines an equivalence relation on any topological space X. If x and y are points of X we write x ≡ y for "x and y are topologically indistinguishable".

Suppose A is a set of impartial combinatorial games that is finitely-generated with respect to disjunctive sums and closed in both of the following senses: (1) Additive closure: If G and H are games in A, then their disjunctive sum G + H is also in A. (2) Hereditary closure: If G is a game in A and H is an option of G, then H is also in A. Next, define on A the indistinguishability congruence ≈ that relates two games G and H if for every choice of a game X in A, the two positions G+X and H+X have the same outcome (i.e., are either both first- player wins in best play of A, or alternatively are both second-player wins). One easily checks that ≈ is indeed a congruence on the set of all disjunctive position sums in A, and that this is true regardless of whether the game is played in normal or misere play. The totality of all the congruence classes form the indistinguishability quotient.

One way is for the user to use a plugin or software that generates multiple different search queries for every real search query the user makes. This is an indistinguishability solution, and it functions by obscuring the real searches a user makes so that a search engine cannot tell which queries are the software's and which are the user's. Then, it is more difficult for the search engine to use the data it collects on a user to do things like target ads.

One particular development along these lines has been the development of witness- indistinguishable proof protocols. The property of witness- indistinguishability is related to that of zero-knowledge, yet witness- indistinguishable protocols do not suffer from the same problems of concurrent execution. Another variant of zero-knowledge proofs are non-interactive zero- knowledge proofs. Blum, Feldman, and Micali showed that a common random string shared between the prover and the verifier is enough to achieve computational zero-knowledge without requiring interaction.

Note that in practice entropically-secure encryption algorithms are only "secure" provided that the message distribution possesses high entropy from any reasonable adversary's perspective. This is an unrealistic assumption for a general encryption scheme, since one cannot assume that all likely users will encrypt high-entropy messages. For these schemes, stronger definitions (such as semantic security or indistinguishability under adaptive chosen ciphertext attack) are appropriate. However, there are special cases in which it is reasonable to require high entropy messages.

In cryptography, a distinguishing attack is any form of cryptanalysis on data encrypted by a cipher that allows an attacker to distinguish the encrypted data from random data. Modern symmetric-key ciphers are specifically designed to be immune to such an attack. In other words, modern encryption schemes are pseudorandom permutations and are designed to have ciphertext indistinguishability. If an algorithm is found that can distinguish the output from random faster than a brute force search, then that is considered a break of the cipher.

It has been proven that any algorithm which decrypts a Rabin- encrypted value can be used to factor the modulus n. Thus, Rabin decryption is at least as hard as the integer factorization problem, something that has not been proven for RSA. It is generally believed that there is no polynomial-time algorithm for factoring, which implies that there is no efficient algorithm for decrypting a Rabin-encrypted value without the private key (p,q). The Rabin cryptosystem does not provide indistinguishability against chosen plaintext attacks since the process of encryption is deterministic.

Consequently, semantic security is now considered an insufficient condition for securing a general-purpose encryption scheme. Indistinguishability under Chosen Plaintext Attack (IND-CPA) is commonly defined by the following experiment: # A random pair (pk,sk) is generated by running Gen(1^n). # A probabilistic polynomial time-bounded adversary is given the public key pk , which it may use to generate any number of ciphertexts (within polynomial bounds). # The adversary generates two equal-length messages m_0 and m_1, and transmits them to a challenge oracle along with the public key.

These detectors have a short functional lifetime (5–10 years) when doing heavy ion analysis. One of the main advantages of silicon detectors is their simplicity. However, they have to be used with a so-called “range foil” to range out the forward scattered heavy beam ions. Therefore, the simple range foil ERD has two major disadvantages: first, the loss of energy resolution due to the energy straggle and second, thickness inhomogeneity of the range foil, and the intrinsic indistinguishability of the signals for the various different recoiled target elements.

