Howard Mark Wiseman

Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox

The concept of steering was introduced by Schrödinger in 1935 as a generalization of the Einstein-Podolsky-Rosen paradox for arbitrary pure bipartite entangled states and arbitrary measurements by one party. Until now, it has never been rigorously defined, so it has not been known (for example) what mixed states are steerable (that is, can be used to exhibit steering). We provide an operational definition, from which we prove (by considering Werner states and isotropic states) that steerable states are a strict subset of the entangled states, and a strict superset of the states that can exhibit Bell nonlocality. For arbitrary bipartite Gaussian states we derive a linear matrix inequality that decides the question of steerability via Gaussian measurements, and we relate this to the original Einstein-Podolsky-Rosen paradox.

Entanglement-free Heisenberg-limited phase estimation

Measurement underpins all quantitative science. A key example is the measurement of optical phase, used in length metrology and many other applications. Advances in precision measurement have consistently led to important scientific discoveries. At the fundamental level, measurement precision is limited by the number N of quantum resources (such as photons) that are used. Standard measurement schemes, using each resource independently, lead to a phase uncertainty that scales as 1/—known as the standard quantum limit. However, it has long been conjectured that it should be possible to achieve a precision limited only by the Heisenberg uncertainty principle, dramatically improving the scaling to 1/N (ref. 3). It is commonly thought that achieving this improvement requires the use of exotic quantum entangled states, such as the NOON state. These states are extremely difficult to generate. Measurement schemes with counted photons or ions have been performed with N ≤ 6 (refs 6–15), but few have surpassed the standard quantum limit and none have shown Heisenberg-limited scaling. Here we demonstrate experimentally a Heisenberg-limited phase estimation procedure. We replace entangled input states with multiple applications of the phase shift on unentangled single-photon states. We generalize Kitaev’s phase estimation algorithm using adaptive measurement theory to achieve a standard deviation scaling at the Heisenberg limit. For the largest number of resources used (N = 378), we estimate an unknown phase with a variance more than 10 dB below the standard quantum limit; achieving this variance would require more than 4,000 resources using standard interferometry. Our results represent a drastic reduction in the complexity of achieving quantum-enhanced measurement precision.

One-sided device-independent quantum key distribution: Security, feasibility, and the connection with steering

We analyze the security and feasibility of a protocol for quantum key distribution (QKD) in a context where only one of the two parties trusts his measurement apparatus. This scenario lies naturally between standard QKD, where both parties trust their measurement apparatuses, and device-independent QKD (DI-QKD), where neither do, and can be a natural assumption in some practical situations. We show that the requirements for obtaining secure keys are much easier to meet than for DI-QKD, which opens promising experimental opportunities. We clarify the link between the security of this one-sided DI-QKD scenario and the demonstration of quantum steering, in analogy to the link between DI-QKD and the violation of Bell inequalities.

Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox

We formally link the concept of steering (a concept created by Schrodinger but only recently formalized by Wiseman, Jones and Doherty Phys. Rev. Lett. 98 140402 (2007)]) and the criteria for demonstrations of Einstein-Podolsky-Rosen (EPR) paradox introduced by Reid Phys. Rev. A 40 913 (1989)]. We develop a general theory of experimental EPR-steering criteria, derive a number of criteria applicable to discrete as well as continuous-variable observables, and study their efficacy in detecting that form of nonlocality in some classes of quantum states. We show that previous versions of EPR-type criteria can be rederived within this formalism, thus unifying these efforts from a modern quantum-information perspective and clarifying their conceptual and formal origin. The theory follows in close analogy with criteria for other forms of quantum nonlocality (Bell nonlocality and entanglement), and because it is a hybrid of those two, it may lead to insights into the relationship between the different forms of nonlocality and the criteria that are able to detect them.

