The role of the timing and order of quantum measurements is not just a fundamental question of quantum mechanics, but also a puzzling one. Any part of a quantum system that has finished evolving, can be measured immediately or saved for later, without affecting the final results, regardless of the continued evolution of the rest of the system. In addition, the non-locality of quantum mechanics, as manifested by entanglement, does not apply only to particles with spatial separation, but also with temporal separation. Here we demonstrate these principles by generating and fully characterizing an entangled pair of photons that never coexisted. Using entanglement swapping between two temporally separated photon pairs we entangle one photon from the first pair with another photon from the second pair. The first photon was detected even before the other was created. The observed quantum correlations manifest the non-locality of quantum mechanics in spacetime.
In this paper we discuss four different proposals of entangling atomic states of particles which have never interacted. The experimental realization proposed makes use of the interaction of Rydberg atoms with a micromaser cavity prepared in either a coherent state or in a superposition of the zero and one field Fock states. We consider atoms in either a three-level cascade or lambda configuration
Quantum optics and classical optics have coexisted for nearly a century as two distinct, self-consistent descriptions of light. What influences there were between the two domains all tended to go in one direction, as concepts from classical optics were incorporated into quantum theory's early development. But it's becoming increasingly clear that a significant quantum presence exists in classical territory-and, in particular, that the quintessential quantum attribute, entanglement, can be seen, studied and exploited in classical optics. This blurring of the classical-quantum boundary has opene…
We show that no entanglement is necessary to distribute entanglement; that is, two distant particles can be entangled by sending a third particle that is never entangled with the other two. Similarly, two particles can become entangled by continuous interaction with a highly mixed mediating particle that never itself becomes entangled. We also consider analogous properties of completely positive maps, in which the composition of two separable maps can create entanglement.
Quantum systems that have never interacted can become nonlocally correlated through a process called entanglement swapping. To characterize nonlocality in this context, we introduce local models where quantum systems that are initially uncorrelated are described by uncorrelated local variables. While a pair of maximally entangled qubits prepared in the usual way (i.e., emitted from a common source) requires a visibility close to 70% to violate a Bell inequality, we show that an entangled pair generated through entanglement swapping will already violate a Bell inequality for visibilities as low…
Simple examples are constructed that show the entanglement of two qubits being both increased and decreased by interactions on just one of them. One of the two qubits interacts with a third qubit, a control, that is never entangled or correlated with either of the two entangled qubits and is never entangled, but becomes correlated, with the system of those two qubits. The two entangled qubits do not interact, but their state can change from maximally entangled to separable or from separable to maximally entangled. Similar changes for the two qubits are made with a swap operation between one of…
Bound entanglement is the noisy entanglement which cannot be distilled to a singlet form. Thus it cannot be used alone for quantum communication purposes. Here we show that, nevertheless, the bound entanglement can be, in a sense, pumped into single pair of free entangled particles. It allows for teleportation via the pair with the fidelity impossible to achieve without support of bound entanglement. The result also suggests that the distillable entanglement may be not additive.
We study continuous-variable entanglement of bright quantum states in a pair of evanescently coupled nonlinear $χ^{(2)}$ waveguides operating in the regime of degenerate down-conversion. We consider the case where only the energy of the nonlinearly generated fields is exchanged between the waveguides while the pump fields stay independently guided in each original waveguide. We show that this device, when operated in the depletion regime, entangles the two non-interacting bright pump modes due to a nonlinear cascade effect. It is also shown that two-colour quadripartite entanglement can be pro…
We investigate the entanglement properties of a finite size 1+1 dimensional Ising spin chain, and show how these properties scale and can be utilized to reconstruct the ground state wave function. Even at the critical point, few terms in a Schmidt decomposition contribute to the exact ground state, and to physical properties such as the entropy. Nevertheless the entanglement here is prominent due to the lower-lying states in the Schmidt decomposition.