The first quasi-set theory was proposed by D. Krause in his PhD thesis, in 1990 (see Krause 1992). A related physics theory, based on the logic of adding fundamental indistinguishability to equality and inequality, was developed and elaborated independently in the book The Theory of Indistinguishables by A. F. Parker-Rhodes.A. F. Parker-Rhodes, The Theory of Indistinguishables: A Search for Explanatory Principles below the level of Physics, Reidel (Springer), Dordecht (1981). On the use of quasi-sets in philosophical discussions of quantum identity and individuality, see French (2006) and French and Krause (2006).

Natanson was head of Theoretical Physics at Kraków University from 1899 to 1935. Theoretical Physics in Poland Before 1939, Retrieved March 29, 2010 He published a series of papers on thermodynamically irreversible processes, gaining him recognition in the rapidly growing field. He was the first to consider the distinguishability of photons in the statistical analysis of elementary processes, a precursor of the concept of quantum indistinguishability. He discovered a quantum statistics, rediscovered 11 years later by Satyendra Nath Bose and generalized by Albert Einstein – the Bose–Einstein statistics.

For electrons the energy loss is slightly different due to their small mass (requiring relativistic corrections) and their indistinguishability, and since they suffer much larger losses by Bremsstrahlung, terms must be added to account for this. Fast charged particles moving through matter interact with the electrons of atoms in the material. The interaction excites or ionizes the atoms, leading to an energy loss of the traveling particle. The non-relativistic version was found by Hans Bethe in 1930; the relativistic version (shown below) was found by him in 1932.

Cryptocat uses a Double Ratchet Algorithm in order to obtain forward and future secrecy across messages, after a session is established using a four-way Elliptic-curve Diffie–Hellman handshake. The handshake mixes in long-term identity keys, an intermediate-term signed pre- key, and a one-time use prekey. The approach is similar to the encryption protocol adopted for encrypted messaging by the Signal mobile application. Cryptocat's goal is for its messages to obtain confidentiality, integrity, source authenticity, forward and future secrecy and indistinguishability even over a network controlled by an active attacker.

While her classmates generally saw Youko as a timid pushover or other negative views of her general indistinguishability, Ritsuko tells her husband that Youko was well-behaved, gentle, and predictable. In the anime, Ritsuko eventually learns of her daughter's fate from Yuka Sugimoto when she returns from the Twelve Kingdoms. Although she was saddened that Youko will not come back, she is satisfied to know that Youko is doing well where she is. In the novels, it is unknown if her mother ever learns what became of Youko.

As already mentioned above, for the implementation of a boson sampling machine one necessitates a reliable source of many indistinguishable photons, and this requirement currently remains one of the main difficulties in scaling up the complexity of the device. Namely, despite recent advances in photon generation techniques using atoms, molecules, quantum dots and color centers in diamonds, the most widely used method remains the parametric down-conversion (PDC) mechanism. The main advantages of PDC sources are the high photon indistinguishability, collection efficiency and relatively simple experimental setups. However, one of the drawbacks of this approach is its non-deterministic (heralded) nature.

To counter this problem, cryptographers proposed the notion of "randomized" or probabilistic encryption. Under these schemes, a given plaintext can encrypt to one of a very large set of possible ciphertexts, chosen randomly during the encryption process. Under sufficiently strong security guarantees the attacks proposed above become infeasible, as the adversary will be unable to correlate any two encryptions of the same message, or correlate a message to its ciphertext, even given access to the public encryption key. This guarantee is known as semantic security or ciphertext indistinguishability, and has several definitions depending on the assumed capabilities of the attacker (see semantic security).

In cryptography, Russian copulation is a method of rearranging plaintext before encryption so as to conceal stereotyped headers, salutations, introductions, endings, signatures, etc.. This obscures clues for a cryptanalyst, and can be used to increase cryptanalytic difficulty in naive cryptographic schemes (however, most modern schemes contain more rigorous defences; see ciphertext indistinguishability). This is of course desirable for those sending messages and wishing them to remain confidential. Padding is another technique for obscuring such clues. The technique is to break the starting plaintext message into two parts and then to invert the order of the parts (similar to circular shift).

