The ``entanglement of formation'' of a mixed state of a bipartite quantum system can be defined in terms of the number of pure singlets needed to create the state with no further transfer of quantum information. We find an exact formula for the entanglement of formation for all mixed states of two qubits having no more than two non-zero eigenvalues, and we report evidence suggesting that the formula is valid for all states of this system.
It is shown that any quantum operation that perfectly clones the entanglement of all maximally-entangled qubit pairs cannot preserve separability. This ``entanglement no-cloning'' principle naturally suggests that some approximate cloning of entanglement is nevertheless allowed by quantum mechanics. We investigate a separability-preserving optimal cloning machine that duplicates all maximally-entangled states of two qubits, resulting in 0.285 bits of entanglement per clone, while a local cloning machine only yields 0.060 bits of entanglement per clone.
We investigate new features, especially of entanglement dynamics, which arise in a quantum-classical hybrid. As a model, we study the coupling between two quantum mechanical two-level systems, i.e. two q-bits, and a classical harmonic oscillator. Their interaction is described by a hybrid coupling, in accordance with a recently developed quantum-classical hybrid theory. We discuss various situations in which entanglement of the q-bits does (not) evolve. Furthermore, we point out an experimental application in a hybrid cooling scheme and indicate topics for future study.
It is proven that recently introduced states with perfectly secure bits of cryptographic key (private states representing secure bit) [K. Horodecki et al., Phys. Rev. Lett. 94, 160502 (2005)] as well as its multipartite and higher dimension generalizations always represent distillable entanglement. The corresponding lower bounds on distillable entanglement are provided. We also present a simple alternative proof that for any bipartite quantum state entanglement cost is an upper bound on distillable cryptographic key in bipartite scenario.
We consider the entanglement manipulation capabilities of the universal covariant quantum cloner or quantum processor circuit for quantum bits. We investigate its use for cloning a member of a bipartite or a genuine tripartite entangled state of quantum bits. We find that for bipartite pure entangled states a nontrivial behavior of concurrence appears, while for GHZ entangled states a possibility of the partial extraction of bipartite entanglement can be achieved.
Entanglement and quantum communication are paradigmatic resources in quantum information science leading to correlations between systems that have no classical analogue. Correlations due to entanglement when communication is absent have for long been studied in Bell scenarios. Correlations due to quantum communication when entanglement is absent have been studied extensively in prepare-and-measure scenarios in the last decade. Here, we set out to understand and investigate correlations in scenarios that involve both entanglement and communication, focusing on entanglement-assisted prepare-and-…
The separability problem is one of the basic and emergent problems in the present and future quantum information processing. The latter focuses on information and computing based on quantum mechanics and uses quantum bits as its basic information units. In this paper, we present an overview of the progress in the separability problem in bipartite systems, more specifically in two quantum bits systems from the criterion based on the inequalities of Bell in $1964$ to the recent criteria of separability in 2018.
Can quantum communication be more efficient than its classical counterpart? Holevo's theorem rules out the possibility of communicating more than n bits of classical information by the transmission of n quantum bits --- unless the two parties are entangled, in which case twice as many classical bits can be communicated but no more. In apparent contradiction, there are distributed computational tasks for which quantum communication cannot be simulated efficiently by classical means. In extreme cases, the effect of transmitting quantum bits cannot be achieved classically short of transmitting an…
We show that quantum entanglement can be used as a substitute for communication when the goal is to compute a function whose input data is distributed among remote parties. Specifically, we show that, for a particular function among three parties (each of which possesses part of the function's input), a prior quantum entanglement enables one of them to learn the value of the function with only two bits of communication occurring among the parties, whereas, without quantum entanglement, three bits of communication are necessary. This result contrasts the well-known fact that quantum entanglemen…
The entanglement dynamics of a pair of donor-based charge qubits is obtained in analytical form. The disentanglement is induced by off resonant scattering of acoustical phonons in the semiconductor host. According to our results a rather unusual recovery of entanglement occurs that depends on the geometrical configuration of the qubits. In addition, for large times a non-vanishing stationary entanglement is predicted. For the cases of one and two initial excitations a simple kinetic interpretation allows for an adequate analysis of the observed dynamics. Our results also reveal a direct relati…
We prove that as conjectured by Ac\'ın et al. [Phys. Rev. A 93, 040102(R) (2016)], two bits of randomness can be certified in a device-independent way from one bit of entanglement using the maximal quantum violation of Gisin's elegant Bell inequality. This suggests a surprising connection between maximal entanglement, complete sets of mutually unbiased bases, and elements of symmetric informationally complete positive operator-valued measures, on one side, and the optimal way of certifying maximal randomness, on the other.
