We discuss the communication complexity of establishing a shared reference frame, in particular examining the case of aligning spatial axes via the exchange of spin-1/2 particles. Unlike previous work we allow for multiple rounds of communication, and we give several simple examples demonstrating that nontrivial tradeoffs between the number of rounds and the type of communication required exist. We then give an explicit protocol for aligning spatial axes via the exchange of spin-1/2 particles which makes no use of either exchanged entangled states or of joint measurements. Rather it works by performing a simple type of distributed quantum computation. To facilitate comparison with previous work, we show that this protocol achieves a worst case fidelity for the much studied problem of "direction finding" that is asymptotically equivalent (up to polylog factors) to the optimal average case fidelity achievable via a single forward communication of entangled states.
We show that communication without a shared reference frame is possible using entangled states. Both classical and quantum information can be communicated with perfect fidelity without a shared reference frame at a rate that asymptotically approaches one classical bit or one encoded qubit per transmitted qubit. We present an optical scheme to communicate classical bits without a shared reference frame using entangled photon pairs and linear optical Bell state measurements.
We show that a Shared Singlet State (SSS) can supersede a Shared Reference Frame (SRF) in certain quantum communication tasks, i.e. tasks in which two remote players are required to estimate certain parameters of a two particle state sent to them. This shows that task specific value of resources maybe some what different from their common values based on their exchange possibilities.
We show that private shared reference frames can be used to perform private quantum and private classical communication over a public quantum channel. Such frames constitute a novel type of private shared correlation (distinct from private classical keys or shared entanglement) useful for cryptography. We present optimally efficient schemes for private quantum and classical communication given a finite number of qubits transmitted over an insecure channel and given a private shared Cartesian frame and/or a private shared reference ordering of the qubits. We show that in this context, it is use…
In a recent Letter [G. Chiribella et al., Phys. Rev. Lett. 98, 120501 (2007)], four protocols were proposed to secretly transmit a reference frame. Here We point out that in these protocols an eavesdropper can change the transmitted reference frame without being detected, which means the consistency of the shared reference frames should be reexamined. The way to check the above consistency is discussed. It is shown that this problem is quite different from that in previous protocols of quantum cryptography.
Any quantum communication task requires a common reference frame (i.e. phase, coordinate system). In particular, Quantum Key Distribution requires different bases for preparation and measurements of states which are obviously based on the existence of a common frame of reference. Here we show how QKD can be achieved in the absence of any common frame of reference. We study the coordinate reference frame, where the two parties do not even share a single direction, but the method can be generalized to other general frames of reference, pertaining to other groups of transformations.
Multipartite entanglement constitutes one of the key resources in quantum information processing. We exploit correlation tensor norms to develop a framework for its experimental detection without the need for shared frames of reference. By bounding these norms for partially separable states and states of limited dimension we achieve an extensive characterization of entanglement in multipartite systems in an experimentally feasible way. Furthermore we show that both bi- and multipartite dimensionality of entanglement can be revealed by our methods.