Experimental EPR-steering using Bell-local states

Erwin Schrodinger introduced in 1935 the concept of ‘steering’, which generalizes the famed Einstein–Podolsky–Rosen paradox. Steering sits in between quantum entanglement and non-locality — that is, entanglement is necessary for steering, but steering can be achieved, as has now been demonstrated experimentally, with states that cannot violate a Bell inequality (and therefore non-locality).

Measurement of Quantum Weak Values of Photon Polarization

We experimentally determine weak values for a single photon’s polarization, obtained via a weak measurement that employs a two-photon entangling operation, and postselection. The weak values cannot be explained by a semiclassical wave theory, due to the two-photon entanglement. We observe the variation in the size of the weak value with measurement strength, obtaining an average measurement of the S1 Stokes parameter more than an order of magnitude outside of the operator’s spectrum for the smallest measurement strengths.

Loophole-free Einstein-Podolsky-Rosen experiment via quantum steering

Tests of the predictions of quantum mechanics for entangled systems have provided increasing evidence against local realistic theories. However, there remains the crucial challenge of simultaneously closing all major loopholes—the locality, freedom-of-choice and detection loopholes—in a single experiment. An important sub-class of local realistic theories can be tested with the concept of ‘steering’. The term ‘steering’ was introduced by Schrodinger in 1935 for the fact that entanglement would seem to allow an experimenter to remotely steer the state of a distant system as in the Einstein–Podolsky–Rosen (EPR) argument. Einstein called this ‘spooky action at a distance’. EPR-steering has recently been rigorously formulated as a quantum information task opening it up to new experimental tests. Here, we present the first loophole-free demonstration of EPR-steering by violating three-setting quadratic steering inequality, tested with polarization-entangled photons shared between two distant laboratories. Our experiment demonstrates this effect while simultaneously closing all loopholes: both the locality loophole and a specific form of the freedom-of-choice loophole are closed by having a large separation of the parties and using fast quantum random number generators, and the fair-sampling loophole is closed by having high overall detection efficiency. Thereby, we exclude—for the first time loophole-free—an important class of local realistic theories considered by EPR. Besides its foundational importance, loophole-free steering also allows the distribution of quantum entanglement secure event in the presence of an untrusted party.

All-optical versus electro-optical quantum-limited feedback.

All-optical feedback can be effected by putting the output of a source cavity through a Faraday isolator and into a second cavity which is coupled to the source cavity by a nonlinear crystal. If the driven cavity is heavily damped, then it can be adiabatically eliminated and a master equation or quantum Langevin equation derived for the first cavity alone. This is done for an input bath in an arbitrary state, and for an arbitrary nonlinear coupling. If the intercavity coupling involves only the intensity (or one quadrature) of the driven cavity, then the effect on the source cavity is identical to that which can be obtained from electro-optical feedback using direct (or homodyne) detection. If the coupling involves both quadratures, this equivalence no longer holds and a coupling linear in the source amplitude can produce a nonclassical state in the source cavity. The analogous electro-optic scheme using heterodyne detection introduces extra noise which prevents the production of nonclassical light. Unlike the electro-optical case, the all-optical feedback loop has an output beam (reflected from the second cavity). We show that this may be squeezed, even if the source cavity remains in a classical state.

The entanglement of indistinguishable particles shared between two parties

Using an operational definition we quantify the entanglement, E(P), between two parties who share an arbitrary pure state of N indistinguishable particles. We show that E(P)< or =E(M), where E(M) is the bipartite entanglement calculated from the mode-occupation representation. Unlike E(M), E(P) is superadditive. For example, E(P)=0 for any single-particle state, but the state |1>|1>, where both modes are split between the two parties, has E(P)=1/2. We discuss how this relates to quantum correlations between particles, for both fermions and bosons.

Entanglement-enhanced measurement of a completely unknown optical phase

We demonstrate a method for achieving phase measurements with accuracy beyond the standard quantum limit using entangled states. A sophisticated feedback scheme means that no initial estimate of the phase is required.