It is shown how the evidence state space in quantum bit commitment may be made to depend on the bit value 0 or 1 with split entangled pairs. As a consequence, one can obtain a protocol that is perfectly concealing, but is also $ε$-binding because the bit-value dependent evidence space prevents the committing party from cheating by means of a local transformation that is independent of the part of evidence state space that has never been in his possession.
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.
While single boson entanglement is known to be equivalent to standard non-identical particle entanglement, the use of fermionic entanglement is constrained by a parity superselection rule. Nevertheless we show that within the framework of second quantization, where local modes play the role of qubits, the analogy with ordinary entanglement holds: two entangled spinless fermion modes can be used to teleport a single local fermion mode and to perform standard dense coding. Entanglement concentration and dilution are possible for fermions. We clarify the meaning of our results by discussing the c…
Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. In particular we will focus our attention to composite quantum systems composed of identical constituents, with the purpose of dealing with subtle issues, which have never been adequately discussed in the literature, originating from the true indistinguishability of the subsystems involved.
A strong entanglement monotone, which never increases under local operations and classical communications (LOCC), restricts quantum entanglement manipulation more strongly than the usual monotone since the usual one does not increase on average under LOCC. We propose new strong monotones in mixed-state entanglement manipulation under LOCC. These are related to the decomposability and 1-positivity of an operator constructed from a quantum state, and reveal geometrical characteristics of entangled states. These are lower bounded by the negativity or generalized robustness of entanglement.
We use Nuclear Magnetic Resonance (NMR) to experimentally generate a bound entangled (more precisely: pseudo bound entangled) state, i.e. a quantum state which is non-distillable but nevertheless entangled. Our quantum system consists of three qubits. We characterize the produced state via state tomography to show that the created state has a positive partial transposition with respect to any bipartite splitting, and we use a witness operator to prove its entanglement.
Based on a scheme that produces an entanglement between the spin and the path variables of a single spin-1/2 particle (qubit) using a beam-splitter and a spin-flipper, we formulate a procedure for transferring this intraparticle hybrid entanglement to an interparticle entanglement between the spin variables of two other spatially separated spin-1/2 particles which never interact with each other during the entire process. This procedure of entanglement swapping is accomplished by a Mach-Zehnder setup in conjunction with the Stern-Gerlach measuring device, using suitable unitary operations. The …
We propose a curious protocol for swapping the intra-photon entanglement between path and polarization degrees of freedom of a single photon to inter-photon entanglement between two spatially separated photons which have never interacted. This is accomplished by using an experimental setup consisting of three suitable Mach-Zehnder interferometers along with number of beam splitters, polarization rotators and detectors. Using the same setup, we have also demonstrated an interesting quantum state transfer protocol, symmetric between Alice and Bob. Importantly, the Bell-basis discrimination is no…
Entanglement is the central resource of quantum information processing and the precise characterization of entangled states is a crucial issue for the development of quantum technologies. This leads to the necessity of a precise, experimental feasible measure of entanglement. Nevertheless, such measurements are limited both from experimental uncertainties and intrinsic quantum bounds. Here we present an experiment where the amount of entanglement of a family of two-qubit mixed photon states is estimated with the ultimate precision allowed by quantum mechanics.
We show that there is a stronger form of bipartite quantum nonlocality in which systems that never interacted are as nonlocal as allowed by no-signaling. For this purpose, we first show that nonlocal boxes, theoretical objects that violate a bipartite Bell inequality as much as the no-signaling principle allows and which are physically impossible for most scenarios, are feasible if the two parties have 3 measurements with 4 outputs. Then we show that, in this case, entanglement swapping allows us to prepare mixtures of nonlocal boxes using systems that never interacted.