The question of testing the nonlocality of a single photon has raised much debate over the last years. The controversy is intimately related to the issue of providing a common reference frame for the observers to perform their local measurements. Here we address this point by presenting a simple scheme for demonstrating the nonlocality of a single photon which does not require a shared reference frame. Specifically, Bell inequality violation can be obtained with certainty with unaligned devices, even if the relative frame fluctuates between each experimental run of the Bell test. Our scheme ap…
We present an experimental realization of a robust quantum communication scheme [Phys. Rev. Lett. 93, 220501 (2004)] using pairs of photons entangled in polarization and time. Our method overcomes errors due to collective rotation of the polarization modes (e.g., birefringence in optical fiber or misalignment), is insensitive to the phase's fluctuation of the interferometer, and does not require any shared reference frame including time reference, except the need to label different photons. The practical robustness of the scheme is further shown by implementing a variation of the Bennett-Brass…
Non-classical correlations arising in complex quantum networks are attracting growing interest, both from a fundamental perspective and for potential applications in information processing. In particular, in an entanglement swapping scenario a new kind of correlations arise, the so-called nonbilocal correlations that are incompatible with local realism augmented with the assumption that the sources of states used in the experiment are independent. In practice, however, bilocality tests impose strict constraints on the experimental setup and in particular to presence of shared reference frames …
We present a new scheme for teleporting a quantum state between two parties whose local reference frames are misaligned by the action of a finite symmetry group. Unlike other proposals, our scheme requires the same amount of classical communication and entangled resources as conventional teleportation, does not reveal any reference frame information, and is robust against changes in reference frame alignment while the protocol is underway. The mathematical foundation of our scheme is a unitary error basis which is permuted up to a phase by the conjugation action of the group. We completely cla…
Alice wants to convey the value of a parameter to Bob with whom she does not share a reference frame. What physical object can she use for this task? Shall she encode this value into the angle between two physical vectors such as the angle between two spins? Can she benefit from using entanglement? We approach these questions here and show that an entangled state of two qubits has three parameters that are invariant under changes of the reference frame. We also calculate the average information gain, when each one of these parameters is used for communication. We compare our result with the sp…
We show that sharing a quantum reference frame requires sharing measurement operators that identify the reference frame in addition to operators that measure its state. Observers restricted to finite resources cannot, in general, operationally determine that they share such operators. Uncertainty about whether system-identification operators are shared induces decoherence.
We generalize a quantum communication protocol introduced by Bartlett et al. [New. J. Phys. 11, 063013 (2009)] in which two parties communicating do not share a classical reference frame, to the case where changes of their reference frames form a one-dimensional noncompact Lie group. Alice sends to Bob the state $ρ_R \otimes ρ_S$, where $ρ_S$ is the state of the system Alice wishes to communicate and $ρ_R$ is the state of an ancillary system serving as a token of her reference frame. Because Bob is ignorant of the relationship between his reference frame and Alice's, he will describe the state…
We show how to reliably encode quantum information and send it between two arbitrary general-relativistic observers without a shared reference frame. Any information stored in a quantum field will inevitably be destroyed by an unknown Bogolyubov transformation relating the observers. However certain quantum correlations between different, independent fields will be preserved, no matter what transformation is applied. We show how to efficiently use these correlations in communication between arbitrary observers.
Multipartite nonlocality is of great fundamental interest and constitutes a useful resource for many quantum information protocols. However, demonstrating it in practice, by violating a Bell inequality, can be difficult. In particular, standard experimental setups require the alignment of distant parties' reference frames, which can be challenging or impossible in practice. In this work we study the violation of certain Bell inequalities, namely the Mermin, Mermin-Klyshko and Svetlichny inequalities, without shared reference frames, when parties share a Greenberger-Horne-Zeilinger (GHZ) state.…
Standard quantum key distribution (QKD) protocols typically assume that the distant parties share a common reference frame. In practice, however, establishing and maintaining a good alignment between distant observers is rarely a trivial issue, which may significantly restrain the implementation of long-distance quantum communication protocols. Here we propose simple QKD protocols that do not require the parties to share any reference frame, and study their security and feasibility in both the usual device-dependent case--in which the two parties use well characterized measurement devices--as …
An efficient implementation of many multiparty protocols for quantum networks requires that all the nodes in the network share a common reference frame. Establishing such a reference frame from scratch is especially challenging in an asynchronous network where network links might have arbitrary delays and the nodes do not share synchronised clocks. In this work, we study the problem of establishing a common reference frame in an asynchronous network of $n$ nodes of which at most $t$ are affected by arbitrary unknown error, and the identities of the faulty nodes are not known. We present a prot…
We have recently introduced a measure of the bipartite entanglement of identical particles, E_P, based on the principle that entanglement should be accessible for use as a resource in quantum information processing. We show here that particle entanglement is limited by the lack of a reference phase shared by the two parties, and that the entanglement is constrained to reference-phase invariant subspaces. The super-additivity of E_P results from the fact that this constraint is weaker for combined systems. A shared reference phase can only be established by transferring particles between the pa…
The genuine concurrence is a standard quantifier of multipartite entanglement, detection and quantification of which still remains a difficult problem from both theoretical and experimental point of view. Although many efforts have been devoted toward the detection of multipartite entanglement (e.g., using entanglement witnesses), measuring the degree of multipartite entanglement, in general, requires some knowledge about an exact shape of a density matrix of the quantum state. An experimental reconstruction of such density matrix can be done by full state tomography which amounts to having th…
Superselection rules (SSRs) limit the mechanical and quantum processing resources represented by quantum states. However SSRs can be violated using reference systems to break the underlying symmetry. We show that there is a duality between the ability of a system to do mechanical work and to act as a reference system. Further, for a bipartite system in a globally symmetric pure state, we find a triality between the system's ability to do local mechanical work, its ability to do ``logical work'' due to its accessible entanglement, and its ability to act as a shared reference system.
