The advent of Bell's inequalities provoked the possibility that entangled quantum phenomena is non-local in nature. Since teleportation only requires a finite amount of classical information, i.e. two bits, the author asks whether or not it is possible to further characterize the nature of internal correlation in terms of information. Towards this end, the issue of the amount of information that is transferred internally and non-locally is addressed. There are two possibilities: the amount is infinite or the amount is finite. A partial answer to this problem is given: it is shown that models exist whereby the amount is finite. The EPR-Bell cosine correlation can be reproduced exactly using on average 1.48 bits. The issue of simultaneity and the problems it poses are also examined in this context. Several extensions are suggested.
Measurements performed on distant parts of an entangled quantum state can generate correlations incompatible with classical theories respecting the assumption of local causality. This is the phenomenon known as quantum non-locality that, apart from its fundamental role, can also be put to practical use in applications such as cryptography and distributed computing. Clearly, developing ways of quantifying non-locality is an important primitive in this scenario. Here, we propose to quantify the non-locality of a given probability distribution via its trace distance to the set of classical correl…
We show here that the recent work of Wolf and Wullschleger (quant-ph/0502030) on oblivious transfer apparently opens the possibility that non-local correlations which are stronger than those in quantum mechanics could be used for bit-commitment. This is surprising, because it is the very existence of non-local correlations which in quantum mechanics prevents bit-commitment. We resolve this apparent paradox by stressing the difference between non-local correlations and oblivious transfer, based on the time-ordering of their inputs and outputs, which prevents bit-commitment.
So-called non-local boxes, which have been introduced as an idealization-in different respects-of the behavior of entangled quantum states, have been known to allow for unconditional bit commitment between the two involved parties. We show that, actually, any possible non-local correlation which produces random bits on both sides can be used to implement bit commitment, and that this holds even when the parties are allowed to delay their inputs to the box. Since a particular example is the behavior of an EPR pair, this resource allows for implementing unconditionally secure bit commitment as l…
Oblivious transfer, a central functionality in modern cryptography, allows a party to send two one-bit messages to another who can choose one of them to read, remaining ignorant about the other, whereas the sender does not learn the receiver's choice. Oblivious transfer the security of which is information-theoretic for both parties is known impossible to achieve from scratch. - The joint behavior of certain bi-partite quantum states is non-local, i.e., cannot be explained by shared classical information. In order to better understand such behavior, which is classically explainable only by com…
According to quantum theory, the outcomes obtained by measuring an entangled state necessarily exhibit some randomness if they violate a Bell inequality. In particular, a maximal violation of the CHSH inequality guarantees that 1.23 bits of randomness are generated by the measurements. However, by performing measurements with binary outcomes on two subsystems one could in principle generate up to two bits of randomness. We show that correlations that violate arbitrarily little the CHSH inequality or states with arbitrarily little entanglement can be used to certify that close to the maximum of…
In a no-signaling world, the outputs of a nonlocal box cannot be completely predetermined, a feature that is exploited in many quantum information protocols exploiting non-locality, such as device-independent randomness generation and quantum key distribution. This relation between non-locality and randomness can be formally quantified through the min-entropy, a measure of the unpredictability of the outputs that holds conditioned on the knowledge of any adversary that is limited only by the no-signaling principle. This quantity can easily be computed for the noisy Popescu-Rohrlich (PR) box, t…
Recently, a series of different measures quantifying memory effects in the quantum dynamics of open systems has been proposed. Here, we derive a mathematical representation for the non-Markovianity measure based on the exchange of information between the open system and its environment which substantially simplifies its numerical and experimental determination, and fully reveals the locality and universality of non-Markovianity in the quantum state space. We further illustrate the application of this representation by means of an all-optical experiment which allows the measurement of the degre…
The mathematical notion of incompleteness (eg of rational numbers, Turing-computable functions, and arithmetic proof) does not play a key role in conventional physics. Here, a reformulation of the kinematics of quantum theory is attempted, based on an inherently granular and discontinuous state space, in which the quantum wavefunction is associated with a finite set of finite bit strings, and the unitary transformations of complex Hilbert space are reformulated as finite permutation and related operators incorporating complex and hyper-complex structure. Such a reformulation, consistent with W…
Within a global physical theory, a notion of locality allows us to find and justify information-processing primitives, like non-signalling between distant agents. Here we propose exploring the opposite direction: to take agents as the basic building blocks through which we test a physical theory, and recover operational notions of locality from signalling conditions. First we introduce an operational model for the effective state spaces of individual agents, as well as the range of their actions. We then formulate natural secrecy conditions between agents and identify the aspects of locality r…
This work provides a comprehensive approach to analyze the entanglement between subsystems generated by identical particles, based on the symmetric/exterior algebra (SEA) and microcausality. Our method amends the no-labeling approach (NLA) to quantify any type of identical particles' entanglement, especially fermions with the parity superselection rule. We can analyze the non-local properties of identical particles' states in a fundamentally equivalent way to those for non-identical particles, which is achieved by the factorizability of the total Hilbert space of identical particles. This form…
In multi-prover interactive proofs (MIPs), the verifier is usually non-adaptive. This stems from an implicit problem which we call ``contamination'' by the verifier. We make explicit the verifier contamination problem, and identify a solution by constructing a generalization of the MIP model. This new model quantifies non-locality as a new dimension in the characterization of MIPs. A new property of zero-knowledge emerges naturally as a result by also quantifying the non-locality of the simulator.
