This philosophical dialogue explores the idea that the foundational principles of quantum mechanics need not be interpreted as describing a new physics, but may instead arise from the logical necessity of formalising the act of measurement within a coherent algebraic framework. By pushing this perspective to its extreme, the dialogue argues that the core structures of quantum mechanics can be derived independently of any specifically quantum properties of atomic particles, and can be formulated within an otherwise classical theory once limitations of observability and measurement context are taken seriously.
The mean King problem is a conditional retrodiction problem. In this problem Alice prepares a two prime-dimensional particles state and avails one of the particles to the King who measures its state in one of mutually unbiased bases of his choice. The King tells Alice his choice of basis after she completes a control measurement on his particle. Conditioned on this knowledge, she now infers the state observed by the King by utilizing the outcome of her control measurement. In the extended mean King problem, studied in this paper, the King does not tell Alice his measurement basis, but instead …
Bob hides a ball in one of four drawers. Alice is to locate it. Classically she has to open up to three drawers, quantally just one. The fundamental reason for this quantum speedup is not known. The usual representation of the quantum algorithm is limited to the process of solving the problem. We extend it to the process of setting the problem. The number of the drawer with the ball becomes a unitary transformation of the random outcome of the preparation measurement. This extended, time-symmetric, representation brings in relational quantum mechanics. It is with respect to Bob and any externa…
A new pure quantum state, isotropic in spin variables, is defined in an extended spin phase space beyond standard quantum mechanics. It allows to represent the entangled singlet state in separable form. The statistical correlations between Alice and Bob measurements become self correlations between hidden spin values for each particle, together with perfect anti correlation between spin values on the pair. Alice determines through measurement on her particle the value of spin in some direction. Spin in another direction is inferred from Bob measurement on the companion. Bell's inequalities are…
Asymmetric steering is an effect whereby an inseparable bipartite system can be found to be described by either quantum mechanics or local hidden variable theories depending on which one of Alice or Bob makes the required measurements. We show that, even with an inseparable bipartite system, situations can arise where Gaussian measurements on one half are not sufficient to answer the fundamental question of which theory gives an adequate description and the whole system must be considered. This phenomenon is possible because of an asymmetry in the definition of the original Einstein-Podolsky-R…
Blind quantum computation is a new secure quantum computing protocol which enables Alice who does not have sufficient quantum technology to delegate her quantum computation to Bob who has a fully-fledged quantum computer in such a way that Bob cannot learn anything about Alice's input, output, and algorithm. In previous protocols, Alice needs to have a device which generates quantum states, such as single-photon states. Here we propose another type of blind computing protocol where Alice does only measurements, such as the polarization measurements with a threshold detector. In several experim…
Correlations of spins in a system of entangled particles are inconsistent with Kolmogorov's probability theory (KPT), provided the system is assumed to be non-contextual. In the Alice-Bob EPR paradigm, non-contextuality means that the identity of Alice's spin (i.e., the probability space on which it is defined as a random variable) is determined only by the axis \alphai chosen by Alice, irrespective of Bob's axis \betaj (and vice versa). Here, we study contextual KPT models, with two properties: (1) Alice's and Bob's spins are identified as Aij and Bij, even though their distributions are dete…
Assume Alice and Bob share some bipartite $d$-dimensional quantum state. A well-known result in quantum mechanics says that by performing two-outcome measurements, Alice and Bob can produce correlations that cannot be obtained locally, i.e., with shared randomness alone. We show that by using only two bits of communication, Alice and Bob can classically simulate any such correlations. All previous protocols for exact simulation required the communication to grow to infinity with the dimension $d$. Our protocol and analysis are based on a power series method, resembling Krivine's bound on Groth…