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…
It is suggested that quantum entanglement emerges from the holographic principle stating that all of the information of a region (bulk bits) can be described by the bits on its boundary surface. There are redundancy and information loss in the bulk bits that lead to the nonlocal correlation among the bulk bits. Quantum field theory overestimates the independent degrees of freedom in the bulk. The maximum entanglement in the universe increases as the size of the cosmic horizon and this could be related with the arrow of time and dark energy.
In general, generation of entangled photon pairs and also the random choice of measurement basis can be implemented with passive optical devices in entanglement based quantum key distribution (QKD) system. However, auxiliary random numbers are still mandatory for conducting the privacy amplification procedure. In this paper, we propose a fully passive entanglement based QKD scheme in which certified random bits for privacy amplification are extracted from detection events of measurement-basis-mismatched entangled photon pairs. The privacy of these random bits can be certified by estimating the…
We present a classical protocol for simulating correlations obtained by bipartite POVMs on an EPR pair. The protocol uses shared random variables (also known as local hidden variables) augmented by six bits of expected communication.
``Beam me over,'' Alice: A cricket's quantum journey This thesis addresses two known quantities in quantum information science: (1) entanglement cost, and (2) Holevo capacity. These quantities will be crucial values when teleportation becomes common in daily life, perhaps centuries from now. Assume that Alice desires to send a singing Japanese cricket to her friend Bob in America, and that Alice and Bob already share a quantum entanglement. First, Alice sends Bob a mass of information bits resulting from the interaction between the cricket she holds in her hand and half of the entanglement. Su…
We experimentally and theoretically investigate the quantum trajectories of jointly monitored transmon qubits embedded in spatially separated microwave cavities. Using nearly quantum-noise limited superconducting amplifiers and an optimized setup to reduce signal loss between cavities, we can efficiently track measurement-induced entanglement generation as a continuous process for single realizations of the experiment. The quantum trajectories of transmon qubits naturally split into low and high entanglement classes corresponding to half-parity collapse. The distribution of concurrence is foun…
We consider a variation of the multi-party communication complexity scenario where the parties are supplied with an extra resource: particles in an entangled quantum state. We show that, although a prior quantum entanglement cannot be used to simulate a communication channel, it can reduce the communication complexity of functions in some cases. Specifically, we show that, for a particular function among three parties (each of which possesses part of the function's input), a prior quantum entanglement enables them to learn the value of the function with only three bits of communication occurri…
We report two key distribution schemes achieved by swapping quantum entanglement. Using two Bell states, two bits of secret key can be shared between two distant parties that play symmetric and equal roles. We also address eavesdropping attacks against the schemes.