A quantum system interacts with its environment, if ever so slightly, no matter how much care is put into isolating it. As a consequence, quantum bits (qubits) undergo errors, putting dauntingly difficult constraints on the hardware suitable for quantum computation. New strategies are emerging to circumvent this problem by encoding a qubit non-locally across the phase space of a physical system. Since most sources of decoherence are due to local fluctuations, the foundational promise is to exponentially suppress errors by increasing a measure of this non-locality. Prominent examples are topolo…
Contextuality is central to both the foundations of quantum theory and to the novel information processing tasks. Although it was recognized before Bell's nonlocality, despite some recent proposals, it still faces a fundamental problem: how to quantify its presence? In this work, we provide a framework for quantifying contextuality. We conduct two complementary approaches: (i) bottom-up approach, where we introduce a communication game, which grasps the phenomenon of contextuality in a quantitative manner; (ii) top-down approach, where we just postulate two measures - relative entropy of conte…
A local and deterministic model of quantum correlations is always possible, as shown explicitly by Brans in 1988: one simply needs the physical systems being measured to have a suitable statistical correlation with the physical systems performing the measurement, via some common cause. Hence, to derive no-go results such as Bell inequalities, an assumption of measurement independence is crucial. It is a surprisingly strong assumption -- less than 1/15 bits of prior correlation suffice for a local model of the singlet state of two qubits -- with ramifications for the security of quantum communi…
We use the 'bit thread' formulation of holographic entanglement entropy to highlight the distinction between the universally-valid strong subadditivity and the more restrictive relation called monogamy of mutual information (MMI), known to hold for geometrical states (i.e. states of holographic theories with gravitational duals describing a classical bulk geometry). In particular, we provide a novel proof of MMI, using bit threads directly. To this end, we present an explicit geometrical construction of cooperative flows which we build out of disjoint thread bundles. We conjecture that our met…
A closed vacuum-dominated Friedmann universe is asymptotic to a de Sitter space with a cosmological event horizon for any observer. The holographic principle says the area of the horizon in Planck units determines the number of bits of information about the universe that will ever be available to any observer. The wavefunction describing the probability distribution of mass quanta associated with bits of information on the horizon is the boundary condition for the wavefunction specifying the probability distribution of mass quanta throughout the universe. Local interactions between mass quanta…
Here we propose a general relativistic quantum framework for cryptography that exploits the fascinating connection of quantum non-locality and special theory of relativity with cryptography. The underlying principle of unconditional security is causality and two-fold quantum non-local correlations: first entanglement swapping and then teleportation over causally independent entangled systems. We show that the proposed framework has following remarkable and novel features in mistrustful cryptography: (i) It helps in defining a new notion of oblivious transfer where both the data transferred and…
We propose the first correct special-purpose quantum circuits for preparation of Bell-diagonal states (BDS), and implement them on the IBM Quantum computer, characterizing and testing complex aspects of their quantum correlations in the full parameter space. Among the circuits proposed, one involves only two quantum bits but requires adapted quantum tomography routines handling classical bits in parallel. The entire class of Bell-diagonal states is generated, and a number of characteristic indicators, namely entanglement of formation, CHSH non-locality, steering and discord, are experimentally…
Quantum information processing is the emerging field that defines and realizes computing devices that make use of quantum mechanical principles, like the superposition principle, entanglement, and interference. In this review we study the information counterpart of computing. The abstract form of the distributed computing setting is called communication complexity. It studies the amount of information, in terms of bits or in our case qubits, that two spatially separated computing devices need to exchange in order to perform some computational task. Surprisingly, quantum mechanics can be used t…
The behavior of entangled quantum systems can generally not be explained as being determined by shared classical randomness. In the first part of this paper, we propose a simple game for n players demonstrating this non-local property of quantum mechanics: While, on the one hand, it is immediately clear that classical players will lose the game with substantial probability, it can, on the other hand, always be won by players sharing an entangled quantum state. The simplicity of the classical analysis of our game contrasts the often quite involved analysis of previously proposed examples of thi…
Schrödinger held that a local quantum system has some objectively real quantum state and no other (hidden) properties. He therefore took the Einstein-Podolsky-Rosen (EPR) phenomenon, which he generalized and called `steering', to require nonlocal wavefunction collapse. Because this would entail faster-than-light (FTL) information transmission, he doubted that it would be seen experimentally. Here we report a demonstration of EPR steering with entangled photon pairs that puts--in Schrödinger's interpretation--a non-zero lower bound on the amount of FTL information transmission. We develop a fam…