Blind quantum computing [A. Broadbent, J. Fitzsimons, and E. Kashefi, Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science 517 (2009)] is a secure cloud quantum computing protocol which enables a client (who does not have enough quantum technology at her disposal) to delegate her quantum computation to a server (who has a universal quantum computer) without leaking any relevant information to the server. In [T. Morimae and K. Fujii, Phys. Rev. A {\bf87}, 050301(R) (2013)], a new blind quantum computing protocol, so called the measuring-Alice protocol, was proposed. …
Bell's theorem basically states that local hidden variable theory cannot predict the correlations produced by quantum mechanics. It is based on the assumption that Alice and Bob can choose measurements from a measurement set containing multiple elements. We establish a new paradigm that departs from Bell's paradigm by assuming that there are no choices for Alice and Bob and that the measurements Alice and Bob will make are fixed from the start. We include a process of quantum computation in our model. To the best of our knowledge, we are the first to connect quantum computation and nonlocality…
The uncertainty principle is the most important feature of quantum mechanics, which can be called the heart of quantum mechanics. This principle sets a lower bound on the uncertainties of two incompatible measurement. In quantum information theory, this principle is expressed in terms of entropic measures. Entropic uncertainty bound can be altered by considering a particle as a quantum memory. In this work we investigate the entropic uncertainty relation under the relativistic motion. In relativistic uncertainty game Alice and Bob agree on two observables, $\hat{Q}$ and $\hat{R}$, Bob prepares…
Blind quantum computation is a two-party protocol which involves a server Bob who has rich quantum computational resource and provides quantum computation service and a client Alice who wants to delegate her quantum computation to Bob without revealing her quantum algorithms and her input to (resp., output from) the algorithms. Since Bob may be truant and pretend to execute some computation, Alice wants to verify Bob's computation. Verifiable blind quantum computation enables Alice to check whether Bob is cheating or not. If Bob is cheating and claims his innocence, Alice can refute the denial…
Secure communication protocols are becoming increasingly important, e.g. for internet-based communication. Quantum key distribution allows two parties, commonly called Alice and Bob, to generate a secret sequence of 0s and 1s called a key that is only known to themselves. Classically, Alice and Bob could never be certain that their communication was not compromised by a malicious eavesdropper. Quantum mechanics however makes secure communication possible. The fundamental principle of quantum mechanics that taking a measurement perturbs the system (unless the measurement is compatible with the …
Quantum Key Distribution (QKD) with classical Bob has recently been suggested and proven robust. Following this work, QKD with classical Alice was also suggested and proven robust. The above protocols are ideal in the sense that they make use of qubits. However, in the past, well-known QKD protocols that were proven robust and even proven unconditionally secure, when qubits are used, were found to be totally insecure when photons are used. This is due to sensitivity to photon losses (e.g., Bennett's two-state protocol) or sensitivity to losses combined with multi-photon states (e.g., the photo…
In quantum weak oblivious transfer, Alice sends Bob two bits and Bob can learn one of the bits at his choice. It was found that the security of such a protocol is bounded by $2P_{Alice}^{\ast }+P_{Bob}^{\ast }\geq 2$, where $P_{Alice}^{\ast }$ is the probability with which Alice can guess Bob's choice, and $P_{Bob}^{\ast }$ is the probability with which Bob can guess both of Alice's bits\ given that he learns one of the bits with certainty. Here we propose a protocol and show that as long as Alice is restricted to individual measurements, then both $P_{Alice}^{\ast }$ and $P_{Bob}^{\ast }$ can…
We propose a two-way secure-communication protocol in which Alice uses an amplified spontaneous emission source while Bob employs binary phase-shift keying and an optical amplifier. Against an eavesdropper who captures all the light lost in fibers linking Alice and Bob, this protocol is capable of 3.5 Gbps quantum-secured direct communication at 50 km range. If Alice augments her terminal with a spontaneous parametric downconverter and both Alice and Bob add channel monitors, they can realize 2 Gbps quantum key distribution at that range against an eavesdropper who injects her own light into B…
We introduce a simple protocol for verifiable measurement-only blind quantum computing. Alice, a client, can perform only single-qubit measurements, whereas Bob, a server, can generate and store entangled many-qubit states. Bob generates copies of a graph state, which is a universal resource state for measurement-based quantum computing, and sends Alice each qubit of them one by one. Alice adaptively measures each qubit according to her program. If Bob is honest, he generates the correct graph state, and therefore Alice can obtain the correct computation result. Regarding the security, whateve…