The unitary group acting on the Hilbert space of three quantum bits admits a Lie subgroup, of elements which permute with the symmetric group of permutations. Under the action of such Lie subgroup, the Hilbert space splits into three invariant subspaces of dimensions 4, 2 and 2 respectively, each corresponding to an irreducible representation of su(2). The subspace of dimension 4 is uniquely determined and corresponds to states that are themselves invariant under the action of the symmetric group. This is the so called symmetric sector. We provide an analysis of pure states in the symmetric se…
We argue that several claims of paper Phys. Rev. Lett 79, 1953 (1997), by Lu-Ming Duan and Guang-Can Guo, are questionable. In particular we stress that the environmental noise considered by the authors belongs to a very special class
Quantum resources can be more powerful than classical resources - a quantum computer can solve certain problems exponentially faster than a classical computer, and computing a function of two people's inputs can be done with exponentially less communication with quantum messages than with classical ones. Here we consider a task between two players, Alice and Bob where quantum resources are infinitely more powerful than classical ones. Alice is given a string of length n, and Bob's task is to exclude certain combinations of bits that Alice might have. If Alice must send classical messages, then…
We investigate the amount of communication that must augment classical local hidden variable models in order to simulate the behaviour of entangled quantum systems. We consider the scenario where a bipartite measurement is given from a set of possibilities and the goal is to obtain exactly the same correlations that arise when the actual quantum system is measured. We show that, in the case of a single pair of qubits in a Bell state, a constant number of bits of communication is always sufficient--regardless of the number of measurements under consideration. We also show that, in the case of a…
Superdense coding uses entanglement as a resource to communicate classical information securely through quantum channels. A superdense coding method is optimal when its capacity reaches Holevo bound. We show that for optimality, maximal entanglement is a necessity across the bipartition of Alice and Bob, but neither absolute nor genuine multipartite entanglement is required. Unlike the previous schemes, which can transmit either even or odd bits of information, we have demonstrated a generalized dense coding protocol using the genuine multipartite entangled GHZ state to send arbitrary informat…
Entanglement swapping between Einstein-Podolsky-Rosen (EPR) pairs can be used to generate the same sequence of random bits in two remote places. A quantum key distribution protocol based on this idea is described. The scheme exhibits the following features. (a) It does not require that Alice and Bob choose between alternative measurements, therefore improving the rate of generated bits by transmitted qubit. (b) It allows Alice and Bob to generate a key of arbitrary length using a single quantum system (three EPR pairs), instead of a long sequence of them. (c) Detecting Eve requires the compari…
A black box with two input bits and two output bits is called a non-local PR box, if the XOR of the output bits equals the AND of the input bits. In a recent article, Cerf et al. show that Alice and Bob, using such a PR box, can effectively simulate entanglement without the need of communication. We show that an adaptation of a model due to Dirk Aerts, yields a realistic simulation of the non-local PR box without communication. Because the model is entirely realistic, it cannot violate relativistic constraints. Like a non-local box, it can be used to simulate the singlet state coincidence prob…
A new protocol for quantum key distribution based on entanglement swapping is presented. In this protocol, both certain key and random key can be generated without any loss of security. It is this property differs our protocol from the previous ones. The rate of generated key bits per particle is improved which can approach six bits (4 random bits and 2 certain bits) per four particles.
Imagine that Alice and Bob, unable to communicate, are both given a 16-bit string such that the strings are either equal, or they differ in exactly 8 positions. Both parties are then supposed to output a 4-bit string in such a way that these short strings are equal if and only if the original longer strings given to them were equal as well. It is known that this task can be fulfilled without failure and without communication if Alice and Bob share 4 maximally entangled quantum bits. We show that, on the other hand, they CANNOT win the same game with certainty if they only share classical bits,…
We present a scheme for hiding bits in Bell states that is secure even when the sharers Alice and Bob are allowed to carry out local quantum operations and classical communication. We prove that the information that Alice and Bob can gain about a hidden bit is exponentially small in $n$, the number of qubits in each share, and can be made arbitrarily small for hiding multiple bits. We indicate an alternative efficient low-entanglement method for preparing the shared quantum states. We discuss how our scheme can be implemented using present-day quantum optics.
We find a protocol transmitting two quantum states crossly in the butterfly network only with prior entanglement between two senders. This protocol requires only one qubit transmission or two classical bits transmission in each channel in the butterfly network. It is also proved that it is impossible without prior entanglement. More precisely, an upper bound of average fidelity is given in the butterfly network when prior entanglement is not allowed.