We consider the amount of work which can be extracted from a heat bath using a bipartite state shared by two parties. In general it is less then the amount of work extractable when one party is in possession of the entire state. We derive bounds for this "work deficit" and calculate it explicitly for a number of different cases. For pure states the work deficit is exactly equal to the distillable entanglement of the state, and this is also achievable for maximally correlated states. In these cases a form of complementarity exists between physical work which can be extracted and distillable ent…
The non-local correlations exhibited when measuring entangled particles can be used to certify the presence of genuine randomness in Bell experiments. While non-locality is necessary for randomness certification, it is unclear when and why non-locality certifies maximal randomness. We provide here a simple argument to certify the presence of maximal local and global randomness based on symmetries of a Bell inequality and the existence of a unique quantum probability distribution that maximally violates it. Using our findings, we prove the existence of N-party Bell test attaining maximal global…
It has recently been shown that all causal correlations between two parties which output each one bit, a and b, when receiving each one bit, x and y, can be expressed as convex combinations of local correlations (i.e., correlations that can be simulated with local random variables) and non-local correlations of the form a+b=xy mod 2. We show that a single instance of the latter elementary non-local correlation suffices to simulate exactly all possible projective measurements that can be performed on the singlet state of two qubits, with no communication needed at all. This elementary non-local…
Bell's inequality fundamentally changed our understanding of quantum mechanics. Bell's insight that non-local correlations between quantum systems cannot be explained classically can be verified experimentally, and has numerous applications in modern quantum information. Today, the CHSH inequality is probably the most well-known Bell inequality and it has given us a wealth of understanding in what differentiates the classical from the quantum world. Yet, there are certainly other means of quantifying "Bell non-locality without inequalities" such as the famous Hardy's paradox. As such, one may …
In quantum superdense coding, two parties previously sharing entanglement can communicate a two bit message by sending a single qubit. We study this feature in the broader framework of general probabilistic theories. We consider a particular class of theories in which the local state space of the communicating parties corresponds to Euclidean hyperballs of dimension n (the case n = 3 corresponds to the Bloch ball of quantum theory). We show that a single n-ball can encode at most one bit of information, independently of n. We introduce a bipartite extension of such theories for which there exi…
Device-Independent (DI) security is the best form of quantum cryptography, providing information-theoretic security based on the very laws of nature. In its highest form, security is guaranteed against adversaries limited only by the no-superluminal signalling rule of relativity. The task of randomness amplification, to generate secure fully uniform bits starting from weakly random seeds, is of both cryptographic and foundational interest, being important for the generation of cryptographically secure random numbers as well as bringing deep connections to the existence of free-will. DI no-sign…
Wheeler's {\it observer-participancy} and the related {\it it from bit} credo refer to quantum non-locality and contextuality. The mystery of these concepts slightly starts unveiling if one encodes the (in)compatibilities between qubit observables in the relevant finite geometries. The main objective of this treatise is to outline another conceptual step forward by employing Grothendieck's {\it dessins d'enfants} to reveal the topological and (non)algebraic machinery underlying the measurement acts and their information content.
The notion of the Einstein-Podolsky-Rosen (EPR) "element of reality" is much discussed in the literature on the foundations of quantum mechanics. Recently, it has become particularly relevant due to a proposed criterion of the physical reality of a given quantum mechanical observable [A. L. O. Bilobran and R. M. Angelo, Europhys. Lett. 112, 40005 (2015)]. We examine this proposal and its consequently related measure of non-locality [V. S. Gomez and R. M. Angelo, Phys. Rev. A 97, 012123, (2018)] and argue that the criterion is ill-described as quantifying physical reality without introducing se…
It is proven that any deterministic hidden-variables theory, that reproduces quantum theory for a 'quantum equilibrium' distribution of hidden variables, must predict the existence of instantaneous signals at the statistical level for hypothetical 'nonequilibrium ensembles'. This 'signal-locality theorem' generalises yet another feature of the pilot-wave theory of de Broglie and Bohm, for which it is already known that signal-locality is true only in equilibrium. Assuming certain symmetries, lower bounds are derived on the 'degree of nonlocality' of the singlet state, defined as the (equilibri…
A non-local unitary transformation of two qubits occurs when some Hamiltonian interaction couples them. Here we characterize the amount, as measured by time, of interaction required to perform two--qubit gates, when also arbitrarily fast, local unitary transformations can be applied on each qubit. The minimal required time of interaction, or interaction cost, defines an operational notion of the degree of non--locality of gates. We characterize a partial order structure based on this notion. We also investigate the interaction cost of several communication tasks, and determine which gates are …
If reality has finite information content, space has finite fidelity. The quantum wave function that encodes spatial relationships may be limited to information that can be transmitted in a "Planck broadcast", with a bandwidth given by the inverse of the Planck time, about $2\times 10^{43}$ bits per second. Such a quantum system can resemble classical space-time on large scales, but locality emerges only gradually and imperfectly. Massive bodies are never perfectly at rest, but very slightly and slowly fluctuate in transverse position, with a spectrum of variation given by the Planck time. Thi…