All of Einstein's major contributions to the old quantum theory were arrived at via statistical argument. This includes his 1905 paper arguing that light has particle properties, his 1906 work on specific heats, his 1909 introduction of the concept of wave-particle duality, his 1916 work presenting an improved derivation of the blackbody radiation formula, and his 1924 work that introduced the concept of indistinguishability. Mirror in a cavity containing particles of an ideal gas and filled with fluctuating black body radiation. Einstein's 1909 arguments for the wave-particle duality of light were based on a thought experiment.

Ken Tucker from Entertainment Weekly, declared it as the "song of the summer", and praised it for being "a piece of psychedelic pop at once so 60s and so 90s that to sully it with a 'shagalicious' joke would be an insult... The way [Madonna] has of making her voice merge into indistinguishability with the surging instrumentation in the chorus, the way she sings the title phrase with an ache in her voice, that's at once urgent and playful." Matthew Jacobs from The Huffington Post ranked the song 22 on their list of "The Definitive Ranking Of Madonna Singles".

In economics, fungibility is the property of a good or a commodity whose individual units are essentially interchangeable, and each of its parts is indistinguishable from another part. For example, gold is fungible since a specified amount of pure gold is equivalent to that same amount of pure gold, whether in the form of coins, ingots, or in other states. Other fungible commodities include sweet crude oil, company shares, bonds, other precious metals, and currencies. Fungibility refers only to the equivalence and indistinguishability of each unit of a commodity with other units of the same commodity, and not to the exchange of one commodity for another.

The terms "Hausdorff", "separated", and "preregular" can also be applied to such variants on topological spaces as uniform spaces, Cauchy spaces, and convergence spaces. The characteristic that unites the concept in all of these examples is that limits of nets and filters (when they exist) are unique (for separated spaces) or unique up to topological indistinguishability (for preregular spaces). As it turns out, uniform spaces, and more generally Cauchy spaces, are always preregular, so the Hausdorff condition in these cases reduces to the T0 condition. These are also the spaces in which completeness makes sense, and Hausdorffness is a natural companion to completeness in these cases.

The topological indistinguishability relation on a space X can be recovered from a natural preorder on X called the specialization preorder. For points x and y in X this preorder is defined by :x ≤ y if and only if x ∈ cl{y} where cl{y} denotes the closure of {y}. Equivalently, x ≤ y if the neighborhood system of x, denoted Nx, is contained in the neighborhood system of y: :x ≤ y if and only if Nx ⊂ Ny. It is easy to see that this relation on X is reflexive and transitive and so defines a preorder. In general, however, this preorder will not be antisymmetric.

The aufbau principle rests on a fundamental postulate that the order of orbital energies is fixed, both for a given element and between different elements; in both cases this is only approximately true. It considers atomic orbitals as "boxes" of fixed energy into which can be placed two electrons and no more. However, the energy of an electron "in" an atomic orbital depends on the energies of all the other electrons of the atom (or ion, or molecule, etc.). There are no "one-electron solutions" for systems of more than one electron, only a set of many-electron solutions that cannot be calculated exactlyElectrons are identical particles, a fact that is sometimes referred to as "indistinguishability of electrons".

Granular computing (GrC) is an emerging computing paradigm of information processing that concerns the processing of complex information entities called "information granules", which arise in the process of data abstraction and derivation of knowledge from information or data. Generally speaking, information granules are collections of entities that usually originate at the numeric level and are arranged together due to their similarity, functional or physical adjacency, indistinguishability, coherency, or the like. At present, granular computing is more a theoretical perspective than a coherent set of methods or principles. As a theoretical perspective, it encourages an approach to data that recognizes and exploits the knowledge present in data at various levels of resolution or scales.

Indistinguishability under non- adaptive and adaptive Chosen Ciphertext Attack (IND-CCA1, IND-CCA2) uses a definition similar to that of IND-CPA. However, in addition to the public key (or encryption oracle, in the symmetric case), the adversary is given access to a decryption oracle which decrypts arbitrary ciphertexts at the adversary's request, returning the plaintext. In the non-adaptive definition, the adversary is allowed to query this oracle only up until it receives the challenge ciphertext. In the adaptive definition, the adversary may continue to query the decryption oracle even after it has received a challenge ciphertext, with the caveat that it may not pass the challenge ciphertext for decryption (otherwise, the definition would be trivial).