We show how shared entanglement, together with classical communication and local quantum operations, can be used to perform an arbitrary collective quantum operation upon N spatially-separated qubits. A simple teleportation-based protocol for achieving this, which requires 2(N-1) ebits of shared, bipartite entanglement and 4(N-1) classical bits, is proposed. In terms of the total required entanglement, this protocol is shown to be optimal for even N in both the asymptotic limit and for `one-shot' applications.
An (n,m,p) Random Access Code (RAC) allows to encode n bits in an m bit message, in such a way that a receiver of the message can guess any of the original $n$ bits with probability p, greater than 1/2. In Quantum RAC's (QRACs) one transmits n qubits. The full set of primitive Entanglement Assisted Random Access Codes (EARACs) is introduced, in which parties are allowed to share a two-qubit singlet. It is shown that via a concatenation of these, one can build for any n an (n,1,p) EARAC. QRAC's for n>3 exist only if parties additionally share classical randomness (SR). We show that EARACs outpe…
Many quantum algorithms seek to output a specific bitstring solving the problem of interest--or a few if the solution is degenerate. It is the case for the quantum approximate optimization algorithm (QAOA) in the limit of large circuit depth, which aims to solve quadratic unconstrained binary optimization problems. Hence, the expected final state for these algorithms is either a product state or a low-entangled superposition involving a few bitstrings. What happens in between the initial $N$-qubit product state $\vert 0\rangle^{\otimes N}$ and the final one regarding entanglement? Here, we con…
A key goal of quantum communication is to determine the maximum number of bits shared between two quantum systems. An important example of this is in entanglement based quantum key distribution (QKD) schemes. A realistic treatment of this general communication problem must take account of the nonideal nature of the entanglement source and the detectors. The aim of this paper is to give such a treatment. We obtain analytic expression for the mutual information in terms of experimental parameters. The results are applied to communication schemes that rely on spontaneous parametric down conversio…
A deterministic direct quantum communication protocol by using swapping quantum entanglement and local unitary operations is proposed in this paper. A set of ordered EPR pairs in one of the four Bell states is used. For each pair, each of the two legitimate users owns a photon of the entangled pair via quantum channel. The pairs are divided into two types of group, i.e., the checking groups and the encoding-decoding groups. In the checking groups, taking advantage of the swapping quantum entanglement and Alice's (the message sender's) public announcement, the eavesdropping can be detected prov…
We provide several formulas that determine the optimal number of entangled bits (ebits) that a general entanglement-assisted quantum code requires. Our first theorem gives a formula that applies to an arbitrary entanglement-assisted block code. Corollaries of this theorem give formulas that apply to a code imported from two classical binary block codes, to a code imported from a classical quaternary block code, and to a continuous-variable entanglement-assisted quantum block code. Finally, we conjecture two formulas that apply to entanglement-assisted quantum convolutional codes.
We analyse the role of entanglement for transmission of classical information through a memoryless depolarising channel. Using the isotropic character of this channel we prove analytically that the mutual information cannot be increased by encoding classical bits into entangled states of two qubits.
The selection of random subspaces plays a role in quantum information theory analogous to the role of random strings in classical information theory. Recent applications have included protocols achieving the quantum channel capacity and methods for extending superdense coding from bits to qubits. In addition, random subspaces have proved useful for studying the structure of bipartite and multipartite entanglement.
