We show that communication without a shared reference frame is possible using entangled states. We prove that the amount of classical information that can be communicated without a shared reference frame asymptotically approaches one classical bit per qubit sent, and that the number of encoded qubits which can be communicated per transmitted qubit also asymptotically approaches unity. We present an optical scheme to communicate classical bits without a shared reference frame using entangled photon pairs and linear optical Bell state measurements. PACS numbers: 03.67. Hk, 03.65.Ta, 03.65.Ud Quantum physics allows for powerful new communication tasks that are not possible classically, such as secure communication [1] and entanglement-enhanced classical communication [2] . In investigations of these and other communication tasks, considerable effort has been devoted to identifying the physical resources that are required for their implementation. It is generally presumed, at least implicitly, that a shared reference frame (SRF) between the communicating parties is such a resource, with the precise nature of the reference frame being dictated by the particular physical systems involved. For example, if the sender (Alice) and receiver (Bob) are communicating via spin-1/2 systems, it is generally presumed that they must share a reference frame for spatial orientation so that they may prepare and measure spin components relative to this frame. Despite the ubiquity of this presumption, we shall be asking whether it is necessitated by the laws of quantum physics. The question of the necessity or otherwise of a shared reference frame is clearly of interest for pragmatic reasons. In general, establishing a perfect SRF requires infinite communication (i.e., transmitting a system with an infinite-dimensional Hilbert space, or an infinite number of systems with finite-dimensional Hilbert spaces [3, 4] . As such, from a communication theory perspective, a perfect SRF is analogous to sharing an infinite number of correlated classical bits. For example, if a reference frame is shared only between Alice and Bob, then it can be used by them to securely generate an arbitrarily long secret key suitable for cryptography [17] . In practice, perfect SRFs are an idealization, and any finite (i.e., approximate) SRF should be viewed as a quantitative physical resource. Along with requiring communication to establish, any finite SRF that is treated quantum mechanically will inevitably suffer disturbances during measurements, causing it to degrade. We also note that shared prior entanglement, a valuable resource in quantum information theory, can be consumed to establish SRFs [5] . In addition to these pragmatic issues, the presumed necessity of SRFs also touches upon a number of more foundational questions in quantum mechanics. For instance, it has been argued [6] that the physical nature of SRFs is the key issue in Bohr's reply to Einstein, Podolsky and Rosen. In this context, it is interesting that all currently proposed schemes for violating Bell inequalities presume the existence of a SRF -the results presented here indicate that this presumption is in fact unnecessary. In this letter, we show that both classical and quantum communication can be performed without first establishing a SRF by using entangled states of multiple qubits. We prove that, without any prior SRF, the minimum number of qubits required to transmit a classical bit of information is two, and that four qubits can transmit an encoded "logical" qubit. Allowing increasingly more qubits to be entangled improves these ratios, and we prove that communication of one classical bit per transmitted qubit or one logical qubit per transmitted qubit can be achieved asymptotically. As an explicit example of the practicality of our scheme for classical communication without a SRF, we propose a feasible experiment using existing optical technology to communicate one classical bit of information per entangled photon pair. We begin by defining the notion of quantum communication between two parties who do not possess a SRF. For simplicity, we consider a noiseless channel that transmits qubits (our results can be extended to noisy channels or higher-dimensional systems). Such a channel defines an isomorphism between Alice's and Bob's local experimental operations. Specifically, representing Alice's experimental operations using one qubit Hilbert space and Bob's using another, the isomorphism is given by a unitary map R(Ω), Ω ∈ SU(2) between them. We define the lack of a SRF as a lack of any knowledge of this isomorphism; i.e., a lack of any knowledge of Ω. If Alice prepares a qubit in the state ρ and transmits it to Bob, he represents the state of this received qubit as a mixed density operator
Finally, the work in REF have proved that both quantum and classical information are able to communicate without sharing a reference signal by using the correlation of the entangled photon for such purpose.
Classical and Quantum Communication without a Shared Reference Frame
Physical review letters
Physical review letters
Physics Medicine