Since topological indistinguishability is an equivalence relation on any topological space X, we can form the quotient space KX = X/≡. The space KX is called the Kolmogorov quotient or T0 identification of X. The space KX is, in fact, T0 (i.e. all points are topologically distinguishable). Moreover, by the characteristic property of the quotient map any continuous map f : X → Y from X to a T0 space factors through the quotient map q : X → KX. Although the quotient map q is generally not a homeomorphism (since it is not generally injective), it does induce a bijection between the topology on X and the topology on KX. Intuitively, the Kolmogorov quotient does not alter the topology of a space.

Telegram's default chat function missed points because the communications were not encrypted with keys the provider didn't have access to, users could not verify contacts' identities, and past messages were not secure if the encryption keys were stolen. Telegram's optional secret chat function, which provides end-to-end encryption, received a score of 7 out of 7 points on the scorecard. The EFF said that the results "should not be read as endorsements of individual tools or guarantees of their security", and that they were merely indications that the projects were "on the right track". In December 2015, two researchers from Aarhus University published a report in which they demonstrated that MTProto does not achieve indistinguishability under chosen-ciphertext attack (IND-CCA) or authenticated encryption.

The definition of security achieved by Cramer–Shoup is formally termed "indistinguishability under adaptive chosen ciphertext attack" (IND-CCA2). This security definition is currently the strongest definition known for a public key cryptosystem: it assumes that the attacker has access to a decryption oracle which will decrypt any ciphertext using the scheme's secret decryption key. The "adaptive" component of the security definition means that the attacker has access to this decryption oracle both before and after he observes a specific target ciphertext to attack (though he is prohibited from using the oracle to simply decrypt this target ciphertext). The weaker notion of security against non- adaptive chosen ciphertext attacks (IND-CCA1) only allows the attacker to access the decryption oracle before observing the target ciphertext.

Fermi heap and Fermi hole refer to two closely related quantum phenomena that occur in many-electron atoms. They arise due to the Pauli exclusion principle, according to which no two electrons can be in the same quantum state in a system (which, accounting for electrons' spin, means that there can be up to two electrons in the same orbital). Due to indistinguishability of elementary particles, the probability of a measurement yielding a certain eigenvalue must be invariant when electrons are exchanged, which means that the probability amplitude must either remain the same or change sign. For instance, consider an excited state of the helium atom in which electron 1 is in the 1s orbital and electron 2 has been excited to the 2s orbital.

She noted the game's "serious attitude" and "very gritty view of sports", and similar to hockey, felt that the non-disc action was "one of the nicest aspects" of the game. She praised the graphics and environments, surround sound, the array of unlockables, the single-player, and its replay value, but bemoaned the lack of options to change between camera views, the Action view in general, and the indistinguishability between players. Goldstein regarded Deathrows profanity as the "best use of endless cursing in a game... ever". Herold of The New York Times noted violence's centrality to the game and figured that the game's age restrictions were likely due to the "savage profanities", which he felt gave the game personality unlike other sports video games.

For example, conservation of energy is a consequence of the shift symmetry of time (no moment of time is different from any other), while conservation of momentum is a consequence of the symmetry (homogeneity) of space (no place in space is special, or different than any other). The indistinguishability of all particles of each fundamental type (say, electrons, or photons) results in the Dirac and Bose quantum statistics which in turn result in the Pauli exclusion principle for fermions and in Bose–Einstein condensation for bosons. The rotational symmetry between time and space coordinate axes (when one is taken as imaginary, another as real) results in Lorentz transformations which in turn result in special relativity theory. Symmetry between inertial and gravitational mass results in general relativity.

In physics, he is remembered partly for his founding contribution to combinatorial physics, based on his elucidation of "combinatorial hierarchy", a mathematical structure of bit-strings generated by an algorithm based on discrimination (exclusive-or between bits). He published some of his ideas in fundamental physics (based on a logical "level below physics") in the book The Theory of Indistinguishables (1981).The Theory of Indistinguishables: A Search for Explanatory Principles below the level of Physics, Springer (1981) It identifies a logic based on adding to equality and inequality a third fundamental relationship which is neither one: indistinguishability-in- principle. For example, even with infinite knowledge, the three dimensions of a completely empty space are totally indistinguishable from one another, but they are still three, not one (contradicting Leibniz's Identity of Indiscernibles).