A major obstacle in the way of practical quantum computing is achieving scalable and robust high-fidelity entangling gates. To this end, quantum control has become an essential tool, as it can make the entangling interaction resilient to sources of noise. Nevertheless, it may be difficult to identify an appropriate quantum control technique for a particular need given the breadth of work pertaining to robust entanglement. To this end, we attempt to consolidate the literature by providing a non-exhaustive summary and critical analysis. The quantum control methods are separated into two categori…
Entanglement and nonlocality are both fundamental aspects of quantum theory, and play a prominent role in quantum information science. The exact relation between entanglement and nonlocality is however still poorly understood. Here we make progress in this direction by showing that, contrary to what previous work suggested, quantum nonlocality does not imply entanglement distillability. Specifically, we present analytically a 3-qubit entangled state that is separable along any bipartition. This implies that no bipartite entanglement can be distilled from this state, which is thus fully bound e…
The usual entanglement swapping protocol can entangle two particles that never interact. Here we demonstrate an all-versus-nothing violation of local realism for a partial entanglement swapping process. A Clauser-Horne-Shimony-Holt-type inequality for two particles entangled by entanglement swapping is proposed for a practical experiment and can be violated quantum mechanically up to 4 beyond Cirel'son's bound 2sqr(2). Our result uncovers the intriguing nonlocal character of entanglement swapping and may lead to a conclusive (loophole-free) test of local realism versus quantum mechanics. The e…
Entanglement distribution with separable states has recently attracted considerable attention. Recent results suggest that quantum discord - a measure for quantum correlations beyond entanglement - is responsible for this counterintuitive phenomenon. In this work we study this question from a different perspective, and find minimal requirements for a separable state to be useful for entanglement distribution. Surprisingly, we find that the presence of quantum discord is not sufficient to ensure entanglement distribution: there exist states with nonzero quantum discord which nevertheless cannot…
A complete treatment of the entanglement of two-level systems, which evolves through the contact with a thermal bath, must include the fact that the system and the bath are not fully separable. Therefore, quantum coherent superpositions of system and bath states, which are almost never fully included in theoretical models, are invariably present when an entangled state is prepared experimentally. We show their importance for the time evolution of the entanglement of two qubits coupled to independent baths. In addition, our treatment is able to handle slow and low-temperature thermal baths.
Quantum teleportation strikingly underlines the peculiar features of the quantum world. We present an experimental proof of its quantum nature, teleporting an entangled photon with such high quality that the nonlocal quantum correlations with its original partner photon are preserved. This procedure is also known as entanglement swapping. The nonlocality is confirmed by observing a violation of Bell's inequality by 4.5 standard deviations. Thus, by demonstrating quantum nonlocality for photons that never interacted our results directly confirm the quantum nature of teleportation.
We present a protocol for performing entanglement connection between pairs of atomic ensembles in the single excitation regime. Two pairs are prepared in an asynchronous fashion and then connected via a Bell measurement. The resulting state of the two remaining ensembles is mapped to photonic modes and a reduced density matrix is then reconstructed. Our observations confirm for the first time the creation of coherence between atomic systems that never interacted, a first step towards entanglement connection, a critical requirement for quantum networking and long distance quantum communications…
The notion of entanglement fidelity is to measure entanglement preservation through quantum channels. Nevertheless, the amount of entanglement present in a state of a quantum system at any time is measured by quantities known as measures of entanglement. Since there are different types of measures of entanglement, one may expect an entanglement fidelity to associate with its own measure of entanglement counterpart. Here, we aim to investigate association between the so called entanglement fidelity and some measures of entanglement, namely, entanglement of formation, concurrence and negativity.…