We construct generally applicable short-time perturbative expansions for some fidelities, such as the input-output fidelity, the entanglement fidelity, and the average fidelity. Successive terms of these expansions yield characteristic times for the damping of the fidelities involving successive powers of the Hamiltonian. The second-order results, which represent the damping rates of the fidelities, are extensively discussed. As an interesting application of these expansions, we use them to study the spatially-correlated dissipation of quantum bits. Spatial correlations in the dissipation are …
In quantum teleportation, the role of entanglement has been much discussed. It is known that entanglement is necessary for achieving non-classical teleportation fidelity. Here we focus on the amount of classical communication that is necessary to obtain non-classical fidelity in teleportation. We quantify the amount of classical communication that is sufficient for achieving non-classical fidelity for two independent 1-bit and single 2-bits noisy classical channels. It is shown that on average 0.208 bits of classical communication is sufficient to get non-classical fidelity. We also find the n…
The phenomenon of quantum entanglement is fundamental to the implementation of quantum computation, and requires at least two qubits for its demonstration. However, both Deutsch algorithm and Grover's search algorithm for two bits do not use entanglement. We develop a Deutsch-like problem, where we consider all possible binary functions for two bit inputs and distinguish their even or odd nature. The quantum algorithm to solve this problem requires entanglement at the level of two qubits. The final solution suggests that an NMR implementation of the problem would lead to interesting results.
A scheme is proposed for protecting quantum states from both independent decoherence and cooperative decoherence. The scheme operates by pairing each qubit (two-state quantum system) with an ancilla qubit and by encoding the states of the qubits into the corresponding coherence-preserving states of the qubit-pairs. In this scheme, the amplitude damping (loss of energy) is prevented as well as the phase damping (dephasing) by a strategy called the free-Hamiltonian-elimination We further extend the scheme to include quantum gate operations and show that loss and decoherence during the gate opera…
Quantum entanglement cannot be used to achieve direct communication between remote parties, but it can reduce the communication needed for some problems. Let each of k parties hold some partial input data to some fixed k-variable function f. The communication complexity of f is the minimum number of classical bits required to be broadcasted for every party to know the value of f on their inputs. We construct a function G such that for the one-round communication model and three parties, G can be computed with n+1 bits of communication when the parties share prior entanglement. We then show tha…
Ideal dense coding protocols allow one to use prior maximal entanglement to send two bits of classical information by the physical transfer of a single encoded qubit. We investigate the case when the prior entanglement is not maximal and the initial state of the entangled pair of qubits being used for the dense coding is a mixed state. We find upper and lower bounds on the capability to do dense coding in terms of the various measures of entanglement and in terms of the average mutual distinguishability of the signal states.
We prove a general lower bound on the bounded-error entanglement-assisted quantum communication complexity of Boolean functions. The bound is based on the concept that any classical or quantum protocol to evaluate a function on distributed inputs can be turned into a quantum communication protocol. As an application of this bound, we give a very simple proof of the statement that almost all Boolean functions on n+n bits have linear communication complexity, even in the presence of unlimited entanglement.
Entanglement is a well-known resource in quantum information, in particular it can be exploited for quantum key distribution (QKD). In this paper we define a two-way QKD scheme employing GHZ-type states of three qubits obtaining an extension of the standard E91 protocol with a significant increasing of the number of shared bits. Eavesdropping attacks can be detected measuring violation of the CHSH inequality and the secret key rate can be estimated in a device-independent scenario.
We describe the experimental implementation of a recently proposed quantum algorithm involving quantum entanglement at the level of two qubits using NMR. The algorithm solves a generalisation of the Deutsch problem and distinguishes between even and odd functions using fewer function calls than is possible classically. The manipulation of entangled states of the two qubits is essential here, unlike the Deutsch-Jozsa algorithm and the Grover's search algorithm for two bits.