The `no communication' theorem prohibits superluminal communication by showing that any measurement by Alice on an entangled system cannot change the reduced density matrix of Bob's state, and hence the expectation value of any measurement operator that Bob uses remains the same. We argue that the proof of the `no communication' theorem is incomplete and superluminal communication is possible through state discrimination in a higher-dimensional Hilbert space using ancilla qubits. We propose two quantum algorithms through state discrimantion for communication between two observers Alice and Bob…
Here, we present the quantum version of a very famous statistical decision problem, whose classical version is counter-intuitive to many. The Monty Hall game can be phrased as a two person game between Alice and Bob. In their pioneering work, Flitney and Abbott [Phys. Rev. A 65, 062318 (2002)] showed that by using a maximally entangled system for Alice and Bob's choices, and using quantum strategies, Bob and Alice can win or lose depending on the strategy chosen by either of the players. Here we develop a new quantum algorithm with quantum circuits for playing the quantum Monty Hall game by a …
We propose a homomorphic search protocol based on quantum homomorphic encryption, in which a client Alice with limited quantum ability can give her encrypted data to a powerful but untrusted quantum server and let the server search for her without decryption. By outsourcing the interactive key-update process to a trusted key center, Alice only needs to prepare and encrypt her original data and to decrypt the ciphered search result in linear time. Besides, we also present a compact and perfectly secure quantum homomorphic evaluation protocol for Cliford circuits, where the decryption key can be…
A symmetric device-independent quantum key distribution (DIQKD) protocol is proposed in this paper, with Holevo limit and subadditivity of von Neumann entropy, one can bound Eve's ability with collective attack. Together with symmetry of this protocol, the state Eve prepared for Alice and Bob, and at the same time, her eavesdropping on Alice's and Bob's measurements can be definitely inferred at the assumption that Eve aims at maximizing her information gain. The optimal state under this circumstance can be solely bounded with Alice and Bob's statistical results on the quantity of Clauser-Horn…
Quantum teleportation of an unknown quantum state is one of the few communication tasks which has no classical counterpart. Usually the aim of teleportation is to send an unknown quantum state to a receiver. But is it possible in some way that the receiver's state has more quantum discord than the sender's state? We look at a scenario where Alice and Bob share a pure quantum state and Alice has an unknown quantum state. She performs joint measurement on her qubits and channel to prepare Bob's qubits in a mixed state which has higher quantum discord than hers. We also observe an interesting fea…
When two qubits A and B are in an appropriate state, Alice can remotely steer Bob's system B into different ensembles by making different measurements on A. This famous phenomenon is known as quantum steering, or Einstein-Podolsky-Rosen steering. Importantly, quantum steering establishes the correspondence not only between a measurement on A (made by Alice) and an ensemble of B (owned by Bob) but also between each of Alice's measurement outcomes and an unnormalized conditional state of Bob's system. The unnormalized conditional states of B corresponding to all possible measurement outcomes of …
Quantum nonlocality can be revealed "via local contextuality" in qudit-qudit entangled systems with $d > 2$, that is, through the violation of inequalities containing Alice-Bob correlations that admit a local description, and Alice-Alice correlations (between the results of sequences of measurements on Alice's subsystem) that admit a local (but contextual) description. A fundamental question to understand the respective roles of entanglement and local contextuality is whether nonlocality via local contextuality exists when the parties have only qubit-qubit entanglement. Here we respond affirma…
The discrimination of quantum measurements is an important subject of quantum information processes. In this paper we present a novel protocol for local quantum measurement discrimination with multi-qubit entanglement systems. It is shown that, in the case of Bob did not know Alice's result of measurement, if both two observers (Alice and Bob) agreed in advance that Alice should measure her qubits before an appointed time t, the local discrimination of two different kinds of measurement can be completed via numerous eight-qubit GHZ entangled states and selective projective measurement.