Quantum steering, loosely speaking the distribution of entanglement from an untrusted party, is a form of quantum nonlocality which is intermediate between entanglement and Bell nonlocality. Determining which states can be steered is important from a conceptual point of view, but also for applications, e.g. in quantum cryptography. Here we show that bound entanglement, although it represents the weakest form of entanglement, can nevertheless lead to quantum steering. This is done by noticing that steering inequalities can be derived from entropic uncertainty relations. Our result has implicati…
The question whether global entanglement of a multiparticle quantum system can be inferred from local properties is of great relevance for the theory of quantum correlations as well as for experimental implementations. We present a method to systematically find quantum states, for which the two- or three-body marginals do not contain any entanglement, nevertheless, the knowledge of these reduced states is sufficient to prove genuine multiparticle entanglement of the global state. With this, we show that the emergence of global entanglement from separable local quantum states occurs frequently …
Entanglement swapping allows to establish entanglement between independent particles that never interacted nor share any common past. This feature makes it an integral constituent of quantum repeaters. Here, we demonstrate entanglement swapping with time-synchronized independent sources with a fidelity high enough to violate a Clauser-Horne-Shimony-Holt inequality by more than four standard deviations. The fact that both entangled pairs are created by fully independent, only electronically connected sources ensures that this technique is suitable for future long-distance quantum communication …
Entanglement is a unique nature of quantum theory and has tremendous potential for application. Nevertheless, the complexity of quantum entanglement grows exponentially with an increase in the number of entangled particles. Here we introduce a quantum state concentration scheme which decomposes the multipartite entangled state into a set of bipartite and tripartite entangled states. It is shown that the complexity of the entanglement induced by the large number of particles is transformed into the high dimensions of bipartite and tripartite entangled states for pure quantum systems. The result…
We introduce a scheme for remote entanglement generation for the photon polarization. The technique is based on transferring the initial frequency correlations to specific polarization-frequency correlations by local dephasing and their subsequent removal by frequency up-conversion. On fundamental level, our theoretical results show how to create and transfer entanglement, to particles which never interact, by means of local operations. This possibility stems from the multi-path interference and its control in frequency space. For applications, the developed techniques and results allow for th…
We propose a new training algorithm for supervised quantum classifiers. Here, we have harnessed the property of quantum entanglement to build a model that can simultaneously manipulate multiple training samples along with their labels. Subsequently a Bell-inequality based cost function is constructed, that can encode errors from multiple samples, simultaneously, in a way that is not possible by any classical means. We show that upon minimizing this cost function one can achieve successful classification in benchmark datasets. The results presented in this paper are for binary classification pr…
Recently M. Horodecki, P. Horodecki and R. Horodecki have introduced a set of density matrices of two spin-1 particles from which it is not possible to distill any maximally entangled states, even though the density matrices are entangled. Thus these density matrices do not allow reliable teleportation. However it might nevertheless be the case that these states can be used for teleportation, not reliably, but still with fidelity greater than that which may be achieved with a classical scheme. We show that, at least for some of these density matrices, teleportation cannot be achieved with bett…
Bohr's complementarity and Schrödinger's entanglement are two prominent physical characters of quantum systems. In this letter, we formally connect them. It is known that complementarity relations for wave-particle duality are saturated only for pure, single-quanton, quantum states. For mixed states, the wave-particle quantifiers never saturate a complementarity relation and can even reach zero for a maximally mixed state. To fully characterize a quanton, it is not enough to consider its wave-particle aspect; we have also to regard its quantum correlations with other systems. Here we prove tha…
A thermal field, which frequently appears in problems of decoherence, provides us with minimal information about the field. We study the interaction of the thermal field and a quantum system composed of two qubits and find that such a chaotic field with minimal information can nevertheless entangle the qubits which are prepared initially in a separable state. This simple model of a quantum register interacting with a noisy environment allows us to understand how memory of the environment affects the state of a quantum register.