Researchers noticed early on that the shape of intensity-sensitivity curves could be explained by assuming that an intrinsic source of noise in the retina produces random events indistinguishable from those triggered by real photons. Later experiments on rod cells of cane toads (Bufo marinus) showed that the frequency of these spontaneous events is strongly temperature-dependent, which implies that they are caused by the thermal isomerization of rhodopsin. In human rod cells, these events occur about once every 100 seconds on average, which, taking into account the number of rhodopsin molecules in a rod cell, implies that the half-life of a rhodopsin molecule is about 420 years. The indistinguishability of dark events from photon responses supports this explanation, because rhodopsin is at the input of the transduction chain.

Gibbs was well aware that the application of the equipartition theorem to large systems of classical particles failed to explain the measurements of the specific heats of both solids and gases, and he argued that this was evidence of the danger of basing thermodynamics on "hypotheses about the constitution of matter". Gibbs's own framework for statistical mechanics, based on ensembles of macroscopically indistinguishable microstates, could be carried over almost intact after the discovery that the microscopic laws of nature obey quantum rules, rather than the classical laws known to Gibbs and to his contemporaries.Wheeler 1998, pp. 160–161 His resolution of the so-called "Gibbs paradox", about the entropy of the mixing of gases, is now often cited as a prefiguration of the indistinguishability of particles required by quantum physics.

While there is some debate regarding whether the "Standard Interpretation" is that described by Turing or, instead, based on a misreading of his paper, these three versions are not regarded as equivalent, and their strengths and weaknesses are distinct. Huma Shah points out that Turing himself was concerned with whether a machine could think and was providing a simple method to examine this: through human-machine question-answer sessions. Shah argues there is one imitation game which Turing described could be practicalised in two different ways: a) one-to-one interrogator-machine test, and b) simultaneous comparison of a machine with a human, both questioned in parallel by an interrogator. Since the Turing test is a test of indistinguishability in performance capacity, the verbal version generalises naturally to all of human performance capacity, verbal as well as nonverbal (robotic).

In work with Aaron Clauset, David Kempe, and Dimitris Achlioptas, Moore showed that the appearance of power laws in the degree distribution of networks can be illusory: network models such as the Erdős–Rényi model, whose degree distribution does not obey a power law, may nevertheless appear to exhibit one when measured using traceroute-like tools.. In work with Clauset and Mark Newman, Moore developed a probabilistic model of hierarchical clustering for complex networks, and showed that their model predicts clustering robustly in the face of changes to the link structure of the network... Other topics in Moore's research include modeling undecidable problems by physical systems,. phase transitions in random instances of the Boolean satisfiability problem, the unlikelihood of success in the search for extraterrestrial intelligence due to the indistinguishability of advanced signaling technologies from random noise,.. the inability of certain types of quantum algorithm to solve graph isomorphism, and attack-resistant quantum cryptography..

Dipankar Home is among the earliest Indian researchers initiating studies on Foundations of Quantum Mechanics that have gradually become linked with experiments, giving rise to the currently vibrant area of Quantum Information (QI). His manifold contributions include two distinctive Research-level Books: "Conceptual Foundations of Quantum Physics – An Overview from Modern Perspectives" (Plenum) and "Einstein’s Struggles with Quantum Theory: A Reappraisal" (Springer) with Forewords by Anthony Leggett and Roger Penrose respectively (Appendix A), while some of the significant works with his collaborators are: (a) An ingenious idea was formulated by invoking quantum indistinguishability leading to an arbitrarily efficient resource for producing entanglement, applicable for spin-like variables of any two identical bosons/fermions. Entanglement being at the core of QI, this work has stimulated applications of Quantum Statistics in QI processing, apart from being used in studies on free electron Quantum Computation. (b) A hitherto unexplored use of intraparticle path-spin entanglement was conceived for empirically verifying Quantum Contextuality, subsequently tested by the Vienna group, followed recently by suggesting its information-theoretic applications.