Quantum choice can be counterproductive

When abiding by the laws of quantum physics, having options can make an otherwise simple task impossible. A new paper demonstrates that transmitting quantum messages becomes more difficult if the intended recipient offers the sender multiple options for the time and place of delivery.

The strange finding, described online September 16 at arXiv.org, joins other paradoxes such as Schrödinger’s simultaneously dead and alive cat in highlighting the counterintuitive situations allowed by the rules of quantum physics. While the idea of being paralyzed by choice isn’t new (think of trying to pick a meal from an eight-page menu), only in the quantum world can freedom make tasks totally unachievable. “I’m still not quite entirely sure why it works, but I accept that it does,” says MIT quantum physicist Seth Lloyd. “They get full grades for weirdness and paradoxicality.”

Physicists may have to consider the implications of this paradox when building quantum-inspired communication networks, says quantum physicist Adrian Kent of the University of Cambridge. He and Emily Adlam of Cambridge stumbled upon the paradox by thinking about a hypothetical quantum information delivery service. The service can be thought of as a company (called, say, QPS) that has delivery agents located all over the world and shuttles messages encoded in such quantum properties as the spins of electrons. Unfortunately for QPS, agents can’t just measure the spins to decipher the message and then distribute copies — the act of measuring destroys the message. Instead agents have to transmit the fragile quantum states across the company’s network.

Adlam and Kent devised a situation in which a customer submits to QPS a secret message encoded in electron spins. The customer informs QPS that in the future, she will call an agent and request the information back, but not immediately: She will want it delivered to a certain place at an even later but specific time.

Adlam and Kent came to the strange realization that the more flexibility the customer offers, the harder it becomes for QPS to satisfy her request. The researchers devised situations in which, if the customer guaranteed that she would make only one delivery request, then QPS could transmit the message on time to the specified location. But if the customer submitted multiple requests with several drop-off possibilities, then the task would become impossible — even if the customer left it up to QPS to choose among the delivery options. In fact, just the possibility of receiving multiple requests would hamstring the QPS agents.

The dilemma boils down to the complexity in shuttling quantum information, Kent says. If the customer is limited to one request, then as soon as QPS gets the call, agents can work together to execute a procedure for disseminating the message piece by piece across their network. “Having less choice gives you more information,” Kent says. But it’s harder for the agents to collaborate if there can be another request, particularly if several agents receive calls at nearly the same time, dividing their focus.

While there’s no service like QPS now, this choice paradox could come into play in future communication networks that securely shuttle messages encoded in quantum states. “If you want to get information from New York to Tokyo,” Kent says, “then it’s going to be absolutely crucial to know the rules as to what you can and can’t do to deliver the information.”