In an entanglement swapping process two initially uncorrelated qubits become entangled, without any direct interaction. We present a model using local variables aiming at reproducing this remarkable process, under the realistic assumption of finite detection efficiencies. The model assumes that the local variables describing the two qubits are initially completely uncorrelated. Nevertheless, we show that once conditioned on the Bell measurement result, the local variables bear enough correlation to simulate quantum measurement results with correlation very close to the quantum prediction. When…
We report the first experimental realization of entanglement swapping over large distances in optical fibers. Two photons separated by more than two km of optical fibers are entangled, although they never directly interacted. We use two pairs of time-bin entangled qubits created in spatially separated sources and carried by photons at telecommunication wavelengths. A partial Bell state measurement is performed with one photon from each pair which projects the two remaining photons, formerly independent onto an entangled state. A visibility high enough to violate a Bell inequality is reported, …
Entanglement verification and measurement is essential for experimental tests of quantum mechanics and also for quantum communication and information science. Standard methods of verifying entanglement in a bipartite mixed state require detection of both particles and involve coincidence measurement. We present a method that enables us to verify and measure entanglement in a two-photon mixed state without detecting one of the photons, i.e., without performing any coincidence measurement or postselection. We consider two identical sources, each of which can generate the same two-photon mixed st…
We present a protocol for performing entanglement swapping with intense pulsed beams. In a first step, the generation of amplitude correlations between two systems that have never interacted directly is demonstrated. This is verified in direct detection with electronic modulation of the detected photocurrents. The measured correlations are better than expected from a classical reconstruction scheme. In the entanglement swapping process, a four--partite entangled state is generated. We prove experimentally that the amplitudes of the four optical modes are quantum correlated 3 dB below shot nois…
For any quantum algorithm operating on pure states we prove that the presence of multi-partite entanglement, with a number of parties that increases unboundedly with input size, is necessary if the quantum algorithm is to offer an exponential speed-up over classical computation. Furthermore we prove that the algorithm can be classically efficiently simulated to within a prescribed tolerance ηeven if a suitably small amount of global entanglement (depending on η) is present. We explicitly identify the occurrence of increasing multi-partite entanglement in Shor's algorithm. Our results do not ap…
Entanglement swapping, the process to entangle two particles without coupling them in any way, is one of the most striking manifestations of the quantum-mechanical nonlocal characteristic. Besides fundamental interest, this process has applications in complex entanglement manipulation and quantum communication. Here we report a high-fidelity, unconditional entanglement swapping experiment in a superconducting circuit. The measured concurrence characterizing the qubit-qubit entanglement produced by swapping is above 0.75, confirming most of the entanglement of one qubit with its partner is dete…
We investigate the dynamics of entanglement and nonlocality for multipartite quantum systems under collective dephasing. Using an exact and computable measure for genuine entanglement, we demonstrate the possibility of a non trivial phenomenon of time-invariant entanglement for multipartite quantum systems. We find that for four qubits, there exist quantum states, which are changing continously nevertheless their genuine entanglement remains constant. Based on our numerical results, we conjecture that there is no evidence of time-invariant entanglement for quantum states of three qubits. We po…
Gilbert proposed an algorithm for bounding the distance between a given point and a convex set. In this article we apply the Gilbert's algorithm to get an upper bound on the Hilbert-Schmidt distance between a given state and the set of separable states. While Hilbert Schmidt Distance does not form a proper entanglement measure, it can nevertheless be useful for witnessing entanglement. We provide here a few methods based on the Gilbert's algorithm that can reliably qualify a given state as strongly entangled or practically separable, while being computationally efficient. The method also outpu…
Quantum mechanics predicts microscopic phenomena with undeniable success. Nevertheless, current theoretical and experimental efforts still do not yield conclusive evidence that there is, or not, a fundamental limitation on the possibility to observe quantum phenomena at the macroscopic scale. This question prompted several experimental efforts producing quantum superpositions of large quantum states in light or matter. Here we report on the observation of entanglement between a single photon and an atomic ensemble. The certified entanglement stems from a light-matter micro-macro entangled stat…