Shared entanglement is a resource available to parties communicating over a quantum channel, much akin to public coins in classical communication protocols. Whereas shared randomness does not help in the transmission of information, or significantly reduce the classical complexity of computing functions (as compared to private-coin protocols), shared entanglement leads to startling phenomena such as ``quantum teleportation'' and ``superdense coding.'' The problem of characterising the power of prior entanglement has puzzled many researchers. In this paper, we revisit the problem of transmittin…
Entanglement appears under two different forms in quantum theory, namely as a property of states of joint systems and as a property of measurement eigenstates in joint measurements. By combining these two aspects of entanglement, it is possible to generate nonlocality between particles that never interacted, using the protocol of entanglement swapping. We show that even in the more constraining bilocal scenario where distant sources of particles are assumed to be independent, i.e. to share no prior randomness, this process can be simulated classically with bounded communication, using only 9 b…
Basing on the calculation of all the pairwise entanglement in the $n$ ($n \leq 6$)-qubit Heisenberg XX open chain with system impurity, we find an important result: pairwise entanglement can only be transferred through entangled pair. The non-nearest pairwise entanglement will has the possibility to exist as long as there has even number qubit in their middle. This point means that we can get longer distance entanglement in solid system.
The existence of entangled quantum states gives extra power to quantum computers over their classical counterparts. Quantum entanglement shows up qualitatively at the level of two qubits. We show that if no entanglement is envolved then whatever one can do with qubits can also be done with classical optical systems. We demonstrate that the one- and the two-bit Deutsch-Jozsa algorithm does not require entanglement and can be mapped onto a classical optical scheme. It is only for three and more input bits that the DJ algorithm requires the implementation of entangling transformations and in thes…
We propose a scheme to measure the parity of two distant qubits, while ensuring that losses on the quantum channel between them does not destroy coherences within the parity subspaces. This capability enables deterministic preparation of highly entangled qubit states whose fidelity is not limited by the transmission loss. The key observation is that for a probe electromagnetic field in a particular quantum state, namely a superposition of two coherent states of opposite phases, the transmission loss stochastically applies a near-unitary back-action on the probe state. This leads to a parity me…
We consider a Quantum Computer with n quantum-bits (`qubits'), where each qubit is coupled independently to an environment affecting the state in a dephasing or depolarizing way. For mixed states we suggest a quantification for the property of showing {\it quantum} uncertainty on the macroscopic level. We illustrate in which sense a large parameter can be seen as an indicator for large entanglement and give hypersurfaces enclosing the set of separable states. Using methods of the classical theory of maximum likelihood estimation we prove that this parameter is decreasing with 1/\sqrt{n} for al…
We demonstrate a quantum key distribution implementation over deployed dark telecom fibers with polarisation-entangled photons generated at the O-band. One of the photons in the pairs are propagated through 10km of deployed fiber while the others are detected locally. Polarisation drifts experienced by the photons propagating through the fibers are compensated with liquid crystal variable retarders. This ensures continuous and stable QKD operation with an average QBER of 6.4% and a final key rate of 109 bits/s.
An $n\overset{p}{\mapsto}m$ random access code (RAC) is an encoding of $n$ bits into $m$ bits such that any initial bit can be recovered with probability at least $p$, while in a quantum RAC (QRAC), the $n$ bits are encoded into $m$ qubits. Since its proposal, the idea of RACs was generalized in many different ways, e.g. allowing the use of shared entanglement (called entanglement-assisted random access code, or simply EARAC) or recovering multiple bits instead of one. In this paper we generalize the idea of RACs to recovering the value of a given Boolean function $f$ on any subset of fixed si…
A quantum steganography protocol with large payload is proposed, based on dense coding and entanglement swapping of GHZ states. Its super quantum channel is formed by building up the hidden channel within the original quantum secure direct communication (QSDC) scheme. Based on the original QSDC, secrets messages are transmitted by integrating dense coding of GHZ states and entanglement swapping of GHZ states. Its capacity of super quantum channel achieves six bits per round covert communication, much higher than the previous quantum steganography protocols. Its imperceptibility is good, since …
We investigate the entanglement properties of pure quantum states describing $n$ qubits. We characterize all multipartite states which can be maximally entangled to local auxiliary systems using controlled operations. A state has this property iff one can construct out of it an orthonormal basis by applying independent local unitary operations. This implies that those states can be used to encode locally the maximum amount of $n$ bits. Examples of these states are the so--called stabilizer states, which are used for quantum error correction and one--way quantum computing. We give a simple char…