Quantum mechanical effects have enabled the construction of cryptographic primitives that are impossible classically. For example, quantum copy-protection allows for a program to be encoded in a quantum state in such a way that the program can be evaluated, but not copied. Many of these cryptographic primitives are two-party protocols, where one party, Bob, has full quantum computational capabilities, and the other party, Alice, is only required to send random BB84 states to Bob. In this work, we show how such protocols can generically be converted to ones where Alice is fully classical, assum…
We propose an experiment to investigate the possibility of long-distance thermodynamic relationships between two entangled particles. We consider a pair of spin 1/2 particles prepared in an entangled singlet state in which one particle is sent to Alice and the other to her distant mate Bob, who are spatially separated. Our proposed experiment consists of three different setups: First, both particles are coupled to two heat baths with various temperatures. In the second setup, only Alice's particle is coupled to a heat bath and finally, in the last setup, only Bob's particle is coupled to a hea…
Quantum physics exhibits remarkable distinguishing characteristics. For example, it gives only probabilistic predictions (non-determinism) and does not allow copying of unknown state (no-cloning). Quantum correlations may be stronger than any classical ones, nevertheless information cannot be transmitted faster than light (no-signaling). However, all these features do not single out quantum physics. A broad class of theories exist which share such traits with quantum mechanics, while they allow even stronger than quantum correlations. Here, we introduce the principle of Information Causality. …
Einstein-Podolsky-Rosen (EPR) steering is a form of quantum correlation that exhibits a fundamental asymmetry in the properties of quantum systems. Given two observers, Alice and Bob, it is known to exist bipartite entangled states which are one-way steerable in the sense that Alice can steer Bob's state, but Bob cannot steer Alice's state. Here we generalize this phenomenon to three parties and find a cyclic property of tripartite EPR steering. In particular, we identify a three-qubit state whose reduced bipartite states are one-way steerable for arbitrary projective measurements. Moreover, t…
We combine the eyebrow-raising quantum phenomena of erasure and counterfactuality for the first time, proposing a simple yet unusual quantum eraser: A distant Bob can decide to erase which-path information from Alice's photon, dramatically restoring interference, without previously-shared entanglement, and without Alice's photon ever leaving her lab.
This paper proposes a cheat sensitive quantum bit commitment (CSQBC) scheme based on single photons, in which Alice commits a bit to Bob. Here, Bob only can cheat the committed bit with probability close to $0$ with the increasing of used single photons' amount. And if Alice altered her committed bit after commitment phase, she will be detected with probability close to $1$ with the increasing of used single photons' amount. The scheme is easy to be realized with nowadays technology.
We consider a quantum communication task between two users Alice and Bob, in which Alice and Bob exchange their respective quantum information by means of local operations and classical communication assisted by shared entanglement. Here, we assume that Alice and Bob may have quantum side information, not transferred, and classical communication is free. In this work, we derive general upper and lower bounds for the least amount of entanglement which is necessary to perfectly perform this task, called the state exchange with quantum side information. Moreover, we show that the optimal entangle…
Given that any communication is communication through quantum fields, we here study the scenario where a sender, Alice, causes information-carrying disturbances in a quantum field. We track the exact spread of these disturbances in space and time by using the technique of quantum information capsules (QIC). We find that the channel capacity between Alice and a receiver, Bob, is enhanced by Bob placing detectors not only inside but in addition also outside the causal future of Alice's encoding operation. Intuitively, this type of superadditivity arises because the field outside the causal futur…
Quantum steganography is the study of hiding secret quantum information by encoding it into what an eavesdropper would perceive as an innocent-looking message. Here we study an explicit steganographic encoding for a sender, Alice, to hide a secret message in the syndromes of an error-correcting code, so that the encoding simulates a given noisy quantum channel that Eve believes to connect Alice and Bob. The actual physical channel connecting Alice and Bob is noisy, but less noisy than Eve believes. We show that for the bit-flip and depolarizing channels Alice can use Eve's lack of knowledge of…
Blind quantum computation (BQC) allows a client (Alice), who only possesses relatively poor quantum devices, to delegate universal quantum computation to a server (Bob) in such a way that Bob cannot know Alice's inputs, algorithm, and outputs. The quantum channel between Alice and Bob is noisy, and the loss over the long-distance quantum communication should also be taken into account. Here we propose to use decoherence-free subspace (DFS) to overcome the collective noise in the quantum channel for BQC, which we call DFS-BQC. We propose three variations of DFS-BQC protocols. One of them, a coh…
Quantum mechanics ensures that the information stored in a quantum state is secure and the ability to send private information through a quantum channel is at least as great as the coherent information. We derive trade-off relations between quantum privacy, information gain by Eve and the disturbance caused by Eve to the quantum state that is being sent through a noisy channel. For tripartite quantum states, we show that monogamy of privacy exists in the case of a single sender and multiple receivers. When Alice prepares a tripartite entangled state and shares it with Bob and Charlie through t…
The fully symmetric Gaussian tripartite entangled pure states will not exhibit two-mode Einstein Podolsky-Rosen (EPR)-steering. This means that any two participants cannot share quantum secrets using the security of one-sided device independent quantum key distribution (1SDI-QKD) without involving the third. They are restricted at most to standard quantum key distribution (S-QKD), which is less secure. Here we show that least some asymmetric tripartite systems can exhibit bipartite EPR-steering, so that two of the participants can use 1SDI-QKD without involving the other. This is possible beca…