According to the Gottesman-Knill theorem, any quantum algorithm utilising operations chosen exclusively from a particular restricted set are efficiently simulable by a classical computer. Since some of these algorithms involve entangled states, it is commonly concluded that entanglement is insufficient to enable quantum speedup. As I explain, however, the operations belonging to this set are precisely those which will never yield a violation of the Bell inequalities. Thus it should be no surprise that entangled quantum states which only undergo operations in this set are efficiently simulable …
Holonomic phases---geometric and topological---have long been an intriguing aspect of physics. They are ubiquitous, ranging from observations in particle physics to applications in fault tolerant quantum computing. However, their exploration in particles sharing genuine quantum correlations lack in observations. Here we experimentally demonstrate the holonomic phase of two entangled-photons evolving locally, which nevertheless gives rise to an entanglement-dependent phase. We observe its transition from geometric to topological as the entanglement between the particles is tuned from zero to ma…
Quantum entanglement plays a central role in many areas of physics, from quantum information science to many-body systems. In order to grasp the essence of this phenomenon, it is fundamental to understand how different manifestations of entanglement relate to each other. In 1999, Peres conjectured that Bell nonlocality is equivalent to distillability of entanglement. The intuition of Peres was that the non-classicality of an entangled state, as witnessed via Bell inequality violation, implies that pure entanglement can be distilled from this state, hence making it useful for most quantum infor…
We study the full entanglement dynamics of two uniformly accelerated Unruh-DeWitt detectors with no direct interaction in between but each coupled to a common quantum field and moving back-to-back in the field vacuum. For two detectors initially prepared in a separable state our exact results show that quantum entanglement between the detectors can be created by the quantum field under some specific circumstances, though each detector never enters the other's light cone in this setup. In the weak coupling limit, this entanglement creation can occur only if the initial moment is placed early en…
We experimentally demonstrate a non-local generation of entanglement from two independent photonic sources in an ancilla-free process . Two bosons (photons) are entangled in polarization space by steering into a novel interferometer setup, in which they have never meet each other. The entangled photons are delivered to polarization analyzers in different sites, respectively, and a non-local interaction is observed. Entanglement is further verified by the way of the measured violation of a CHSH type Bell's inequality with S-values of 2.54 and 27 standard deviations. Our results will shine a new…
In this paper we illuminate the relation between entanglement and secrecy by providing the first example of a quantum state that is highly entangled, but from which, nevertheless, almost no secrecy can be extracted. More precisely, we provide two bounds on the bipartite entanglement of the totally antisymmetric state in dimension d x d. First, we show that the amount of secrecy that can be extracted from the state is low, to be precise it is bounded by O(1/d). Second, we show that the state is highly entangled in the sense that we need a large amount of singlets to create the state: entangleme…
Two observers (Alice and Bob) independently prepare two sets of singlets. They test one particle of each singlet along an arbitrarily chosen direction and send the other particle to a third observer, Eve. At a later time, Eve performs joint tests on pairs of particles (one from Alice and one from Bob). According to Eve's choice of test and to her results, Alice and Bob can sort into subsets the samples that they have already tested, and they can verify that each subset behaves as if it consisted of entangled pairs of distant particles, that have never communicated in the past, even indirectly …
We prove that a beam splitter, one of the most common optical components, fulfills several classes of majorization relations, which govern the amount of quantum entanglement that it can generate. First, we show that the state resulting from k photons impinging on a beam splitter majorizes the corresponding state with any larger photon number k'>k, implying that the entanglement monotonically grows with k. Then, we examine parametric infinitesimal majorization relations as a function of the beam-splitter transmittance, and find that there exists a parameter region where majorization is again fu…
Multipartite entanglement has been widely regarded as key resources in distributed quantum computing, for instance, multi-party cryptography, measurement based quantum computing, quantum algorithms. It also plays a fundamental role in quantum phase transitions, even responsible for transport efficiency in biological systems. Certifying multipartite entanglement is generally a fundamental task. Since an $N$ qubit state is parameterized by $4^N-1$ real numbers, one is interested to design a measurement setup that reveals multipartite entanglement with as little effort as possible, at least witho…