Quantum communication without a shared reference frame or the construction of a relational quantum theory requires the notion of a quantum reference frame. We analyze aspects of quantum reference frames associated with non-compact groups, specifically the group of spatial translations and Galilean boosts. We begin by demonstrating how the usually employed group average, used to dispense of the notion of an external reference frame, leads to unphysical states when applied to reference frames associated with non-compact groups. However, we show that this average does lead naturally to a reduced …
We demonstrate that the framework of bounded quantum reference frames has application to building quantum-public-key cryptographic protocols and proving their security. Thus, the framework we introduce can be seen as a public-key analogue of the framework of Bartlett et al. (Phys. Rev. A 70, 032307), where a private shared reference frame is shown to have cryptographic application. The protocol we present in this paper is an identification scheme, which, like a digital signature scheme, is a type of authentication scheme. We prove that our protocol is both reusable and secure under the honest-…
In quantum communication protocols the existence of a shared reference frame between two spatially separated parties is normally presumed. However, in many practical situations we are faced with the problem of misaligned reference frames. In this paper, we study communication between two inertial observers who have partial knowledge about the Lorentz transformation that relates their frames of reference. Since every Lorentz transformation can be decomposed into a pure boost followed by a rotation, we begin by analysing the effects on communication when the parties have partial knowledge about …
Protocols for testing or exploiting quantum correlations-such as entanglement, Bell nonlocality, and Einstein-Podolsky-Rosen steering- generally assume a common reference frame between two parties. Establishing such a frame is resource-intensive, and can be technically demanding for distant parties. While Bell nonlocality can be demonstrated with high probability for a large class of two-qubit entangled states when the parties have one or no shared reference direction, the degree of observed nonlocality is measurement-orientation dependent and can be arbitrarily small. In contrast, we theoreti…
Bell tests---the experimental demonstration of a Bell inequality violation---are central to understanding the foundations of quantum mechanics, underpin quantum technologies, and are a powerful diagnostic tool for technological developments in these areas. To date, Bell tests have relied on careful calibration of the measurement devices and alignment of a shared reference frame between the two parties---both technically demanding tasks in general. Surprisingly, we show that neither of these operations are necessary, violating Bell inequalities with near certainty with (i) unaligned, but calibr…
We revisit polarization rotation due to gravity, known as the gravitational Faraday effect, with a view on its role in quantum communications with Earth-orbiting satellites. In a static spherically symmetric gravitational field Faraday rotation is purely a reference frame (gauge) effect. This is so also in the leading post-Newtonian expansion of the Earth's gravitational field. However, establishing the local reference frame with respect to distant stars leads to the nonzero Faraday phase. In communications between a ground station and an Earth-orbiting spacecraft this phase is of the order of…
In the quantization of gauge theories and quantum gravity, it is crucial to treat reference frames such as rods or clocks not as idealized external classical relata, but as internal quantum subsystems. In the Page-Wootters formalism, for example, evolution of a quantum system S is described by a stationary joint state of S and a quantum clock, where time-dependence of S arises from conditioning on the value of the clock. Here, we consider (possibly imperfect) internal quantum reference frames R for arbitrary compact symmetry groups, and show that there is an exact quantitative correspondence b…
